Introduction to MAIHDA

Introduction

The MAIHDA package provides tools for conducting Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy (MAIHDA). This approach is particularly useful for examining intersectional inequalities in health and other outcomes by considering the joint effects of multiple social categories.

Installation

You can install the development version of MAIHDA from GitHub:

# install.packages("devtools")
devtools::install_github("hdbt/MAIHDA")

Basic Workflow

The typical MAIHDA workflow consists of the following steps:

Create intersectional strata from multiple categorical variables
Fit a multilevel model with stratum as a random effect
Summarize the model with variance partitioning
Make predictions at individual or stratum level
Visualize the results

Example Analysis

Step 1: Create Strata

First, we create intersectional strata from multiple social categories:

library(MAIHDA)

# Example dataset
data <- data.frame(
  gender = sample(c("Male", "Female"), 1000, replace = TRUE),
  race = sample(c("White", "Black", "Hispanic"), 1000, replace = TRUE),
  age = rnorm(1000, 50, 10),
  health_outcome = rnorm(1000, 100, 15)
)

# Create strata
strata_result <- make_strata(data, vars = c("gender", "race"))

# View stratum information
print(strata_result)

Step 2: Fit MAIHDA Model

Next, we fit a multilevel model using the created strata:

# Fit model with lme4 (default)
model <- fit_maihda(
  health_outcome ~ age + (1 | stratum),
  data = strata_result$data,
  engine = "lme4"
)

# View model
print(model)

Step 3: Summarize Results

The summary provides variance partition coefficients and stratum-specific estimates:

# Basic summary
summary_result <- summary_maihda(model)
print(summary_result)

# Summary with bootstrap confidence intervals
summary_boot <- summary_maihda(model, bootstrap = TRUE, n_boot = 500)
print(summary_boot)

Step 4: Make Predictions

You can make predictions at both individual and stratum levels:

# Individual-level predictions
pred_ind <- predict_maihda(model, type = "individual")

# Stratum-level predictions
pred_strata <- predict_maihda(model, type = "strata")
head(pred_strata)

Step 5: Visualize Results

The package provides several visualization options:

# Caterpillar plot of stratum random effects
plot_maihda(model, type = "caterpillar")

# Variance partition visualization
plot_maihda(model, type = "vpc")

# Observed vs. shrunken estimates
plot_maihda(model, type = "obs_vs_shrunken")

Comparing Models

You can compare multiple models with bootstrap confidence intervals:

# Fit multiple models
model1 <- fit_maihda(health_outcome ~ age + (1 | stratum), 
                    data = strata_result$data)
model2 <- fit_maihda(health_outcome ~ age + gender + (1 | stratum),
                    data = strata_result$data)

# Compare models
comparison <- compare_maihda(
  model1, model2,
  model_names = c("Base Model", "With Gender"),
  bootstrap = TRUE,
  n_boot = 500
)

print(comparison)

# Plot comparison
plot_comparison(comparison)

Using brms Engine

For Bayesian inference, you can use the brms engine (requires brms package):

# Fit model with brms
model_brms <- fit_maihda(
  health_outcome ~ age + (1 | stratum),
  data = strata_result$data,
  engine = "brms",
  chains = 2,
  iter = 2000
)

# Summary works the same way
summary_brms <- summary_maihda(model_brms)

Interpreting Results

Variance Partition Coefficient (VPC/ICC)

The VPC indicates the proportion of variance in the outcome that is attributable to differences between strata (intersectional categories). A higher VPC suggests greater heterogeneity between strata.

VPC close to 0: Most variation is within strata
VPC close to 1: Most variation is between strata
Typical values: 0.05 - 0.20 for health outcomes

Stratum-Specific Random Effects

The random effects represent deviations from the overall mean for each stratum, after adjusting for fixed effects. Positive values indicate higher outcomes in that stratum; negative values indicate lower outcomes.

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.

MAIHDA Package Authors

2026-03-30