Overview
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).
Key Features
- Create Intersectional Strata: Automatically generate strata from multiple categorical variables
- Interactive Dashboard
: A fully-featured Shiny application (run_maihda_app()) for no-code exploratory data analysis and model fitting - Model Fitting: Support for both lme4 and brms (Bayesian) engines - Summaries & Decompositions: Variance partition coefficients (VPC/ICC), stratum-specific estimates, and stepwise Proportional Change in Variance (PCV) - Multiple Prediction Types: Individual-level and stratum-level predictions - Visualizations: Predicted stratum values, VPC visualizations, risk/effect diagnostics, and observed vs. shrunken estimates - Model Comparison: Compare models with robust bootstrap confidence intervals for VPC/ICC - Proportional Change in Variance (PVC): Quantify how much between-stratum variance is explained by additional predictors
Installation
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")Quick Start
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)Main Functions
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:
- Variance Partition Coefficient (VPC/ICC)
- Variance components decomposition
- Stratum-specific random effects
- Optional bootstrap confidence intervals
predict_maihda()
Makes predictions at two levels:
- Individual: Full predictions including random effects
- Strata: Stratum-specific random effects with uncertainty
plot()
Creates various visualizations:
- Predicted: Predicted stratum values with confidence intervals
- VPC plots: Visualizes variance partitioning
- Observed vs. Shrunken: Shows shrinkage of stratum estimates
- Risk vs Effect: Visualizes baseline strata risk against intersectional effect size
- Effect Decomp: Additive versus specific interaction decompositions
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
Example: Intersectional Health Inequalities
# 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)Using brms for Bayesian Inference
# 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)Model Comparison with Bootstrap
# 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)Calculating Proportional Change in Variance (PVC)
# 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 model1Stepwise Proportional Change in Variance (PCV)
# Incrementally track the explained variables interactively
stepwise_results <- stepwise_pcv(
data = data,
outcome = "health_outcome",
vars = c("gender", "race", "age")
)
print(stepwise_results)Interactive Shiny App
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:
Documentation
For detailed documentation and examples, see the package vignette:
vignette("introduction", package = "MAIHDA")Dependencies
Required:
- R (>= 4.1.0)
- lme4 (>= 1.1-27)
- ggplot2 (>= 3.4.0)
- dplyr (>= 1.0.0)
- tidyr (>= 1.1.0)
- stats, methods, tibble, rlang
Optional:
- brms (>= 2.15.0) - for Bayesian models
- boot (>= 1.3-20) - for bootstrap confidence intervals
References
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.
License
This project is licensed under the MIT License - see the LICENSE file for details.