The MAIHDA package provides a comprehensive toolkit for conducting Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy (MAIHDA). This approach is particularly valuable for examining intersectional inequalities in health and social outcomes by considering the joint effects of multiple social categories (e.g., gender, race, socioeconomic status).
run_maihda_app()) for
no-code exploratory data analysis and model fitting
You can install the development version from GitHub:
# install.packages("devtools")
devtools::install_github("hdbt/MAIHDA")or the current stable version from CRAN:
install.packages("MAIHDA")library(MAIHDA)
data("maihda_health_data")
# 1. Fit a MAIHDA model
model <- fit_maihda(
BMI ~ Age + Poverty + (1 | Gender:Race:Education),
data = maihda_health_data
)
# 2. Summarize the model (Variance Partition Coefficient, stratum estimates)
summary(model)
# 3. Visualize results (Predicted outputs, VPC, Risk vs. Effect, etc.)
plot(model)make_strata()Creates intersectional strata from multiple categorical variables with optional minimum count filtering.
fit_maihda()Fits multilevel models using either lme4 (default) or brms engine. Supports various families including gaussian, binomial, and poisson.
summary()Provides comprehensive model summaries including:
predict_maihda()Makes predictions at two levels:
plot()Creates various visualizations:
maihda_ternary_plot()Generates an advanced ternary plot showing the relative contribution of intercept, additive effects, and unique intersectional interaction effects to the overall outcome for each stratum.
plot_prediction_deviation_panels()Creates an advanced, publication-ready two-panel dashboard for visualizing predicted values and identifying extreme/deviant cases in individual predictions.
compare_maihda()Compares VPC/ICC across multiple models with optional bootstrap confidence intervals.
calculate_pvc()Calculates the proportional change in between-stratum variance (PVC) between two models. This measures how much of the between-stratum variance from a baseline model is explained (or changed) by adding additional predictors in a second model:- Formula: PVC = (Var_model1 - Var_model2) / Var_model1 - Works with both lme4 and brms engines - Supports bootstrap confidence intervals for lme4 models
stepwise_pcv()Evaluates multiple sequential models by iteratively adding covariates step-by-step to quantify precisely which variables explain the structural inequalities.
run_maihda_app()Launches a locally-hosted, interactive Shiny Dashboard that exposes the core functionalities for data modeling, visualization, and summarization visually.
# Fit model adjusting for age, automatically creating strata from gender, race, and education
model <- fit_maihda(
BMI ~ Age + (1 | Gender:Race:Education),
data = maihda_health_data
)
# Get variance partition coefficient
summary <- summary(model, bootstrap = TRUE, n_boot = 1000)
# VPC of 0.15 means 15% of variance is between strata
# This indicates substantial intersectional inequality
# Visualize which strata have higher/lower outcomes using new advanced plots
plot(model, type = "predicted")
plot(model, type = "risk_vs_effect")
# Map out where the specific intersectional variance is emerging
plot(model, type = "ternary")
# Or run it with no type to see them all!
# plot(model)# Requires brms package
model_brms <- fit_maihda(
BMI ~ Age + (1 | Gender:Race:Education),
data = maihda_health_data,
engine = "brms",
chains = 4,
iter = 2000
)
summary_brms <- summary(model_brms)# Fit competing models
model1 <- fit_maihda(outcome ~ age + (1 | gender:race), data = data1)
model2 <- fit_maihda(outcome ~ age + gender + (1 | gender:race), data = data2)
# Compare with bootstrap CI
comparison <- compare_maihda(
model1, model2,
model_names = c("Base", "With Gender"),
bootstrap = TRUE,
n_boot = 1000
)
# Visualize comparison
plot_comparison(comparison)# Fit baseline model
model1 <- fit_maihda(outcome ~ age + (1 | gender:race), data = data)
# Fit model with additional predictor
model2 <- fit_maihda(outcome ~ age + gender + (1 | gender:race), data = data)
# Calculate PVC without bootstrap
pvc_result <- calculate_pvc(model1, model2)
print(pvc_result)
# Calculate PVC with bootstrap confidence intervals
pvc_boot <- calculate_pvc(model1, model2, bootstrap = TRUE, n_boot = 1000)
print(pvc_boot)
# Interpretation: A PVC of 0.25 means that model2 explains 25% of the
# between-stratum variance that was present in model1# Incrementally track the explained variables interactively
stepwise_results <- stepwise_pcv(
data = data,
outcome = "health_outcome",
vars = c("gender", "race", "age")
)
print(stepwise_results)You can access a live, cloud-hosted version of the MAIHDA interactive dashboard directly in your browser without installing R: https://hdbt.shinyapps.io/shiny/
Alternatively, you can run all analyses described above in the browser locally by typing:
library(MAIHDA)
run_maihda_app()For detailed documentation and examples, see the package vignette:
vignette("introduction", package = "MAIHDA")Required:
Optional:
Evans, C. R., Williams, D. R., Onnela, J. P., & Subramanian, S. V. (2018). A multilevel approach to modeling health inequalities at the intersection of multiple social identities. Social Science & Medicine, 203, 64-73.
Merlo, J. (2018). Multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) within an intersectional framework. Social Science & Medicine, 203, 74-80.
Contributions are welcome! Please feel free to submit a Pull Request.
This project is licensed under the MIT License - see the LICENSE file for details.
If you use this package in your research, please cite:
Bulut (2025). *MAIHDA: Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy.* R package version 0.1.8, https://github.com/hdbt/MAIHDA. doi: 10.32614/CRAN.package.MAIHDAA BibTeX entry for LaTeX users is:
@Manual{Bulut2025MAIHDA,
title = {MAIHDA: Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy},
author = {Hamid Bulut},
year = {2025},
note = {R package version 0.1.8},
url = {https://github.com/hdbt/MAIHDA},
doi = {10.32614/CRAN.package.MAIHDA}
}