BasicElectionForensics()

title	Election Forensics Toolkit
author	Kirill Kalinin, Walter Mebane
date	2025-09-24
output	html_document

Cite:

Kirill Kalinin, Walter R. Mebane, Jr. (2019, updated 2025). EFToolkit: Election Forensics Toolkit (Version 2.0.0) [R package]. GitHub. https://github.com/kkalininMI/EFToolkit

BasicElectionForensics()

The BasicElectionForensics function is a comprehensive R tool designed to perform statistical analysis on election data to detect potential irregularities or fraud patterns. This function implements multiple forensic methods commonly used in election integrity research and provides both statistical results and significance testing through bootstrap methods.

BasicElectionForensics(data, Candidates, Level="National", 
                      TotalReg, TotalVotes, Methods, R=1000, cores=2)

Input

Parameter	Type	Description
`data`	data.frame	The input dataset containing election results
`Candidates`	vector	Variable names referring to vote counts for candidates/parties
`Level`	string	Variable name depicting the level of analysis (default: "National")
`TotalReg`	string	Variable name for the total number of eligible voters
`TotalVotes`	string	Variable name for the total number of ballots cast
`Methods`	vector	List of forensic methods to apply (see Methods section)
`R`	numeric	Number of bootstrap simulations (default: 1000)
`cores`	numeric	Number of cores for parallel computing (default: 2)

Output

Output	Type	Description
`table`	`data.frame`	Numerical results of the election forensic tests
`tex`	`xtable`, `data.frame`	LaTeX-formatted results table suitable for academic use
`html`	`datatables`, `htmlwidget`	Interactive HTML table with color-coded significance
`sigMatrix`	`matrix`, `array`	Binary significance matrix for further statistical analysis

Statistical Distribution Tests

_2BL - Second-digit mean test (Benford's Law analysis)
LastC - Last-digit mean test for uniform distribution
P05s - Percentage last-digit 0/5 indicator (for percentages)
C05s - Count last-digit 0/5 indicator (for vote counts)
Skew - Skewness measure (asymmetry from normal distribution)
Kurt - Kurtosis measure (tail heaviness compared to normal distribution)
DipT - Unimodality test (Hartigan's dip test)
Sobyanin - Sobyanin-Sukhovolsky measure (turnout-vote share relationship)
Correlation - Correlation coefficient between turnout and vote share

Key Features

Uses nonparametric bootstrap with configurable number of simulations (R parameter)
Provides confidence intervals for statistical significance
Supports parallel processing for improved performance
Works with various election data formats
Handles missing data appropriately
Supports multi-level analysis (e.g., national, regional, local)

Usage Example

library(EFToolkit)

# Load election data
dat <- read.csv(system.file("extdata/Albania2013.csv", package="EFToolkit"))

# Run forensics analysis
results <- BasicElectionForensics(
  dat,
  Candidates = c("C035", "C050"),
  Level = "Prefectures", 
  TotalReg = "Registered",
  TotalVotes = "Ballots",
  Methods = c("P05s", "C05s", "_2BL", "Sobyanin", 
              "DipT", "Skew", "Kurt", "Correlation"),
  cores = 2, 
  R = 100  # Reduced for faster computation in example
)

# View results
print(results$table)

Interpretation Guidelines

Test	No fraud	Interpretation
Second-digit mean (2BL)	4.187	Values close to 4.19 are consistent with Benford's Law. Systematic deviations (too low or too high) may indicate artificial rounding or human fabrication.
Last-digit mean (LastC)	4.5	Randomly distributed last digits should average 4.5. Substantial deviations suggest that numbers may not be uniformly random (e.g., preferences for certain digits).
Count of last-digit 0/5 ind. mean (C05s)	0.2	About 20% of values should end in 0 or 5. Excess frequency of 0s or 5s may reflect rounding or strategic reporting.
Perc. last-digit 0/5 ind. mean (P05s)	0.2	Same logic applies to percentages; deviations from 0.2 may signal manipulation of turnout or result percentages.
Skewness (Skew)	0	A symmetric distribution has skewness near zero. Positive skew indicates a longer right tail (many low but a few very high values); negative skew the opposite. Significant skewness may indicate anomalous clustering of results.
Kurtosis (Kurt)	3	A normal distribution has kurtosis of 3. Higher values (>3) indicate peakedness (results too concentrated), while lower values (<3) suggest excessive dispersion.
Unimodality test p-value (DipT)	>0.05	A p-value greater than 0.05 supports unimodality (single peak). Values below 0.05 indicate multimodality, possibly reflecting a mixture of normal and manipulated results.
Sobyanin--Sukhovolsky	near 0	Captures the degree of association between turnout and vote share. Under normal conditions, this relationship should be weak or nonexistent; strong positive association may indicate manipulated results.
Correlation coefficient (Corr)	near 0	Measures the correlation between turnout and vote share across precincts. Values close to zero are expected in competitive elections; high positive correlations suggest manipulated results.

BuildMap()

The BuildMap function is a specialized R visualization tool designed to create choropleth maps from election forensics analysis results. This function takes the output from BasicElectionForensics() and combines it with geographic data to produce spatial visualizations of statistical anomalies and patterns in election data.

BuildMap(eforensicsdata, geodata, Geoindex, Colorsig=FALSE, xlab="")

Input

Parameter	Type	Description
`eforensicsdata`	list	Output object from `BasicElectionForensics()` function
`geodata`	sf object	Spatial data frame containing geographic boundaries
`Geoindex`	string	Name of index variable from sf object used to merge geodata with forensics results
`Colorsig`	logical	If TRUE, only statistically significant estimates are mapped (default: FALSE)
`xlab`	string	X-axis label or subtitle for the maps

Output

Output	Type	Description
`figures`	`list`	Collection of generated plots (either `spplot` or `tmap` objects)
`Colorsig`	`logical`	Indicator of whether significance-based coloring was applied (`TRUE/FALSE`)
`shpdata`	`sf` (simple features)	Spatial dataset with election forensics results merged with geodata
`creationdate`	`POSIXct`	Timestamp of when the output was created

Key Features

Spatial Data Integration

Seamlessly merges election forensics results with geographic boundaries
Supports sf (Simple Features) spatial data format
Handles missing data and geographic mismatches gracefully

Flexible Visualization Options

Standard Mode: Displays all forensic values with continuous color scales
Significance Mode: Highlights only statistically significant results
Customizable color schemes using ColorBrewer palettes

Multi-Method Mapping

Automatically generates maps for all forensic methods in the input data
Creates separate visualizations for each candidate-method combination
Supports multiple candidates and analysis levels simultaneously

Usage Example

library(EFToolkit)
library(sf)

# Load election data
dat <- read.csv(system.file("extdata/Albania2013.csv", package="EFToolkit"))

# Run forensics analysis
eldata <- BasicElectionForensics(dat,
                                Candidates=c("C035", "C050"),
                                Level="Prefectures", TotalReg="Registered",
                                TotalVotes="Ballots",
                                Methods=c("P05s", "C05s"), R=100)

# Load geographic data
geodata <- st_read(system.file("extdata/Albania2013_prefectures.shp",
                          package="EFToolkit"), quiet = TRUE)

# Create maps
figures <- BuildMap(eforensicsdata=eldata, geodata=geodata, Geoindex="Level")

# Access individual maps
print(figures$figures$Turn_P05s)  # Turnout P05s method map
print(figures$figures$C035_P05s)  # Candidate C035 P05s method map

The function generates choropleth maps showing spatial patterns of election forensics indicators:

Image 1	Image 2	Image 3	Image 4

Technical Implementation Details

Spatial Data Handling

Uses sf package for modern spatial data processing
Maintains coordinate reference systems throughout analysis
Supports various geographic file formats (shapefile, GeoJSON, etc.)
Implements ColorBrewer "OrRd" (Orange-Red) palette by default
Provides good contrast for highlighting anomalies
Color-blind friendly options available through ColorBrewer

Color Intensity Interpretation

Light Colors: Values close to expected/normal ranges
Medium Colors: Moderate deviations from expected patterns
Dark Colors: Strong deviations suggesting potential irregularities
No Color/White: Missing data or areas excluded from analysis

Spatial Pattern Analysis

Clustering: Adjacent areas with similar colors may indicate systematic issues
Isolated Anomalies: Single areas with extreme values warrant individual investigation
Border Effects: Patterns along administrative boundaries may suggest institutional factors
Urban/Rural Differences: Different patterns by area type are common

ClusterAnalysis()

The ClusterAnalysis function implements sophisticated spatial clustering tests to identify geographic patterns and anomalies in election forensics data. This function uses two complementary statistical methods - Getis-Ord Gi* and Local Moran's I - to detect spatial clusters of unusual values, helping researchers identify areas where election irregularities may be spatially correlated.

ClusterAnalysis(geodata, Vars, IndexCL=NULL, cores=2)

Input

Parameter	Type	Description
`geodata`	sf object/list	Spatial data within a list (supports both polygon and point sf objects) or BuildMap object
`Vars`	character vector	Variable names used for geographic clustering tests
`IndexCL`	string	Index variable name used for merging polygon and point sf objects (optional)
`cores`	numeric	Number of cores for parallel computing (default: 2)

Output

Output	Type	Description
`Moran's I for <Var>`	`ggplot`	A `ggplot` map visualizing local Moran’s I cluster results for variable `<Var>`.
`Getis-Ord for <Var>`	`ggplot`	A `ggplot` map visualizing Getis-Ord G* hot- and cold-spots for variable `<Var>`.

Spatial Clustering Methods

Local Moran's I

Purpose: Identifies local clusters and spatial outliers
Detects: Four types of spatial associations:
- HH (High-High): High values surrounded by high values
- LL (Low-Low): Low values surrounded by low values
- HL (High-Low): High values surrounded by low values
- LH (Low-High): Low values surrounded by high values

Getis-Ord Gi* Statistic

Purpose: Identifies hot spots and cold spots
Detects: Two types of spatial concentrations:
- Hot Spots: Areas with significantly high values clustered together
- Cold Spots: Areas with significantly low values clustered together

The function generates spatial cluster analysis maps showing different types of spatial patterns:

Image 1	Image 2	Image 3	Image 4

Spatial clustering analysis Spatial clustering analysis for Albanian election data - (1) Local Moran's I for P05s method, (2) Getis-Ord hot/cold spots for P05s, (3) Local Moran's I for C05s method, (4) Getis-Ord analysis for C05s method

library(EFToolkit)
library(sf)

# Load election data
dat <- read.csv(system.file("extdata/Albania2013.csv", package="EFToolkit"))

# Obtain election forensics estimates
eldata <- BasicElectionForensics(dat,
                                Candidates=c("C035", "C050"),
                                Level="Prefectures", TotalReg="Registered",
                                TotalVotes="Ballots",
                                Methods=c("P05s", "C05s"), R=100)

# Create the map with results
geodata <- st_read(system.file("extdata/Albania2013_prefectures.shp", 
                              package="EFToolkit"), quiet = TRUE)
figures <- BuildMap(eforensicsdata=eldata, geodata=geodata, 
                   Geoindex="Level", Colorsig=FALSE)

# Using the mapped results, implement cluster analysis
cluster_results <- ClusterAnalysis(figures, Vars=c("C050_P05s", "C050_C05s"))

# View specific cluster maps
print(cluster_results[["Moran's I for C050_P05s"]])
print(cluster_results[["Getis-Ord for C050_P05s"]])

Key Features

Advanced Spatial Statistics

Permutation-based Testing: Uses Monte Carlo permutation tests for statistical significance
False Discovery Rate Control: Implements Benjamini-Hochberg FDR correction for multiple testing
Parallel Processing: Supports multi-core computation for large datasets

Flexible Input Handling

Multiple Data Types: Works with polygon and point spatial data
Integration Ready: Seamlessly processes BuildMap function outputs
Missing Data Handling: Robust treatment of missing or invalid data points

Comprehensive Visualization

Color-coded Results: Uses standardized color schemes for easy interpretation
Multiple Significance Levels: Shows results at 90%, 95%, and 99% confidence levels
Interactive Plotting: Generates ggplot2 objects for further customization

Color Coding System

Local Moran's I Colors

Pattern	99% Level	95% Level	90% Level	Description
HH	Dark Red	Light Red	Pink	High-High clusters
LL	Dark Blue	Light Blue	Light Gray	Low-Low clusters
HL	Dark Orange	Light Orange	Yellow	High-Low outliers
LH	Dark Green	Light Green	Light Green	Low-High outliers
NS	Light Gray	Light Gray	Light Gray	Not significant

Getis-Ord Gi* Colors

Pattern	Description	Color
Hot Spot (99%)	Highly significant hot spot	Dark Red
Hot Spot (95%)	Significant hot spot	Medium Red
Hot Spot (90%)	Moderately significant hot spot	Light Red
Cold Spot (99%)	Highly significant cold spot	Dark Blue
Cold Spot (95%)	Significant cold spot	Medium Blue
Cold Spot (90%)	Moderately significant cold spot	Light Blue
Not Significant	No significant clustering	Light Gray

Local Moran's I Results

High-High Clusters (Red): Areas with high forensic values surrounded by similar high values
- Interpretation: Potential systematic irregularities in neighboring areas
- Action: Priority areas for detailed investigation
Low-Low Clusters (Blue): Areas with low forensic values surrounded by similar low values
- Interpretation: Regions with consistently normal patterns
- Action: Lower priority for investigation
High-Low Outliers (Orange): High values surrounded by low values
- Interpretation: Isolated anomalies or data quality issues
- Action: Investigate for administrative or data collection problems
Low-High Outliers (Green): Low values surrounded by high values
- Interpretation: Unusually clean areas within problematic regions
- Action: Verify data accuracy or investigate protective factors

Getis-Ord Results

Hot Spots (Red Shades): Statistically significant concentrations of high values
- Interpretation: Geographic clustering of potential irregularities
- Action: Focus investigative resources on these areas
Cold Spots (Blue Shades): Statistically significant concentrations of low values
- Interpretation: Areas with consistently normal electoral patterns
- Action: Use as baseline comparisons or control areas

NonparamElectionForensics()

The NonparamElectionForensics function implements a revised version of Shpilkin's method for detecting election fraud through nonparametric analysis of vote distributions. This method identifies anomalous voting patterns by analyzing the relationship between turnout and candidate support, detecting artificial vote inflation through statistical modeling of "clean" electoral behavior.

NonparamElectionForensics(data, Candidates, CandidatesText=NULL,
                         MainCandidate, TotalReg, TotalVotes=NULL,
                         Level=NULL, MaxThreshold=0.8,
                         FigureName, setcolors=NULL,
                         precinctLevel=TRUE, computeSD=NULL,
                         sims=10, mode_search=list(npeaks=5, sortstr=TRUE,
                                                  minpeakdistance=1, pick_by="height"),
                         man_turnout=NULL, grid_type="1D")

Input

Parameter	Type	Description
`data`	data.frame	Electoral data containing vote counts and registration information
`Candidates`	vector	Variable names for all candidates/parties in the election
`CandidatesText`	vector	Display names for candidates/parties (uses `Candidates` if NULL) (default: NULL)
`MainCandidate`	string	Variable name for main/incumbent candidate
`TotalReg`	string	Variable name for total number of eligible voters
`TotalVotes`	string	Variable name for total ballots cast (computed from candidates if NULL) (default: NULL)
`Level`	string	Variable for analysis level (default: "National")
`MaxThreshold`	numeric	Anomalous turnout threshold (default: 0.8)
`FigureName`	string	Title for generated figures
`setcolors`	vector	Custom color palette (random if NULL) (default: NULL)
`precinctLevel`	logical	Whether to compute precinct-level estimates (default: TRUE)
`computeSD`	string	Standard error method: "parametric" or "nonparametric" (default: NULL)
`sims`	numeric	Number of simulations for uncertainty estimation (default: 10)
`mode_search`	list	Clean peak search parameters
`man_turnout`	numeric	Manual clean peak turnout override (default: NULL)
`grid_type`	string	Estimation approach: "1D" or "2D" (default: "1D")

The mode_search parameter accepts a list with the following components:

Parameter	Description
`npeaks`	Maximum number of peaks to identify
`sortstr`	Whether to sort peaks by strength
`minpeakdistance`	Minimum distance between peaks
`pick_by`	Peak selection method: "area", "height", "cluster", "quantile", or "elipse"

Output

Output	Type	Description
`list_graphs`	list	Collection of generated plots (ggplot2/plotly objects)
`base_stats`	list	Basic fraud statistics for the whole dataset
`sim_all_stats`	list	Simulation statistics for the whole dataset (if computeSD specified)
`sim_hetero_stats_base`	data.frame	Base statistics for regional analyses (if Level != "National")
`sim_hetero_stats_sims`	data.frame	Simulation statistics for regional analyses (if Level != "National")
`fraud_precinct_data`	data.frame	Precinct-level fraud estimates with uncertainty measures
`data`	data.frame	Original input data with computed variables
`Level`	character	Analysis level used in the function
`creationdate`	POSIXct	Timestamp of when the output was created

Precinct-Level Fraud Data Structure

When precinctLevel=TRUE, the fraud_precinct_data component contains:

Column	Description
`id`	Unique precinct identifier
`base.fraud.votes`	Point estimate of fraudulent votes
`sim.precinct_mean`	Mean fraud estimate from simulations
`sim.precinct_sd`	Standard deviation of fraud estimates
`sim.sig_all`	Statistical significance indicator
`precinct_mean_hetero`	Regional-level fraud estimates (when Level != "National")

Primary Outputs

Official Turnout: Reported voter participation rate
Real Turnout: Estimated legitimate turnout (clean peak)
Official Support: Reported candidate vote share
Real Support: Estimated legitimate support in clean regions
Ballot Stuffing: Votes added through turnout inflation
Ballot Switching: Votes transferred between candidates
Total Fraud: Combined fraudulent votes
Proportional Fraud: Fraud as percentage of total votes

Uncertainty Quantification

When computeSD is specified, the function provides:

Parametric: Assumes binomial distributions for vote generation
Nonparametric: Uses bootstrap resampling for robust estimates

Clean Peak Detection Methods

"height": Selects clean peak with highest vote count
"area": Chooses clean peak with largest area under curve
"cluster": Uses clustering to identify clean peak
"quantile": Employs mixture models on turnout distribution for clean peak detection
"elipse": Uses robust covariance estimation for clean peak detection

Grid Types

1D Grid: Uses 1D grid of turnout distribution to identify clean peak
2D Method: Uses 2D grid of joint distribution of turnout and incumbent's vote share

Example 1: National-Level Analysis with 1D Grid

library(EFToolkit)

# Load Russian 2000 election data
dat <- read.csv("electionfraud2000.csv")

# National analysis using 1D estimation method
res1 <- NonparamElectionForensics(dat, 
                                 Candidates = paste("P", 1:12, sep=""),
                                 CandidatesText = c("Stanislav Govorukhin", "Umar Dzhabrailov",  
                                                    "Vladimir Zhirinovsky", "Gennady Zuganov", 
                                                    "Ella Pamfilova", "Alexei Podberezkin", 
                                                    "Vladimir Putin", "Yuri Skuratov",
                                                    "Konstantin Titov", "Aman Tuleev",
                                                    "Grigorii Yavlinsky", "Against All"),
                                 MainCandidate = "P7",
                                 TotalReg = "NVoters",
                                 TotalVotes = "NValid",
                                 Level = "National",
                                 MaxThreshold = 0.8,
                                 mode_search = list(npeaks = 5, sortstr = TRUE,
                                                    minpeakdistance = 1, pick_by = "height"),
                                 FigureName = "Russian Presidential Elections, 2000",
                                 setcolors = c("royalblue2", "springgreen1","blue", 
                                               "red", "green","brown2",
                                               "darkgreen", "yellow", "lawngreen", 
                                               "purple","chartreuse1", "orange"),
                                 precinctLevel = TRUE, 
                                 computeSD = "nonparametric",
                                 sims = 10, 
                                 grid_type = "1D")

# Summary of precinct-level fraud estimates
total_fraud <- sum(res1$fraud_precinct_data$base.fraud.votes, na.rm=TRUE)
# Result: 2,685,246 fraudulent votes detected

# Statistically significant fraud only
significant_fraud <- sum(res1$fraud_precinct_data$sim.precinct_mean[
  res1$fraud_precinct_data$sim.sig_all==TRUE], na.rm=TRUE)
# Result: 811,501 significant fraudulent votes

> res1$base_stats
$`Whole dataset`
official_turnout     real_turnout official_support     real_support  ballot_stuffing ballot_switching 
    6.820000e+01     6.700000e+01     5.330000e+01     5.200000e+01     1.258868e+06     1.426378e+06 
     total_fraud       prop_fraud 
    2.685246e+06     6.990511e-02 
    
# Display the table of region-level measures
View(round(res1$sim_hetero_stats_base, 3))

Image 1	Image 2	Image 3

Example 2: Regional-Level Analysis with 1D Grid

# Regional analysis across all federal subjects
res2 <- NonparamElectionForensics(dat, 
                                 Candidates = paste("P", 1:12, sep=""),
                                 CandidatesText = c("Stanislav Govorukhin", "Umar Dzhabrailov",  
                                                    "Vladimir Zhirinovsky", "Gennady Zuganov", 
                                                    "Ella Pamfilova", "Alexei Podberezkin", 
                                                    "Vladimir Putin", "Yuri Skuratov",
                                                    "Konstantin Titov", "Aman Tuleev",
                                                    "Grigorii Yavlinsky", "Against All"),
                                 MainCandidate = "P7",
                                 TotalReg = "NVoters",
                                 TotalVotes = "NValid",
                                 Level = "regname",  # Regional analysis
                                 MaxThreshold = 0.8,
                                 mode_search = list(npeaks = 5, sortstr = TRUE,
                                                    minpeakdistance = 1, pick_by = "height"),
                                 FigureName = "Russian Presidential Elections, 2000",
                                 setcolors = c("royalblue2", "springgreen1","blue", 
                                               "red", "green","brown2",
                                               "darkgreen", "yellow", "lawngreen", 
                                               "purple","chartreuse1", "orange"),
                                 precinctLevel = TRUE, 
                                 computeSD = "nonparametric",
                                 sims = 10, 
                                 grid_type = "1D")

# Regional fraud estimates
regional_fraud <- sum(res2$fraud_precinct_data$precinct_mean_hetero, na.rm=TRUE)
# Result: 1,693,742 fraudulent votes across regions

# Statistically significant regional fraud
significant_regional_fraud <- sum(res2$fraud_precinct_data$precinct_mean_hetero[
  res2$fraud_precinct_data$sim.sig_all==TRUE], na.rm=TRUE)
# Result: 1,125,151 significant fraudulent votes

Image 1	Image 2	Image 3	Image 4

Example 3: National Analysis with 2D Grid

# 2D analysis using parametric uncertainty estimation
res3 <- NonparamElectionForensics(dat, 
                                 Candidates = paste("P", 1:12, sep=""),
                                 CandidatesText = c("Stanislav Govorukhin", "Umar Dzhabrailov",  
                                                    "Vladimir Zhirinovsky", "Gennady Zuganov", 
                                                    "Ella Pamfilova", "Alexei Podberezkin", 
                                                    "Vladimir Putin", "Yuri Skuratov",
                                                    "Konstantin Titov", "Aman Tuleev",
                                                    "Grigorii Yavlinsky", "Against All"),
                                 MainCandidate = "P7",
                                 TotalReg = "NVoters",
                                 TotalVotes = "NValid",
                                 Level = "National",
                                 MaxThreshold = 0.8,
                                 mode_search = list(npeaks = 5, sortstr = TRUE,
                                                    minpeakdistance = 1, pick_by = "height"),
                                 FigureName = "Russian Presidential Elections, 2000",
                                 setcolors = c("royalblue2", "springgreen1","blue", 
                                               "red", "green","brown2",
                                               "darkgreen", "yellow", "lawngreen", 
                                               "purple","chartreuse1", "orange"),
                                 precinctLevel = TRUE, 
                                 computeSD = "parametric",
                                 sims = 10, 
                                 grid_type = "2D")

# 2D method fraud estimates
fraud_2d <- sum(res3$fraud_precinct_data$sim.precinct_mean, na.rm=TRUE)
# Result: -15,724,742 (negative values suggest model limitations)

# Significant fraud in 2D analysis
significant_2d_fraud <- sum(res3$fraud_precinct_data$sim.precinct_mean[
  res3$fraud_precinct_data$sim.sig_all==TRUE], na.rm=TRUE)
# Result: 0 (no significant fraud detected with 2D method)

# Display the table of region-level measures
View(round(res3$sim_hetero_stats_base, 3))

Image 1	Image 2	Image 3

Example 4: Analysis of Selected Regions with 2D Grid

# Focus on specific regions of interest
selected_regions <- c("Respublika Dagestan", "Gorod Moskva", 
                      "Samarskaya Oblast`", "Volgogradskaya Oblast`")  
dat_subset <- dat[dat$regname %in% selected_regions,]

res4 <- NonparamElectionForensics(dat_subset, 
                                 Candidates = paste("P", 1:12, sep=""),
                                 CandidatesText = c("Stanislav Govorukhin", "Umar Dzhabrailov",  
                                                    "Vladimir Zhirinovsky", "Gennady Zuganov", 
                                                    "Ella Pamfilova", "Alexei Podberezkin", 
                                                    "Vladimir Putin", "Yuri Skuratov",
                                                    "Konstantin Titov", "Aman Tuleev",
                                                    "Grigorii Yavlinsky", "Against All"),
                                 MainCandidate = "P7",
                                 TotalReg = "NVoters",
                                 TotalVotes = "NValid",
                                 Level = "regname",
                                 MaxThreshold = 0.8,
                                 mode_search = list(npeaks = 5, sortstr = TRUE,
                                                    minpeakdistance = 1, pick_by = "height"),
                                 FigureName = "Russian Presidential Elections, 2000",
                                 setcolors = c("royalblue2", "springgreen1","blue", 
                                               "red", "green","brown2",
                                               "darkgreen", "yellow", "lawngreen", 
                                               "purple","chartreuse1", "orange"),
                                 precinctLevel = TRUE, 
                                 computeSD = "nonparametric",
                                 sims = 10, 
                                 grid_type = "2D")

# Access regional comparison results
print(res4$stats_summary)

Image 1	Image 2	Image 3

Image 4	Image 5	Image 6

Advanced Features

Multi-Level Analysis

When Level parameter specifies administrative units, the function:

Performs analysis for the entire dataset
Conducts separate analyses for each administrative unit
Aggregates results across regions
Provides comparative statistics

Robust Peak Detection

The algorithm implements multiple fallback strategies:

Primary method specified in pick_by
Alternative clustering approaches if primary fails
Simple peak detection as ultimate fallback
Manual override through man_turnout parameter

Precinct-Level Estimation

When precinctLevel=TRUE, the function:

Estimates fraud at individual precinct level
Uses post-stratification for statistical adjustment
Provides significance testing for precinct estimates
Enables spatial analysis integration

Best Practices

Method Selection

Start with 1D analysis for initial exploration
Use regional-level analysis for heterogeneous countries
Apply nonparametric uncertainty for robust estimates
Test multiple pick_by methods for sensitivity analysis

Parameter Tuning

Increase sims for more precise uncertainty estimates
Adjust MaxThreshold based on country-specific context
Experiment with mode_search parameters for optimal peak detection
Use custom setcolors for publication-quality visualizations

Result Validation

Compare across estimation methods (1D vs 2D)
Examine statistical significance alongside magnitude
Cross-validate with other forensic indicators
Consider substantive electoral context

Finite Mixture Model()

ComputeFiniteMixtureModel - A legacy implementation of Walter Mebane's Finite Mixture Model for electoral data analysis.

The model uses Bayesian estimation techniques with EM-algorithm-like iterations to estimate the posterior probabilities of each precinct belonging to each fraud category.

⚠️ Important Note: This function is legacy code that is no longer actively maintained or supported. It may have dependencies on outdated packages or contain unoptimized algorithms.

ComputeFiniteMixtureModel(dat, MainCandidate = "Votes", TotalReg = "NVoters", 
                         TotalVotes = "NValid", cores = 2, itstartmax = 1)

Input

Parameter	Type	Description
`dat`	data.frame	Electoral dataset containing voting data
`MainCandidate`	character	Variable name for the major/incumbent candidate votes (default: "Votes")
`TotalReg`	character	Variable name for total number of eligible voters (default: "NVoters")
`TotalVotes`	character	Variable name for total number of ballots cast (default: "NValid")
`cores`	integer	Number of cores for parallel computing (default:2)
`itstartmax`	integer	Maximum number of iterations for optimization (default: 1)

Output

Returns a list containing FMM estimates with the following structure:

list(
  FF_null = matrix,    # Null model results (estimates and standard deviations)
  FFlist_null = list,  # Full null model output including posterior probabilities
  FF = matrix,         # Main model results (estimates and standard deviations)
  FFlist = list        # Full main model output including posterior probabilities
)

The output matrices contain the following parameters:

Parameter	Description
`incremental`	Proportion of incremental fraud
`extreme`	Proportion of extreme fraud
`alpha`	Fraud intensity parameter
`turnout`	Turnout rate parameter
`winprop`	Winning proportion parameter
`sigma`	Standard deviation for vote proportions
`stdAtt`	Standard deviation for attendance
`theta`	Convergence test parameter
`loglik`	Log-likelihood value
`df`	Degrees of freedom

Usage Example

library(EFToolkit)

# Load sample data
dat <- read.csv(system.file("extdata/ruspres2020.csv", package = "EFToolkit"))
dat <- subset(dat, select = c("region", "NVoters", "NValid", "Votes"))
datc <- dat[dat$region == "Volgogradskaya Oblast`", ]

# Run FMM analysis (commented out due to long computation time)
# res <- ComputeFiniteMixtureModel(datc,
#                                 MainCandidate = "Votes",
#                                 TotalReg = "NVoters", 
#                                 TotalVotes = "NValid")

Key Features

Mixture Modeling: Implements a finite mixture model with multiple fraud components
Parallel Computing: Supports multi-core processing for faster computation
Robust Estimation: Uses genetic algorithms (rgenoud) for parameter optimization
Statistical Inference: Provides estimates with standard errors

Limitations & Considerations

Computational Intensity: The function can be very slow for large datasets
Legacy Status: No longer actively supported or maintained
Algorithm Complexity: Implements sophisticated statistical models that may require domain expertise to interpret
Parameter Sensitivity: Results may be sensitive to starting values and iteration limits

Klimek Model()

ComputeKlimekModel - Implements the Klimek et al. (2012) simulation-based method for detecting electoral anomalies through histogram analysis of vote distributions.

⚠️ Legacy Function Notice: This function is legacy code that is no longer actively maintained or supported. It remains available for historical reference and research reproducibility but may have dependencies on outdated packages or contain unoptimized algorithms.

Key Features:

Histogram-based analysis: Compares observed vote distributions with simulated ones
Fraud simulation: Models incremental and extreme fraud scenarios
Parameter estimation: Estimates fraud parameters through iterative simulation
Statistical testing: Uses chi-square goodness-of-fit tests to evaluate model fit

ComputeKlimekModel(data, Candidates, Level = "National", TotalReg, TotalVotes, 
                   R = 1000, cores = 2)

Input

Parameter	Description
`data`	Data frame containing electoral data
`Candidates`	Variable name(s) for vote counts of candidates/parties
`Level`	Variable indicating geographic level of analysis (default: "National")
`TotalReg`	Variable name for total number of eligible voters
`TotalVotes`	Variable name for total number of ballots cast
`R`	Number of simulations to run (default: 1000)
`cores`	Number of CPU cores for parallel computation (default: 2)

Output

Column	Description
`Level`	Geographic level of analysis
`Candidate`	Candidate/party name
`KSimI`	Estimated proportion of incremental fraud
`KSimE`	Estimated proportion of extreme fraud
`KSimalpha`	Fraud intensity parameter
`KSimturnout`	Estimated turnout rate parameter
`KSimwinprop`	Estimated winning proportion parameter
`KSimsigma`	Standard deviation for vote proportions
`KSimstdAtt`	Standard deviation for attendance rates
`KSimtheta`	Convergence test parameter
`Obs`	Number of observations used in analysis

Usage Example

library(EFToolkit)

# Load sample data
dat <- read.csv(system.file("Albania2013.csv", package = "EFToolkit"))

# Run Klimek analysis with reduced simulations for speed
klimek <- ComputeKlimekModel(dat, 
                            Candidates = "C050", 
                            Level = "National",
                            TotalReg = "Registered", 
                            TotalVotes = "Ballots", 
                            cores = 1, 
                            R = 100)

# Access results
print(klimek$table)      # Data frame with results
print(klimek$html)       # HTML formatted table
print(klimek$tex)        # LaTeX formatted table

The function computes several goodness-of-fit measures:

Winner.HFit.Klimek: Histogram fit statistic for winning candidate
Winner.HFit.chi2: Chi-square histogram fit
Winner.Fit.chi2: Chi-square vote count fit
Overall chi2: Comprehensive model fit statistic

Key Functions:

Estimate(): Initial parameter estimation from vote distributions
Sim_Vote(): Simulates electoral outcomes under fraud scenarios
Sim.Histo(): Generates histogram distributions from simulated data
Iteration_sim(): Main optimization loop for parameter estimation

Simulation Parameters:

f1range: Incremental fraud proportion range (0.0 to 1.0)
f2range: Extreme fraud proportion range (0.0 to 0.3)
arange: Fraud intensity range (0.5 to 1.0)
iterations: Number of optimization iterations (default: 10)

Interpretation Guidelines

Low fraud estimates (KSimI, KSimE near 0): Suggest clean election
High incremental fraud: Indicates widespread small-scale manipulation
High extreme fraud: Suggests concentrated large-scale fraud
Model fit statistics: Lower values indicate better model fit to observed data

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NAMESPACE		NAMESPACE
README.aux		README.aux
README.bbl		README.bbl
README.blg		README.blg
README.html		README.html
README.log		README.log
README.md		README.md
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BasicElectionForensics()

Input

Output

Statistical Distribution Tests

Key Features

Usage Example

Interpretation Guidelines

BuildMap()

Input

Output

Key Features

Spatial Data Integration

Flexible Visualization Options

Multi-Method Mapping

Usage Example

Technical Implementation Details

Spatial Data Handling

Color Intensity Interpretation

Spatial Pattern Analysis

ClusterAnalysis()

Input

Output

Spatial Clustering Methods

Local Moran's I

Getis-Ord Gi* Statistic

Key Features

Advanced Spatial Statistics

Flexible Input Handling

Comprehensive Visualization

Color Coding System

Local Moran's I Colors

Getis-Ord Gi* Colors

Local Moran's I Results

Getis-Ord Results

NonparamElectionForensics()

Input

Output

Precinct-Level Fraud Data Structure

Primary Outputs

Uncertainty Quantification

Clean Peak Detection Methods

Grid Types

Example 1: National-Level Analysis with 1D Grid

Example 2: Regional-Level Analysis with 1D Grid

Example 3: National Analysis with 2D Grid

Example 4: Analysis of Selected Regions with 2D Grid

Advanced Features

Multi-Level Analysis

Robust Peak Detection

Precinct-Level Estimation

Best Practices

Method Selection

Parameter Tuning

Result Validation

Finite Mixture Model()

Input

Output

Usage Example

Key Features

Limitations & Considerations

Klimek Model()

Key Features:

Input

Output

Usage Example

Key Functions:

Simulation Parameters:

Interpretation Guidelines

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