loglinear-models

Overview

This repository contains an analysis of bidimensional contingency tables measured on an ordinal scale using log-linear models. The goal is to explore associations between pairs of variables, identify the best-fitting model for each table, and test for marginal homogeneity between rows and columns.

Data

The dataset tablasb.xlsx contains multiple 5x5 contingency tables extracted from observational data. Each table corresponds to a pair of ordinal variables.
Directory structure: data/tablasb.xlsx

Methods

We fit several log-linear models to each table:

1. Null model: Assumes constant cell counts across the table.
2. Saturated model: Fits all possible interactions (perfect fit).
3. Independence model: Assumes row and column variables are independent.
4. Uniform association model: Includes a linear-by-linear association term.
5. Symmetry model: Assumes the table is symmetric.
6. Quasi-symmetry model: Combines symmetry with main effects.
7. Quasi-independence model: Independence with adjustment for structural zeros.
8. Row effects model: Adjusts for row-specific effects.
9. Column effects model: Adjusts for column-specific effects.

For each model, we calculate:

• Deviance and goodness-of-fit p-values
• AIC for model comparison

We select the best-fitting model based on minimum AIC and interpret the estimated parameters, checking the adjusted odds ratios. Additionally, we test for marginal homogeneity between rows and columns (SI vs QS models).

Code

All analysis is implemented in R. The script is: script/loglinear_analysis.R

Example Usage

# Load libraries and data
library(readxl)
tablasb <- read_excel("data/tablasb.xlsx", col_names = FALSE)

# Extract tables
t1 <- tablasb[1:5, ]
t2 <- tablasb[8:12, ]

# Run analysis
source("script/loglinear_analysis.R")
models(t1)
models(t2)

Results

Results are saved in the results/ folder. Each table's output includes:

• P-values for goodness-of-fit tests for all models
• Summary of the best-fitting model
• Test of marginal homogeneity

License

This project is licensed under the MIT License.