Chicago Influenza Binary Classification

dataset

License: No license information was provided.

Executive Summary

Objective

This report presents the development and evaluation of a binary classification model designed to predict influenza cases (is_influenza) within Chicago’s healthcare data. Utilizing a comprehensive dataset spanning clinical visits from 2015 to 2025, the model aims to enhance early detection and resource allocation for influenza management.

Data Insights

1. Continuous Variables Analysis

Week Distribution: Data exhibits a uniform distribution across weeks, ensuring temporal coverage.
Percent Variable: Heavily skewed towards lower values, indicating most observations have low percentage metrics.
Class Imbalance: The target variable is_influenza is significantly imbalanced, with non-influenza cases predominating. This imbalance poses challenges for accurate prediction, potentially biasing the model towards non-influenza outcomes.

2. Categorical Variables Analysis

Seasonal Representation: Data is primarily concentrated between 2019 and 2024, with sparse entries for the 2024-2025 season.
Visit Types: Emergency Department (ED) visits dominate, while outpatient visits are infrequent.
Respiratory Categories: Influenza, RSV, and COVID-19 are well-represented, reflecting prevalent respiratory conditions.
Demographics: Balanced distribution across key demographic groups, particularly among individuals aged 65+, and various racial/ethnic categories.

3. Advanced Visualizations

Dodged Bar Charts & Heatmaps: Highlight consistent high counts of Influenza and RSV, with notable COVID-19 spikes during 2020-2023. ED visits remain the primary mode of healthcare engagement, especially among older populations during pandemic periods.
Box and Violin Plots: Reveal increased variability in the percent variable during pandemic years, with significant outliers in younger (0-4) and older (65+) age groups.
Correlation Analysis: Minimal correlations between week, percent, and is_influenza (with a weak positive correlation of 0.21 between percent and is_influenza), indicating limited linear relationships among these variables.
Trend Analysis: Demonstrates upward trends in percentage metrics over weeks, particularly in recent seasons, and consistent increases in ED visits across demographics.

Model Development and Selection

Model Evaluation

Model 96: Exhibited overfitting, compromising its generalizability.
Model 99: Encountered convergence issues, likely due to multicollinearity or excessive complexity.
Model 117: Selected as the optimal model due to its balance between performance and simplicity. Key metrics include:
- Accuracy: 80.21%
- ROC AUC: 0.696
- Complexity: 14 coefficients, reducing the risk of overfitting and enhancing stability during training.

Implications

The selected Model 117 demonstrates robust performance with adequate accuracy and discriminative ability, making it suitable for deployment in predicting influenza cases. Its simplicity ensures better generalization to new data, essential for real-world applications in public health surveillance and response.

Recommendations and Next Steps

Address Class Imbalance: Implement techniques such as resampling, synthetic data generation, or algorithmic adjustments to mitigate the impact of class imbalance and improve predictive performance for influenza cases.
Feature Engineering: Explore additional features or interactions that may enhance model performance, particularly focusing on demographic and temporal patterns.
Model Validation: Conduct further validation using external datasets to ensure the model's reliability and applicability across different populations and timeframes.
Deployment and Monitoring: Integrate the model into public health systems for real-time influenza prediction and continuously monitor its performance to facilitate timely interventions.

Conclusion

The development of a stable and effective influenza prediction model, supported by thorough data analysis and careful model selection, provides a valuable tool for enhancing public health strategies in Chicago. By addressing existing data challenges and refining predictive capabilities, this model holds significant potential for improving influenza case management and resource allocation.

Import Main Modules & Dataset

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

import itertools

import statsmodels.formula.api as smf

df = pd.read_csv('Inpatient__Emergency_Department__and_Outpatient_Visits_for_Respiratory_Illnesses.csv')

Perform Basic Analysis

df.shape

(48181, 13)

df.dtypes

mmwr_week                 int64
week                      int64
week_start               object
week_end                 object
season                   object
data_source              object
essence_category         object
respiratory_category     object
visit_type               object
demographic_category     object
demographic_group        object
percent                 float64
current_week_ending      object
dtype: object

_ = [print(f'{df[column].value_counts()}\n') for column in df.columns]

mmwr_week
202043    131
202119    131
202347    131
202237    131
202036    131
         ... 
201838     66
201816     66
201630     66
201725     66
201936     66
Name: count, Length: 471, dtype: int64

week
40    1050
42    1050
41    1050
43     919
52     919
7      919
1      919
18     919
50     919
47     919
20     919
14     919
10     919
48     919
25     919
36     919
9      919
2      919
28     919
51     919
38     919
12     919
15     919
16     919
3      919
5      919
4      919
32     919
34     919
39     919
6      919
29     919
49     919
26     919
24     919
37     919
30     919
11     919
8      919
46     919
35     919
27     919
44     919
19     919
23     919
21     919
13     919
17     919
45     919
33     919
22     919
31     919
Name: count, dtype: int64

week_start
10/18/2020    131
05/09/2021    131
11/19/2023    131
09/11/2022    131
08/30/2020    131
             ... 
09/16/2018     66
04/15/2018     66
07/24/2016     66
06/18/2017     66
09/01/2019     66
Name: count, Length: 471, dtype: int64

week_end
10/24/2020    131
05/15/2021    131
11/25/2023    131
09/17/2022    131
09/05/2020    131
             ... 
09/22/2018     66
04/21/2018     66
07/30/2016     66
06/24/2017     66
09/07/2019     66
Name: count, Length: 471, dtype: int64

season
2020-2021    6812
2019-2020    6812
2023-2024    6812
2021-2022    6812
2022-2023    6812
2016-2017    3432
2017-2018    3432
2015-2016    3432
2018-2019    3432
2024-2025     393
Name: count, dtype: int64

data_source
ESSENCE    47710
ILINet       471
Name: count, dtype: int64

essence_category
CDC Influenza DD v1                      9542
CDC Respiratory Syncytial Virus DD v1    9542
CDC Broad Acute Respiratory DD v1        9542
Influenza-like Illness                   9542
CDC COVID-Specific DD v1                 9542
Not Applicable                            471
Name: count, dtype: int64

respiratory_category
ILI                        10013
Influenza                   9542
RSV                         9542
Broad Acute Respiratory     9542
COVID-19                    9542
Name: count, dtype: int64

visit_type
ED Visits            30615
Admissions           17095
Outpatient Visits      471
Name: count, dtype: int64

demographic_category
Age Group         22020
Race/Ethnicity    22020
ALL                4141
Name: count, dtype: int64

demographic_group
ALL                       4141
65+                       3670
Asian Non-Hispanic        3670
45_64                     3670
Age Unknown               3670
Other Race/Ethnicity      3670
Hispanic or Latino        3670
Unknown Race/Ethnicity    3670
18_44                     3670
Black Non-Hispanic        3670
White Non-Hispanic        3670
05_17                     3670
00_04                     3670
Name: count, dtype: int64

percent
0.00     14089
0.02       641
0.05       537
0.07       496
0.03       476
         ...  
28.46        1
35.93        1
21.96        1
22.14        1
34.50        1
Name: count, Length: 2827, dtype: int64

current_week_ending
10/05/2024    1050
10/19/2024    1050
10/12/2024    1050
10/26/2024     919
12/28/2024     919
02/15/2025     919
01/04/2025     919
05/03/2025     919
12/14/2024     919
11/23/2024     919
05/17/2025     919
04/05/2025     919
03/08/2025     919
11/30/2024     919
06/21/2025     919
09/06/2025     919
03/01/2025     919
01/11/2025     919
07/12/2025     919
12/21/2024     919
09/20/2025     919
03/22/2025     919
04/12/2025     919
04/19/2025     919
01/18/2025     919
02/01/2025     919
01/25/2025     919
08/09/2025     919
08/23/2025     919
09/27/2025     919
02/08/2025     919
07/19/2025     919
12/07/2024     919
06/28/2025     919
06/14/2025     919
09/13/2025     919
07/26/2025     919
03/15/2025     919
02/22/2025     919
11/16/2024     919
08/30/2025     919
07/05/2025     919
11/02/2024     919
05/10/2025     919
06/07/2025     919
05/24/2025     919
03/29/2025     919
04/26/2025     919
11/09/2024     919
08/16/2025     919
05/31/2025     919
08/02/2025     919
Name: count, dtype: int64

df.nunique()

mmwr_week                471
week                      52
week_start               471
week_end                 471
season                    10
data_source                2
essence_category           6
respiratory_category       5
visit_type                 3
demographic_category       3
demographic_group         13
percent                 2827
current_week_ending       52
dtype: int64

Create Binary Target Variable: 1 for `Influenza`, 0 Everything Else

df['is_influenza'] = df['respiratory_category'].apply(lambda x: 1 if x == 'Influenza' else 0)

df.is_influenza.value_counts()

is_influenza
0    38639
1     9542
Name: count, dtype: int64

Verify/Handle Missing Values

df.isna().sum()

mmwr_week                 0
week                      0
week_start                0
week_end                  0
season                    0
data_source               0
essence_category          0
respiratory_category      0
visit_type                0
demographic_category      0
demographic_group         0
percent                 217
current_week_ending       0
is_influenza              0
dtype: int64

df_copy = df.copy()

df_copy = df_copy.dropna()

df_copy.isna().sum()

mmwr_week               0
week                    0
week_start              0
week_end                0
season                  0
data_source             0
essence_category        0
respiratory_category    0
visit_type              0
demographic_category    0
demographic_group       0
percent                 0
current_week_ending     0
is_influenza            0
dtype: int64

Drop Irrelevant Variables

df_copy = df_copy.drop(columns=['mmwr_week', 
                                'week_start', 
                                'week_end', 
                                'data_source', 
                                'current_week_ending'])

Perform Basic Analysis - Cleaned Dataset

df_copy.shape

(47964, 9)

df_copy.dtypes

week                      int64
season                   object
essence_category         object
respiratory_category     object
visit_type               object
demographic_category     object
demographic_group        object
percent                 float64
is_influenza              int64
dtype: object

_ = [print(f'{df_copy[column].value_counts()}\n') for column in df_copy.columns]

week
41    1050
42    1046
40    1045
36     919
22     919
45     919
35     919
13     919
5      919
1      919
18     919
20     919
33     919
9      919
51     919
24     919
26     919
29     919
15     919
38     915
7      915
12     915
3      915
43     915
31     915
17     915
39     915
6      915
37     915
27     915
34     915
25     914
19     914
28     914
2      914
11     914
32     914
52     911
8      911
10     911
44     911
21     911
48     910
14     910
46     910
47     910
50     910
30     910
49     910
23     910
16     910
4      910
Name: count, dtype: int64

season
2022-2023    6812
2023-2024    6807
2021-2022    6807
2019-2020    6771
2020-2021    6762
2017-2018    3420
2015-2016    3420
2016-2017    3408
2018-2019    3364
2024-2025     393
Name: count, dtype: int64

essence_category
CDC COVID-Specific DD v1                 9525
CDC Influenza DD v1                      9492
CDC Respiratory Syncytial Virus DD v1    9492
CDC Broad Acute Respiratory DD v1        9492
Influenza-like Illness                   9492
Not Applicable                            471
Name: count, dtype: int64

respiratory_category
ILI                        9963
COVID-19                   9525
Influenza                  9492
RSV                        9492
Broad Acute Respiratory    9492
Name: count, dtype: int64

visit_type
ED Visits            30398
Admissions           17095
Outpatient Visits      471
Name: count, dtype: int64

demographic_category
Race/Ethnicity    22020
Age Group         21803
ALL                4141
Name: count, dtype: int64

demographic_group
ALL                       4141
65+                       3670
Asian Non-Hispanic        3670
45_64                     3670
Other Race/Ethnicity      3670
Hispanic or Latino        3670
Unknown Race/Ethnicity    3670
18_44                     3670
Black Non-Hispanic        3670
White Non-Hispanic        3670
05_17                     3670
00_04                     3670
Age Unknown               3453
Name: count, dtype: int64

percent
0.00     14089
0.02       641
0.05       537
0.07       496
0.03       476
         ...  
28.46        1
35.93        1
21.96        1
22.14        1
34.50        1
Name: count, Length: 2827, dtype: int64

is_influenza
0    38472
1     9492
Name: count, dtype: int64

df_copy.nunique()

week                      52
season                    10
essence_category           6
respiratory_category       5
visit_type                 3
demographic_category       3
demographic_group         13
percent                 2827
is_influenza               2
dtype: int64

Visualize the Marginal Distributions

Continuous Variables: Histograms and Density Plots

The dataset shows a fairly uniform distribution of data over the weeks of the year, but the percent variable is heavily skewed towards lower values, and the target variable is_influenza is highly imbalanced with far more non-influenza cases. This imbalance may affect the model’s ability to predict influenza cases accurately, leading to lower predicted probabilities in many scenarios.

[
    (
        sns.displot(data=df_copy, 
                   x=column, 
                   kind='hist', 
                   bins=20, 
                   kde=True),
        plt.title(f'Distribution of {column.replace("_", " ").title()}', fontsize=16),
        plt.show(),
        plt.close()
    )
    for column in df_copy.select_dtypes(include='number').columns
]
plt.show()

Categorical Variables: Bar Charts

The data visualizations reveal that the dataset is dominated by certain seasons, visit types, and respiratory categories. Notably, the most represented seasons are from 2019 to 2024, with very few entries for 2024-2025. The majority of visit types are ED Visits, while Outpatient Visits are rare. Similarly, certain respiratory categories such as Influenza, RSV, and COVID-19 are well-distributed, but demographic categories and groups show a balanced count distribution, with ALL, 65+, and various racial/ethnic groups being the most represented. This distribution suggests that the dataset is rich in clinical visits during these specific periods and categories.

[
    (
        sns.catplot(data=df_copy, 
                   x=column, 
                   kind='count').set_xticklabels(rotation=90),
        plt.title(f'Count of {column.replace("_", " ").title()}', fontsize=16),
        plt.show(),
        plt.close()
    ) 
    if df_copy[column].nunique() <= 20 
    else (
        sns.catplot(data=df_copy, 
                   x=column, 
                   kind='count').set(xticklabels=[]),
        plt.title(f'Count of {column.replace("_", " ").title()}', fontsize=16),
        plt.show(),
        plt.close()
    )
    for column in df_copy.select_dtypes(exclude='number').columns
]
plt.show()

Visualize the Combinations and Conditional Distributions w/ Categorical-to-Categorical Relationships or Combinations

Categorical-to-Categorical Dodged Bar Charts

The visualizations offer a detailed analysis of respiratory conditions, demographic categories, and visit types over flu seasons from 2015 to 2025. Key findings highlight consistent high counts of conditions like Influenza and RSV, with notable variations during the 2021-2022 and 2022-2023 seasons due to COVID-19. The charts also reveal that ED Visits accounted for the majority of hospitalizations, while specific spikes in conditions like ILI and COVID-19 were observed across age groups, particularly in older populations (65+), and race/ethnicity categories. Overall, the data trends show stability, but pandemic-related seasons reflected significant shifts in case counts and hospitalizations.

[
    (
        sns.catplot(data=df_copy, 
                   x=x_col, 
                   hue=hue_col, 
                   kind='count', 
                   aspect=1.5).set_xticklabels(rotation=90),
        plt.title(
            f'Count of {x_col.replace("_", " ").title()} by {hue_col.replace("_", " ").title()}', 
            fontsize=16
        ),
        plt.show(),
        plt.close()
    )
    for x_col, hue_col in itertools.combinations(df_copy.select_dtypes(include='object').columns, 2)
]
None

Categorical-to-Categorical Heatmaps

The visualizations offer a detailed breakdown of respiratory conditions, visit types, and demographic trends across seasons from 2015 to 2025. Influenza and RSV consistently show high counts, with significant spikes in COVID-19 during the 2020-2023 seasons. The majority of cases occurred through Emergency Department (ED) visits, while admissions remained fewer in comparison. The demographic analysis highlights that older age groups, particularly those 65+, had higher case counts during peak pandemic years. The overall trends illustrate the considerable impact of respiratory illnesses during pandemic-related seasons, with a strong reliance on emergency care.

unique_pairs = list(itertools.combinations(
    df_copy.select_dtypes(include='object').columns, 2
))

[
    (
        plt.figure(figsize=(8, 6)), 
        sns.heatmap(
            pd.crosstab(df_copy[x_col], df_copy[hue_col]), 
            annot=True,                                      
            fmt='d',                                     
            cbar=False                   
        ),
        plt.xticks(rotation=90, ha='right'),  
        plt.yticks(rotation=0), 
        plt.title(
            f'Counts of {x_col.replace("_", " ").title()} by {hue_col.replace("_", " ").title()}', 
            fontsize=16                                           
        ),
        plt.tight_layout(),                              
        plt.show(),                                         
        plt.close()                                     
    )
    for x_col, hue_col in unique_pairs     
]
None

Visualize the Categorical-to-Continuous Relationships or Conditional Distributions

Categorical-to-Continuous Box Plots, Violin Plots, and Point Plots

The visualizations provide a comprehensive analysis of respiratory conditions, visit types, and demographic trends across various seasons, from 2015 to 2025. They show consistent week distributions across seasons, with notable differences for the 2024-2025 season. Percent variability is more pronounced, particularly in recent years like 2021-2022 and 2022-2023, indicating spikes in cases for certain conditions. Broad Acute Respiratory and COVID-19 stand out with higher percentage variability across essence and respiratory categories. ED visits dominate among visit types, with notable outliers in percent trends, while admissions and outpatient visits show fewer percent spikes. Demographic analysis reveals consistency in week distributions across groups but highlights outliers in percent for younger (00-04) and older (65+) age groups, particularly in respiratory conditions. These insights emphasize stability in week reporting but variability in percent outliers during peak illness periods, especially during the pandemic.

[
    (
        sns.catplot(
            data=df_copy, 
            x=x_col, 
            y=y_var,
            kind='box', 
            aspect=1.5
        ).set_xticklabels(rotation=90),
        plt.title(
            f'{y_var.capitalize()} vs. {x_col.replace("_", " ").title()} by {x_col.replace("_", " ").title()}', 
            fontsize=16
        ),
        plt.show(),
        plt.close()
    )
    for x_col in df_copy.select_dtypes(include='object').columns
    for y_var in df_copy.select_dtypes(include='number').columns
    if y_var != 'is_influenza'
]
None

[
    (
        sns.catplot(
            data=df_copy, 
            x=x_col, 
            y=y_var,
            kind='violin', 
            aspect=1.5
        ).set_xticklabels(rotation=90),
        plt.title(
            f'{y_var.capitalize()} vs. {x_col.replace("_", " ").title()} by {x_col.replace("_", " ").title()}', 
            fontsize=16
        ),
        plt.show(),
        plt.close()
    )
    for x_col in df_copy.select_dtypes(include='object').columns
    for y_var in df_copy.select_dtypes(include='number').columns
    if y_var != 'is_influenza'
]
None

[
    (
        sns.catplot(
            data=df_copy, 
            x=x_col, 
            y=y_var,
            kind='point',
            linestyles='',
            aspect=1.5
        ).set_xticklabels(rotation=90),
        plt.title(
            f'{y_var.capitalize()} vs. {x_col.replace("_", " ").title()} by {x_col.replace("_", " ").title()}', 
            fontsize=16
        ),
        plt.show(),
        plt.close()
    )
    for x_col in df_copy.select_dtypes(include='object').columns
    for y_var in df_copy.select_dtypes(include='number').columns
    if y_var != 'is_influenza'
]
None

Visualize the Continuous-to-Continuous Relationships or Conditional Distributions

Pairplot and Correlation Plot

The pairplot visualizes the relationships between the numerical variables: week, percent, and is_influenza. It shows the distributions of each variable along the diagonal and scatter plots illustrating their interactions. The data displays significant clustering of low percentage values, while the week variable shows a consistent distribution. The correlation heatmap highlights minimal correlations between the variables. Week and percent have a near-zero correlation (0.01), while percent and is_influenza show a weak positive correlation (0.21). This suggests that these variables do not have strong linear relationships with one another.

pairplot = sns.pairplot(
    data=df_copy.select_dtypes(include='number').drop(columns=['is_influenza']),
    aspect=1.5
)
pairplot.fig.suptitle('Pairplot of Numerical Variables', fontsize=16)
pairplot.fig.subplots_adjust(top=0.85)
plt.show()

fig, ax = plt.subplots()
sns.heatmap(
    data=df_copy.select_dtypes(include='number').corr(numeric_only=True),
    vmin=-1, 
    vmax=1, 
    center=0,
    cbar=False,
    annot=True, 
    annot_kws={'size': 7},
    fmt='.2f',
    ax=ax
)
plt.title('Correlation Heatmap of Numerical Variables', fontsize=16)
plt.show()

Visualize the Relationship Across Groups

Trend Plots

The visualizations show the relationship between percentage and week across various categories, such as season, essence category, respiratory category, visit type, and demographic categories/groups. In the “Percent vs. Week by Season” chart, there’s a clear upward trend in percentage as the weeks progress, especially for recent seasons like 2021-2022 and 2022-2023. Similar trends are observed across essence categories, where Broad Acute Respiratory and COVID-19 show distinct trends compared to others. The “Percent vs. Week by Visit Type” highlights that emergency department (ED) visits show the most consistent increase over time, while outpatient visits show a more sporadic trend. When broken down by demographic categories, there’s a distinction in trends between age groups and race/ethnicity, with certain groups like 65+ and younger demographics showing more variability over time. These visualizations reflect how respiratory illness trends evolve over weeks and across different population segments, highlighting significant patterns during peak weeks of illness.

numerical_vars = [
    col for col in df_copy.select_dtypes(include=['number']).columns
    if col != 'is_influenza'
]

[
    (
        sns.lmplot(
            data=df_copy,
            x=y_var,
            y=x_var,
            hue=cat_var,
            line_kws={'linewidth': 2},
            scatter_kws={'alpha': 0.5},
            height=5,
            aspect=1.5,
        ),
        plt.title(
            f'{y_var.capitalize()} vs. {x_var.capitalize()} by {cat_var.replace("_", " ").title()}', 
            fontsize=16
        ),
        plt.xticks(rotation=90),
        plt.ylabel(y_var.capitalize(), rotation=0, labelpad=30),
        plt.xlabel(x_var.capitalize()),
        plt.show(),
        plt.close()
    )
    for cat_var in df_copy.select_dtypes(include='object').columns
    for x_var, y_var in itertools.combinations(numerical_vars, 2)
]
None

Summarize the Categorical-to-Continuous Response Relationships or Conditional Distributions

Categorical-to-Continuous Response Relationship Box Plots, Violin Plots, and Point Plots

The visualizations explore the relationship between categorical variables (such as demographic group, essence category, visit type, and season) and continuous responses (week and percent) by segmenting them based on Influenza Status (0 for non-influenza, 1 for influenza). The analysis reveals that week distributions remain consistent across different groups, categories, and influenza status, showing no significant timing shifts between influenza-positive and negative cases. However, the percent variable shows more variability, with non-influenza cases generally displaying wider ranges, especially in categories like Broad Acute Respiratory and visit types like ED visits. Specific demographic groups, such as the very young (00-04) and older adults (65+), exhibit more pronounced percentage spikes, indicating potential areas of differentiation between influenza and non-influenza cases. Violin and point plots further emphasize these patterns, particularly showing a higher concentration of non-influenza cases in certain groups and across different weeks, making percent a more distinctive factor in predicting influenza status.

[
    (
        sns.catplot(
            data=df_copy, 
            kind='box',
            x=var, 
            y=y_var,
            hue='is_influenza',
            height=8,
            aspect=1.5
        ),
        plt.xticks(rotation=90),
        plt.ylabel(y_var.replace('_', ' ').capitalize(), rotation=0, labelpad=30),
        plt.title(
            f'Box Plot of {y_var.replace("_", " ").capitalize()} by {var.replace("_", " ").title()} and Influenza Status', 
            fontsize=16
        ),
        plt.xlabel(var.replace('_', ' ').capitalize()),
        plt.show(),
        plt.close()
    )
    for var in df_copy.select_dtypes(include='object').columns 
    for y_var in df_copy.select_dtypes(include='number').columns 
    if y_var != 'is_influenza' and y_var in df_copy.columns 
]
None

[
    (
        sns.catplot(
            data=df_copy, 
            kind='violin',
            x=var, 
            y=y_var,
            hue='is_influenza',
            height=8,
            aspect=1.5
        ),
        plt.xticks(rotation=90),
        plt.ylabel(y_var.replace('_', ' ').capitalize(), rotation=0, labelpad=30),
        plt.title(
            f'Violin Plot of {y_var.replace("_", " ").capitalize()} by {var.replace("_", " ").title()} and Influenza Status', 
            fontsize=16
        ),
        plt.xlabel(var.replace('_', ' ').capitalize()),
        plt.show(),
        plt.close()
    )
    for var in df_copy.select_dtypes(include='object').columns 
    for y_var in df_copy.select_dtypes(include='number').columns 
    if y_var != 'is_influenza' and y_var in df_copy.columns 
]
None

[
    (
        sns.catplot(
            data=df_copy, 
            kind='point',
            linestyles='',
            x=var, 
            y=y_var,
            hue='is_influenza',
            height=8,
            aspect=1.5
        ),
        plt.xticks(rotation=90),
        plt.ylabel(y_var.replace('_', ' ').capitalize(), rotation=0, labelpad=30),
        plt.title(
            f'Point Plot of {y_var.replace("_", " ").capitalize()} by {var.replace("_", " ").title()} and Influenza Status', 
            fontsize=16
        ),
        plt.xlabel(var.replace('_', ' ').capitalize()),
        plt.show(),
        plt.close()
    )
    for var in df_copy.select_dtypes(include='object').columns 
    for y_var in df_copy.select_dtypes(include='number').columns 
    if y_var != 'is_influenza' and y_var in df_copy.columns 
]
None

Generate Formulas - Binary Classification Model

def generate_formulas(numeric_vars, categorical_vars, target):
    """
    Generates all possible combinations of additive, interaction, and polynomial terms (quadratic, cubic, and quartic) 
    for a binary classification target using numeric and categorical variables.
    
    Params:
        numeric_vars: list
        categorical_vars: list
        target: str

    Returns:
        list
    """

    # initialize an empty list to hold the formulas
    formulas = []

    # helper function to wrap categorical variables with C()
    def wrap_categorical(var_list):
        """
        Wraps categorical variables in the statsmodels C() function.
    
        This function takes a list of variable names and checks if each variable is 
        categorical. If the variable is categorical (found in the `categorical_vars` list), 
        it wraps the variable in `C()` for use with the formula interface in statsmodels. 
        Otherwise, it returns the variable as-is for numeric variables.
    
        Params:
            var_list: list
    
        Returns:
            list
        """
        return [f'C({var})' if var in categorical_vars else var for var in var_list]

    # 1. additive formulas (all combinations of 2 or more variables)
    for r in range(2, len(categorical_vars + numeric_vars) + 1):
        for combo in itertools.combinations(categorical_vars + numeric_vars, r):
            terms = wrap_categorical(combo)
            formulas.append(f'{target} ~ {" + ".join(terms)}')

    # 2. interaction terms (all combinations of 2 or more variables)
    for r in range(2, len(categorical_vars + numeric_vars) + 1):
        for combo in itertools.combinations(categorical_vars + numeric_vars, r):
            terms = wrap_categorical(combo)
            formulas.append(f'{target} ~ {" * ".join(terms)}')

    # 3. polynomial terms (quadratic, cubic, quartic) for numeric variables
    for var in numeric_vars:
        formulas.append(f'{target} ~ {var} + I({var}**2)')
        formulas.append(f'{target} ~ {var} + I({var}**2) + I({var}**3)')
        formulas.append(f'{target} ~ {var} + I({var}**2) + I({var}**3) + I({var}**4)')

    # 4. additive and interaction combinations with polynomials for each pair of numeric and categorical variables
    for num_var in numeric_vars:
        for cat_var in categorical_vars:
            formulas.append(f'{target} ~ {num_var} + I({num_var}**2) + C({cat_var})')
            formulas.append(f'{target} ~ {num_var} * I({num_var}**2) * C({cat_var})')

    # 5. combinations of multiple categorical and numeric variables with interaction and polynomials
    for cat1, cat2 in itertools.combinations(categorical_vars, 2):
        for num_var in numeric_vars:
            formulas.append(f'{target} ~ C({cat1}) + C({cat2}) + {num_var} + I({num_var}**2)')
            formulas.append(f'{target} ~ C({cat1}) * C({cat2}) * {num_var} * I({num_var}**2)')

    # 6. full interaction with polynomial terms across all numeric and categorical variables
    for r in range(2, len(categorical_vars + numeric_vars) + 1):
        for combo in itertools.combinations(categorical_vars + numeric_vars, r):
            numeric_in_combo = [var for var in combo if var in numeric_vars]
            categorical_in_combo = [var for var in combo if var in categorical_vars]
            if numeric_in_combo:  # If numeric variables are present, include polynomial terms
                for num_var in numeric_in_combo:
                    terms = wrap_categorical(combo)
                    formulas.append(f'{target} ~ {" * ".join(terms)} + I({num_var}**2) + I({num_var}**3) + I({num_var}**4)')

    # return the forumlas list
    return formulas

Define Numeric, Categorical and Target Variables

numeric_vars = ['week', 
                'percent']

categorical_vars = ['season', 
                    'essence_category', 
                    'respiratory_category', 
                    'visit_type', 
                    'demographic_category', 
                    'demographic_group']

target = 'is_influenza'

Execute `generate_formulas` Function

formulas = generate_formulas(numeric_vars, categorical_vars, target)

formulas

['is_influenza ~ C(season) + C(essence_category)',
 'is_influenza ~ C(season) + C(respiratory_category)',
 'is_influenza ~ C(season) + C(visit_type)',
 'is_influenza ~ C(season) + C(demographic_category)',
 'is_influenza ~ C(season) + C(demographic_group)',
 'is_influenza ~ C(season) + week',
 'is_influenza ~ C(season) + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category)',
 'is_influenza ~ C(essence_category) + C(visit_type)',
 'is_influenza ~ C(essence_category) + C(demographic_category)',
 'is_influenza ~ C(essence_category) + C(demographic_group)',
 'is_influenza ~ C(essence_category) + week',
 'is_influenza ~ C(essence_category) + percent',
 'is_influenza ~ C(respiratory_category) + C(visit_type)',
 'is_influenza ~ C(respiratory_category) + C(demographic_category)',
 'is_influenza ~ C(respiratory_category) + C(demographic_group)',
 'is_influenza ~ C(respiratory_category) + week',
 'is_influenza ~ C(respiratory_category) + percent',
 'is_influenza ~ C(visit_type) + C(demographic_category)',
 'is_influenza ~ C(visit_type) + C(demographic_group)',
 'is_influenza ~ C(visit_type) + week',
 'is_influenza ~ C(visit_type) + percent',
 'is_influenza ~ C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(demographic_category) + week',
 'is_influenza ~ C(demographic_category) + percent',
 'is_influenza ~ C(demographic_group) + week',
 'is_influenza ~ C(demographic_group) + percent',
 'is_influenza ~ week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category)',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type)',
 'is_influenza ~ C(season) + C(essence_category) + C(demographic_category)',
 'is_influenza ~ C(season) + C(essence_category) + C(demographic_group)',
 'is_influenza ~ C(season) + C(essence_category) + week',
 'is_influenza ~ C(season) + C(essence_category) + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type)',
 'is_influenza ~ C(season) + C(respiratory_category) + C(demographic_category)',
 'is_influenza ~ C(season) + C(respiratory_category) + C(demographic_group)',
 'is_influenza ~ C(season) + C(respiratory_category) + week',
 'is_influenza ~ C(season) + C(respiratory_category) + percent',
 'is_influenza ~ C(season) + C(visit_type) + C(demographic_category)',
 'is_influenza ~ C(season) + C(visit_type) + C(demographic_group)',
 'is_influenza ~ C(season) + C(visit_type) + week',
 'is_influenza ~ C(season) + C(visit_type) + percent',
 'is_influenza ~ C(season) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(season) + C(demographic_category) + week',
 'is_influenza ~ C(season) + C(demographic_category) + percent',
 'is_influenza ~ C(season) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + week + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type)',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(demographic_category)',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(demographic_group)',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + week',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + percent',
 'is_influenza ~ C(essence_category) + C(visit_type) + C(demographic_category)',
 'is_influenza ~ C(essence_category) + C(visit_type) + C(demographic_group)',
 'is_influenza ~ C(essence_category) + C(visit_type) + week',
 'is_influenza ~ C(essence_category) + C(visit_type) + percent',
 'is_influenza ~ C(essence_category) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(essence_category) + C(demographic_category) + week',
 'is_influenza ~ C(essence_category) + C(demographic_category) + percent',
 'is_influenza ~ C(essence_category) + C(demographic_group) + week',
 'is_influenza ~ C(essence_category) + C(demographic_group) + percent',
 'is_influenza ~ C(essence_category) + week + percent',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + C(demographic_category)',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + C(demographic_group)',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + week',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + percent',
 'is_influenza ~ C(respiratory_category) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(respiratory_category) + C(demographic_category) + week',
 'is_influenza ~ C(respiratory_category) + C(demographic_category) + percent',
 'is_influenza ~ C(respiratory_category) + C(demographic_group) + week',
 'is_influenza ~ C(respiratory_category) + C(demographic_group) + percent',
 'is_influenza ~ C(respiratory_category) + week + percent',
 'is_influenza ~ C(visit_type) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(visit_type) + C(demographic_category) + week',
 'is_influenza ~ C(visit_type) + C(demographic_category) + percent',
 'is_influenza ~ C(visit_type) + C(demographic_group) + week',
 'is_influenza ~ C(visit_type) + C(demographic_group) + percent',
 'is_influenza ~ C(visit_type) + week + percent',
 'is_influenza ~ C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(demographic_category) + week + percent',
 'is_influenza ~ C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type)',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(demographic_category)',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(demographic_group)',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + C(demographic_category)',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + C(demographic_group)',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(season) + C(essence_category) + C(demographic_category) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(demographic_category) + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(essence_category) + week + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + C(demographic_category)',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + C(demographic_group)',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + week',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(season) + C(respiratory_category) + C(demographic_category) + week',
 'is_influenza ~ C(season) + C(respiratory_category) + C(demographic_category) + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(respiratory_category) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + week + percent',
 'is_influenza ~ C(season) + C(visit_type) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(season) + C(visit_type) + C(demographic_category) + week',
 'is_influenza ~ C(season) + C(visit_type) + C(demographic_category) + percent',
 'is_influenza ~ C(season) + C(visit_type) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(visit_type) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(visit_type) + week + percent',
 'is_influenza ~ C(season) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(demographic_category) + week + percent',
 'is_influenza ~ C(season) + C(demographic_group) + week + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category)',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_group)',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + week',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(demographic_category) + week',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(demographic_category) + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(demographic_group) + week',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(demographic_group) + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + week + percent',
 'is_influenza ~ C(essence_category) + C(visit_type) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(essence_category) + C(visit_type) + C(demographic_category) + week',
 'is_influenza ~ C(essence_category) + C(visit_type) + C(demographic_category) + percent',
 'is_influenza ~ C(essence_category) + C(visit_type) + C(demographic_group) + week',
 'is_influenza ~ C(essence_category) + C(visit_type) + C(demographic_group) + percent',
 'is_influenza ~ C(essence_category) + C(visit_type) + week + percent',
 'is_influenza ~ C(essence_category) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(essence_category) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(essence_category) + C(demographic_category) + week + percent',
 'is_influenza ~ C(essence_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + C(demographic_category) + week',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + C(demographic_category) + percent',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + C(demographic_group) + week',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + C(demographic_group) + percent',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + week + percent',
 'is_influenza ~ C(respiratory_category) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(respiratory_category) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(respiratory_category) + C(demographic_category) + week + percent',
 'is_influenza ~ C(respiratory_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(visit_type) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(visit_type) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(visit_type) + C(demographic_category) + week + percent',
 'is_influenza ~ C(visit_type) + C(demographic_group) + week + percent',
 'is_influenza ~ C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category)',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_group)',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(demographic_category) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(demographic_category) + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + C(demographic_category) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + C(demographic_category) + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(demographic_category) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + C(demographic_category) + week',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + C(demographic_category) + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + week + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(respiratory_category) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(demographic_category) + week + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(visit_type) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(visit_type) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(visit_type) + C(demographic_category) + week + percent',
 'is_influenza ~ C(season) + C(visit_type) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category) + week',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category) + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_group) + week',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_group) + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + week + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(demographic_category) + week + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(essence_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(essence_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(essence_category) + C(visit_type) + C(demographic_category) + week + percent',
 'is_influenza ~ C(essence_category) + C(visit_type) + C(demographic_group) + week + percent',
 'is_influenza ~ C(essence_category) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + C(demographic_category) + week + percent',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + C(demographic_group) + week + percent',
 'is_influenza ~ C(respiratory_category) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(visit_type) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group)',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category) + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(demographic_category) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + C(demographic_category) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + C(demographic_category) + week + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(visit_type) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category) + week + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_group) + week + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(essence_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + week',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) + C(essence_category) + C(respiratory_category) + C(visit_type) + C(demographic_category) + C(demographic_group) + week + percent',
 'is_influenza ~ C(season) * C(essence_category)',
 'is_influenza ~ C(season) * C(respiratory_category)',
 'is_influenza ~ C(season) * C(visit_type)',
 'is_influenza ~ C(season) * C(demographic_category)',
 'is_influenza ~ C(season) * C(demographic_group)',
 'is_influenza ~ C(season) * week',
 'is_influenza ~ C(season) * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category)',
 'is_influenza ~ C(essence_category) * C(visit_type)',
 'is_influenza ~ C(essence_category) * C(demographic_category)',
 'is_influenza ~ C(essence_category) * C(demographic_group)',
 'is_influenza ~ C(essence_category) * week',
 'is_influenza ~ C(essence_category) * percent',
 'is_influenza ~ C(respiratory_category) * C(visit_type)',
 'is_influenza ~ C(respiratory_category) * C(demographic_category)',
 'is_influenza ~ C(respiratory_category) * C(demographic_group)',
 'is_influenza ~ C(respiratory_category) * week',
 'is_influenza ~ C(respiratory_category) * percent',
 'is_influenza ~ C(visit_type) * C(demographic_category)',
 'is_influenza ~ C(visit_type) * C(demographic_group)',
 'is_influenza ~ C(visit_type) * week',
 'is_influenza ~ C(visit_type) * percent',
 'is_influenza ~ C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(demographic_category) * week',
 'is_influenza ~ C(demographic_category) * percent',
 'is_influenza ~ C(demographic_group) * week',
 'is_influenza ~ C(demographic_group) * percent',
 'is_influenza ~ week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_group)',
 'is_influenza ~ C(season) * C(essence_category) * week',
 'is_influenza ~ C(season) * C(essence_category) * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_group)',
 'is_influenza ~ C(season) * C(respiratory_category) * week',
 'is_influenza ~ C(season) * C(respiratory_category) * percent',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category)',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_group)',
 'is_influenza ~ C(season) * C(visit_type) * week',
 'is_influenza ~ C(season) * C(visit_type) * percent',
 'is_influenza ~ C(season) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(season) * C(demographic_category) * week',
 'is_influenza ~ C(season) * C(demographic_category) * percent',
 'is_influenza ~ C(season) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * week * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_group)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * week',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * percent',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category)',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_group)',
 'is_influenza ~ C(essence_category) * C(visit_type) * week',
 'is_influenza ~ C(essence_category) * C(visit_type) * percent',
 'is_influenza ~ C(essence_category) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(essence_category) * C(demographic_category) * week',
 'is_influenza ~ C(essence_category) * C(demographic_category) * percent',
 'is_influenza ~ C(essence_category) * C(demographic_group) * week',
 'is_influenza ~ C(essence_category) * C(demographic_group) * percent',
 'is_influenza ~ C(essence_category) * week * percent',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_group)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * week',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * percent',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * week',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * percent',
 'is_influenza ~ C(respiratory_category) * C(demographic_group) * week',
 'is_influenza ~ C(respiratory_category) * C(demographic_group) * percent',
 'is_influenza ~ C(respiratory_category) * week * percent',
 'is_influenza ~ C(visit_type) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(visit_type) * C(demographic_category) * week',
 'is_influenza ~ C(visit_type) * C(demographic_category) * percent',
 'is_influenza ~ C(visit_type) * C(demographic_group) * week',
 'is_influenza ~ C(visit_type) * C(demographic_group) * percent',
 'is_influenza ~ C(visit_type) * week * percent',
 'is_influenza ~ C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(demographic_category) * week * percent',
 'is_influenza ~ C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_group)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_group)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(essence_category) * week * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_group)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * week',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * week',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * week * percent',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * week',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * percent',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(visit_type) * week * percent',
 'is_influenza ~ C(season) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(demographic_category) * week * percent',
 'is_influenza ~ C(season) * C(demographic_group) * week * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * week',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * week',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_group) * week',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_group) * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * week * percent',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * week',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * percent',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_group) * week',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_group) * percent',
 'is_influenza ~ C(essence_category) * C(visit_type) * week * percent',
 'is_influenza ~ C(essence_category) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(essence_category) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(essence_category) * C(demographic_category) * week * percent',
 'is_influenza ~ C(essence_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * week',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * percent',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_group) * week',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_group) * percent',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * week * percent',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * week * percent',
 'is_influenza ~ C(respiratory_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(visit_type) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(visit_type) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(visit_type) * C(demographic_category) * week * percent',
 'is_influenza ~ C(visit_type) * C(demographic_group) * week * percent',
 'is_influenza ~ C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * week * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * week * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * week * percent',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group) * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * week * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * week * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * week * percent',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_group) * week * percent',
 'is_influenza ~ C(essence_category) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * week * percent',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_group) * week * percent',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent',
 'is_influenza ~ week + I(week**2)',
 'is_influenza ~ week + I(week**2) + I(week**3)',
 'is_influenza ~ week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ percent + I(percent**2)',
 'is_influenza ~ percent + I(percent**2) + I(percent**3)',
 'is_influenza ~ percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ week + I(week**2) + C(season)',
 'is_influenza ~ week * I(week**2) * C(season)',
 'is_influenza ~ week + I(week**2) + C(essence_category)',
 'is_influenza ~ week * I(week**2) * C(essence_category)',
 'is_influenza ~ week + I(week**2) + C(respiratory_category)',
 'is_influenza ~ week * I(week**2) * C(respiratory_category)',
 'is_influenza ~ week + I(week**2) + C(visit_type)',
 'is_influenza ~ week * I(week**2) * C(visit_type)',
 'is_influenza ~ week + I(week**2) + C(demographic_category)',
 'is_influenza ~ week * I(week**2) * C(demographic_category)',
 'is_influenza ~ week + I(week**2) + C(demographic_group)',
 'is_influenza ~ week * I(week**2) * C(demographic_group)',
 'is_influenza ~ percent + I(percent**2) + C(season)',
 'is_influenza ~ percent * I(percent**2) * C(season)',
 'is_influenza ~ percent + I(percent**2) + C(essence_category)',
 'is_influenza ~ percent * I(percent**2) * C(essence_category)',
 'is_influenza ~ percent + I(percent**2) + C(respiratory_category)',
 'is_influenza ~ percent * I(percent**2) * C(respiratory_category)',
 'is_influenza ~ percent + I(percent**2) + C(visit_type)',
 'is_influenza ~ percent * I(percent**2) * C(visit_type)',
 'is_influenza ~ percent + I(percent**2) + C(demographic_category)',
 'is_influenza ~ percent * I(percent**2) * C(demographic_category)',
 'is_influenza ~ percent + I(percent**2) + C(demographic_group)',
 'is_influenza ~ percent * I(percent**2) * C(demographic_group)',
 'is_influenza ~ C(season) + C(essence_category) + week + I(week**2)',
 'is_influenza ~ C(season) * C(essence_category) * week * I(week**2)',
 'is_influenza ~ C(season) + C(essence_category) + percent + I(percent**2)',
 'is_influenza ~ C(season) * C(essence_category) * percent * I(percent**2)',
 'is_influenza ~ C(season) + C(respiratory_category) + week + I(week**2)',
 'is_influenza ~ C(season) * C(respiratory_category) * week * I(week**2)',
 'is_influenza ~ C(season) + C(respiratory_category) + percent + I(percent**2)',
 'is_influenza ~ C(season) * C(respiratory_category) * percent * I(percent**2)',
 'is_influenza ~ C(season) + C(visit_type) + week + I(week**2)',
 'is_influenza ~ C(season) * C(visit_type) * week * I(week**2)',
 'is_influenza ~ C(season) + C(visit_type) + percent + I(percent**2)',
 'is_influenza ~ C(season) * C(visit_type) * percent * I(percent**2)',
 'is_influenza ~ C(season) + C(demographic_category) + week + I(week**2)',
 'is_influenza ~ C(season) * C(demographic_category) * week * I(week**2)',
 'is_influenza ~ C(season) + C(demographic_category) + percent + I(percent**2)',
 'is_influenza ~ C(season) * C(demographic_category) * percent * I(percent**2)',
 'is_influenza ~ C(season) + C(demographic_group) + week + I(week**2)',
 'is_influenza ~ C(season) * C(demographic_group) * week * I(week**2)',
 'is_influenza ~ C(season) + C(demographic_group) + percent + I(percent**2)',
 'is_influenza ~ C(season) * C(demographic_group) * percent * I(percent**2)',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + week + I(week**2)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * week * I(week**2)',
 'is_influenza ~ C(essence_category) + C(respiratory_category) + percent + I(percent**2)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * percent * I(percent**2)',
 'is_influenza ~ C(essence_category) + C(visit_type) + week + I(week**2)',
 'is_influenza ~ C(essence_category) * C(visit_type) * week * I(week**2)',
 'is_influenza ~ C(essence_category) + C(visit_type) + percent + I(percent**2)',
 'is_influenza ~ C(essence_category) * C(visit_type) * percent * I(percent**2)',
 'is_influenza ~ C(essence_category) + C(demographic_category) + week + I(week**2)',
 'is_influenza ~ C(essence_category) * C(demographic_category) * week * I(week**2)',
 'is_influenza ~ C(essence_category) + C(demographic_category) + percent + I(percent**2)',
 'is_influenza ~ C(essence_category) * C(demographic_category) * percent * I(percent**2)',
 'is_influenza ~ C(essence_category) + C(demographic_group) + week + I(week**2)',
 'is_influenza ~ C(essence_category) * C(demographic_group) * week * I(week**2)',
 'is_influenza ~ C(essence_category) + C(demographic_group) + percent + I(percent**2)',
 'is_influenza ~ C(essence_category) * C(demographic_group) * percent * I(percent**2)',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + week + I(week**2)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * week * I(week**2)',
 'is_influenza ~ C(respiratory_category) + C(visit_type) + percent + I(percent**2)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * percent * I(percent**2)',
 'is_influenza ~ C(respiratory_category) + C(demographic_category) + week + I(week**2)',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * week * I(week**2)',
 'is_influenza ~ C(respiratory_category) + C(demographic_category) + percent + I(percent**2)',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * percent * I(percent**2)',
 'is_influenza ~ C(respiratory_category) + C(demographic_group) + week + I(week**2)',
 'is_influenza ~ C(respiratory_category) * C(demographic_group) * week * I(week**2)',
 'is_influenza ~ C(respiratory_category) + C(demographic_group) + percent + I(percent**2)',
 'is_influenza ~ C(respiratory_category) * C(demographic_group) * percent * I(percent**2)',
 'is_influenza ~ C(visit_type) + C(demographic_category) + week + I(week**2)',
 'is_influenza ~ C(visit_type) * C(demographic_category) * week * I(week**2)',
 'is_influenza ~ C(visit_type) + C(demographic_category) + percent + I(percent**2)',
 'is_influenza ~ C(visit_type) * C(demographic_category) * percent * I(percent**2)',
 'is_influenza ~ C(visit_type) + C(demographic_group) + week + I(week**2)',
 'is_influenza ~ C(visit_type) * C(demographic_group) * week * I(week**2)',
 'is_influenza ~ C(visit_type) + C(demographic_group) + percent + I(percent**2)',
 'is_influenza ~ C(visit_type) * C(demographic_group) * percent * I(percent**2)',
 'is_influenza ~ C(demographic_category) + C(demographic_group) + week + I(week**2)',
 'is_influenza ~ C(demographic_category) * C(demographic_group) * week * I(week**2)',
 'is_influenza ~ C(demographic_category) + C(demographic_group) + percent + I(percent**2)',
 'is_influenza ~ C(demographic_category) * C(demographic_group) * percent * I(percent**2)',
 'is_influenza ~ C(season) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(visit_type) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(visit_type) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(visit_type) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(visit_type) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(visit_type) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(visit_type) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(visit_type) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(visit_type) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(visit_type) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(visit_type) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(visit_type) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(visit_type) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(visit_type) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(visit_type) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(visit_type) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(visit_type) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(visit_type) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(visit_type) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(week**2) + I(week**3) + I(week**4)',
 'is_influenza ~ C(season) * C(essence_category) * C(respiratory_category) * C(visit_type) * C(demographic_category) * C(demographic_group) * week * percent + I(percent**2) + I(percent**3) + I(percent**4)']

Use Stratified Cross-Validation on the Binary Classification Models and Fit within each Fold

Use 5-fold Cross-Validation

from sklearn.model_selection import StratifiedKFold

kf = StratifiedKFold(n_splits=5,
                     shuffle=True,
                     random_state=101)

Fit the Logistic Regression Models w/ Statsmodels

input_names = df_copy.drop(columns=[target]).\
                           copy().\
                           columns.\
                           to_list()

output_name = target

from sklearn.preprocessing import StandardScaler

from sklearn.metrics import roc_auc_score

def my_coefplot(model, figsize_default=(10, 4), figsize_expansion_factor=0.5, max_default_vars=10):
    """
    Function that plots a coefficient plot with error bars for a given statistical model
    and prints out which variables are statistically significant and whether they are positive or negative.
    The graph height dynamically adjusts based on the number of variables.

    Params:
        model: object
        figsize_default: tuple, optional
        figsize_expansion_factor: float, optional
        max_default_vars: int, optional
    """
    # cap the standard errors (bse) to avoid overly large error bars, upper bound set to 2
    capped_bse = model.bse.clip(upper=2)
    
    # calculate the minimum and maximum coefficient values adjusted by the standard errors
    coef_min = (model.params - 2 * capped_bse).min()
    coef_max = (model.params + 2 * capped_bse).max()
    
    # define buffer space for the x-axis limits
    buffer_space = 0.5
    xlim_min = coef_min - buffer_space
    xlim_max = coef_max + buffer_space
    
    # dynamically calculate figure height based on the number of variables
    num_vars = len(model.params)
    if num_vars > max_default_vars:
        height = figsize_default[1] + figsize_expansion_factor * (num_vars - max_default_vars)
    else:
        height = figsize_default[1]
    
    # create the plot
    fig, ax = plt.subplots(figsize=(figsize_default[0], height))
    
    # identify statistically significant and non-significant variables based on p-values
    significant_vars = model.pvalues[model.pvalues < 0.05].index
    not_significant_vars = model.pvalues[model.pvalues >= 0.05].index
    
    # plot non-significant variables with grey error bars
    ax.errorbar(y=not_significant_vars,
                x=model.params[not_significant_vars],
                xerr=2 * capped_bse[not_significant_vars],
                fmt='o', 
                color='grey', 
                ecolor='grey', 
                elinewidth=2, 
                ms=10,
                label='not significant')
    
    # plot significant variables with red error bars
    ax.errorbar(y=significant_vars,
                x=model.params[significant_vars],
                xerr=2 * capped_bse[significant_vars],
                fmt='o', 
                color='red', 
                ecolor='red', 
                elinewidth=2, 
                ms=10,
                label='significant (p < 0.05)')
    
    # add a vertical line at 0 to visually separate positive and negative coefficients
    ax.axvline(x=0, linestyle='--', linewidth=2.5, color='grey')
    
    # adjust the x-axis limits to add some buffer space on either side
    ax.set_xlim(min(-0.5, coef_min - 0.2), max(0.5, coef_max + 0.2))
    ax.set_xlabel('coefficient value')
    
    # add legend to distinguish between significant and non-significant variables
    ax.legend()
    
    # show the plot
    plt.show()
    
    # print the summary of statistically significant variables
    print('\n--- statistically significant variables ---')
    
    # check if there are any significant variables, if not, print a message
    if significant_vars.empty:
        print('No statistically significant variables found.')
    else:
        # for each significant variable, print its coefficient, standard error, p-value, and direction
        for var in significant_vars:
            coef_value = model.params[var]
            std_err = model.bse[var]
            p_val = model.pvalues[var]
            direction = 'positive' if coef_value > 0 else 'negative'
            print(f'variable: {var}, coefficient: {coef_value:.4f}, std err: {std_err:.4f}, p-value: {p_val:.4f}, direction: {direction}')

def train_and_test_logistic_with_cv(model, formula, df, x_names, y_name, cv, threshold=0.5, use_scaler=False):
    """
    Function to train and test a logistic binary classification model with Cross-Validation,
    including accuracy and ROC AUC score calculations.

    Params:
        model: object
        formula: str
        df: object
        x_names: list
        y_name: str
        cv: object
        threshold: float, optional
        use_scaler: bool, optional

    Returns:
        object
    """
    # separate the inputs and output
    input_df = df.loc[:, x_names].copy()
    
    # initialize the performance metric storage lists
    train_res = []
    test_res = []
    train_auc_scores = []
    test_auc_scores = []
    
    # split the data and iterate over the folds
    for train_id, test_id in cv.split(input_df.to_numpy(), df[y_name].to_numpy()):
        
        # subset the training and test splits within each fold
        train_data = df.iloc[train_id, :].copy()
        test_data = df.iloc[test_id, :].copy()

        # if the use_scaler flag is set, standardize the numeric features within each fold
        if use_scaler:
            scaler = StandardScaler()
            
            # identify numeric columns to scale, excluding the target variable
            columns_to_scale = train_data.select_dtypes(include=[np.number]).columns.tolist()
            columns_to_scale = [col for col in columns_to_scale if col != y_name]
            
            # fit scaler on training data
            scaler.fit(train_data[columns_to_scale])
            
            # transform training and test data
            train_data[columns_to_scale] = scaler.transform(train_data[columns_to_scale])
            test_data[columns_to_scale] = scaler.transform(test_data[columns_to_scale])
        
        # fit the model on the training data within the current fold
        a_model = smf.logit(formula=formula, data=train_data).fit()
        
        # predict the training within each fold
        train_copy = train_data.copy()
        train_copy['pred_probability'] = a_model.predict(train_data)
        train_copy['pred_class'] = np.where(train_copy.pred_probability > threshold, 1, 0)
        
        # predict the testing within each fold
        test_copy = test_data.copy()
        test_copy['pred_probability'] = a_model.predict(test_data)
        test_copy['pred_class'] = np.where(test_copy.pred_probability > threshold, 1, 0)
        
        # calculate the performance metric (accuracy) on the training set within the fold
        train_res.append(np.mean(train_copy[y_name] == train_copy.pred_class))
        
        # calculate the performance metric (accuracy) on the testing set within the fold
        test_res.append(np.mean(test_copy[y_name] == test_copy.pred_class))

        # calculate the roc_auc_score for the training set
        train_auc_scores.append(roc_auc_score(train_copy[y_name], train_copy['pred_probability']))
        
        # calculate the roc_auc_score for the testing_set
        test_auc_scores.append(roc_auc_score(test_copy[y_name], test_copy['pred_probability']))
    
    # book keeping to store the results (accuracy)
    train_df = pd.DataFrame({'accuracy': train_res, 'roc_auc': train_auc_scores})
    train_df['from_set'] = 'training'
    train_df['fold_id'] = train_df.index + 1
    test_df = pd.DataFrame({'accuracy': test_res, 'roc_auc': test_auc_scores})
    test_df['from_set'] = 'testing'
    test_df['fold_id'] = test_df.index + 1
    
    # combine the splits together
    res_df = pd.concat([train_df, test_df], ignore_index=True)
    
    # add information about the model
    res_df['model'] = model
    res_df['formula'] = formula
    res_df['num_coefs'] = len(a_model.params)
    res_df['threshold'] = threshold

    # return the results DataFrame
    return res_df

Check Scale of the Data - Standardize vs. Not Standardize

df_copy[input_names].describe()

	week	percent
count	47964.000000	47964.000000
mean	26.610437	3.307313
std	14.998518	6.332838
min	1.000000	0.000000
25%	14.000000	0.000000
50%	27.000000	0.480000
75%	40.000000	3.340000
max	52.000000	100.000000

sns.catplot(data=df_copy.reset_index().\
            rename(columns={'index': 'rowid'}).\
            melt(id_vars=['rowid'], 
                 value_vars=df_copy[input_names].select_dtypes(include=['number']).columns),
            x='variable',
            y='value',
            kind='box', 
            aspect=3)
plt.title('Box Plots of All Numeric Variables for Comparison')
plt.xticks(rotation=90)
plt.show()

sns.catplot(data=pd.DataFrame(StandardScaler().\
                              fit_transform(df_copy[input_names].\
                                            select_dtypes(include=['number'])), 
                              columns=df_copy[input_names].\
                              select_dtypes(include=['number']).\
                              columns).reset_index().\
            rename(columns={'index': 'rowid'}).\
            melt(id_vars=['rowid'], 
                 value_vars=df_copy[input_names].\
                 select_dtypes(include=['number']).\
                 columns),
            x='variable',  
            y='value',
            kind='box', aspect=3)
plt.title('Box Plots of All Numeric Variables (After Scaling)')
plt.xticks(rotation=90)
plt.show()

Test 125 Models

import os

import contextlib

res_list = []
error_log = []

with contextlib.redirect_stdout(open(os.devnull, 'w')), contextlib.redirect_stderr(open(os.devnull, 'w')):
    for model in range(min(125, len(formulas))):
        try:
            res_list.append(train_and_test_logistic_with_cv(model,
                                                            formula=formulas[model],
                                                            df=df_copy,
                                                            x_names=input_names,
                                                            y_name=output_name,
                                                            cv=kf,
                                                            use_scaler=True))
        except Exception as e:
            error_log.append(f'Formula ID {model} failed: {str(e)}')

cv_results = pd.concat(res_list, ignore_index=True)

Review Model Results - Average of Folds

All Models w/ Highest `accuracy` on the `testing` Dataset

cv_results.loc[(cv_results['from_set'] == 'testing') & 
               (cv_results['accuracy'] < 1.0) & 
               (cv_results['roc_auc'] < 1.0)].\
           groupby('model').\
           aggregate({'accuracy': 'mean', 
                      'roc_auc': 'mean', 
                      'num_coefs': 'first'}).\
           reset_index().\
           sort_values(by='accuracy', ascending=False)

	model	accuracy	roc_auc	num_coefs
33	96	0.950485	0.999744	28
34	99	0.844261	0.974864	18
32	83	0.802102	0.697427	15
24	75	0.802102	0.495022	6
25	76	0.802102	0.693318	6
26	77	0.802102	0.486048	16
27	78	0.802102	0.700490	16
28	79	0.802102	0.669038	5
29	80	0.802102	0.489487	16
30	81	0.802102	0.698892	16
31	82	0.802102	0.689041	5
0	2	0.802102	0.488119	12
22	48	0.802102	0.692584	12
35	109	0.802102	0.480564	26
36	110	0.802102	0.484685	15
37	112	0.802102	0.479757	25
38	113	0.802102	0.706227	25
39	115	0.802102	0.483641	25
40	116	0.802102	0.701737	25
41	117	0.802102	0.695748	14
23	74	0.802102	0.486738	17
21	47	0.802102	0.701737	23
1	3	0.802102	0.489829	12
10	23	0.802102	0.498705	4
2	4	0.802102	0.484082	22
3	5	0.802102	0.483389	11
4	6	0.802102	0.695034	11
5	18	0.802102	0.497179	5
6	19	0.802102	0.486738	15
7	20	0.802102	0.498211	4
8	21	0.802102	0.669338	4
9	22	0.802102	0.490298	15
11	24	0.802102	0.689566	4
20	46	0.802102	0.483641	23
12	25	0.802102	0.489487	14
13	26	0.802102	0.698892	14
14	27	0.802102	0.668223	3
15	39	0.802102	0.486121	14
16	40	0.802102	0.480564	24
17	43	0.802102	0.484082	24
18	44	0.802102	0.488469	13
19	45	0.802102	0.697651	13
42	118	0.802102	0.700290	24

Model Selection

Since Model 96 appears to be overfitting, and Model 99 has convergence issues likely due to multicollinearity or overfitting, a more stable and simpler alternative would be Model 117. This model has an accuracy of 0.802102, a reasonable balance between performance and complexity, and an ROC AUC of 0.695748, indicating its ability to distinguish between influenza and non-influenza cases. With only 14 coefficients, Model 117 is less complex, reducing the risk of overfitting and making it more likely to generalize to new data. Its stability during the fitting process also makes it a preferable option, avoiding numerical issues like singular matrices or failed convergence.

best_model = smf.logit(formula=formulas[117], 
                       data=df_copy).fit()

Optimization terminated successfully.
         Current function value: 0.449109
         Iterations 8

best_model.params

Intercept                                   -1.103243
C(season)[T.2016-2017]                       0.045845
C(season)[T.2017-2018]                       0.108385
C(season)[T.2018-2019]                       0.068572
C(season)[T.2019-2020]                       0.190227
C(season)[T.2020-2021]                       0.124803
C(season)[T.2021-2022]                       0.144458
C(season)[T.2022-2023]                       0.129073
C(season)[T.2023-2024]                       0.153577
C(season)[T.2024-2025]                       0.006620
C(demographic_category)[T.Age Group]         0.050765
C(demographic_category)[T.Race/Ethnicity]    0.142890
week                                        -0.000800
percent                                     -0.336332
dtype: float64

best_model.pvalues < 0.05

Intercept                                     True
C(season)[T.2016-2017]                       False
C(season)[T.2017-2018]                       False
C(season)[T.2018-2019]                       False
C(season)[T.2019-2020]                        True
C(season)[T.2020-2021]                        True
C(season)[T.2021-2022]                        True
C(season)[T.2022-2023]                        True
C(season)[T.2023-2024]                        True
C(season)[T.2024-2025]                       False
C(demographic_category)[T.Age Group]         False
C(demographic_category)[T.Race/Ethnicity]     True
week                                         False
percent                                       True
dtype: bool

best_model.params[best_model.pvalues < 0.05].sort_values(ascending=False)

C(season)[T.2019-2020]                       0.190227
C(season)[T.2023-2024]                       0.153577
C(season)[T.2021-2022]                       0.144458
C(demographic_category)[T.Race/Ethnicity]    0.142890
C(season)[T.2022-2023]                       0.129073
C(season)[T.2020-2021]                       0.124803
percent                                     -0.336332
Intercept                                   -1.103243
dtype: float64

my_coefplot(best_model)

--- statistically significant variables ---
variable: Intercept, coefficient: -1.1032, std err: 0.0641, p-value: 0.0000, direction: negative
variable: C(season)[T.2019-2020], coefficient: 0.1902, std err: 0.0545, p-value: 0.0005, direction: positive
variable: C(season)[T.2020-2021], coefficient: 0.1248, std err: 0.0544, p-value: 0.0217, direction: positive
variable: C(season)[T.2021-2022], coefficient: 0.1445, std err: 0.0543, p-value: 0.0078, direction: positive
variable: C(season)[T.2022-2023], coefficient: 0.1291, std err: 0.0542, p-value: 0.0173, direction: positive
variable: C(season)[T.2023-2024], coefficient: 0.1536, std err: 0.0542, p-value: 0.0046, direction: positive
variable: C(demographic_category)[T.Race/Ethnicity], coefficient: 0.1429, std err: 0.0456, p-value: 0.0017, direction: positive
variable: percent, coefficient: -0.3363, std err: 0.0083, p-value: 0.0000, direction: negative

Save Model - Usage in Inference Application

import pickle

with open('logit_model.pkl', 'wb') as file:
    pickle.dump(best_model, file)

Load Model - Usage in Inference Application

with open('logit_model.pkl', 'rb') as file:
    loaded_model = pickle.load(file)

Perform Inference - Validate Production Model

sample_data = pd.DataFrame({
    'week': [22],
    'season': ['2024-2025'],
    'essence_category': ['CDC Influenza DD v1'],
    'respiratory_category': ['Influenza'],
    'visit_type': ['ED Visits'],
    'demographic_category': ['Race/Ethnicity'],
    'demographic_group': ['Black Non-Hispanic'],
    'percent': [65.0]
})

loaded_model.predict(sample_data)

0    1.212773e-10
dtype: float64

Name		Name	Last commit message	Last commit date
Latest commit History 10 Commits
README_files		README_files
.gitignore		.gitignore
Chicago_Influenza_Binary_Classification.ipynb		Chicago_Influenza_Binary_Classification.ipynb
Inpatient__Emergency_Department__and_Outpatient_Visits_for_Respiratory_Illnesses.csv		Inpatient__Emergency_Department__and_Outpatient_Visits_for_Respiratory_Illnesses.csv
LICENSE		LICENSE
README.md		README.md
convert_to_md.sh		convert_to_md.sh
logit_model.pkl		logit_model.pkl

License

mytechnotalent/Chicago-Influenza-Binary-Classifier

Folders and files

Latest commit

History

Repository files navigation