Author: Hamid Bulut
Date: 2026-04-05

# Introduction to MAIHDA

#### Hamid Bulut

#### 2026-04-05

## Introduction

The MAIHDA package provides specialized tools for conducting Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy. This modern epidemiological approach is highly effective for investigating intersectional health inequalities and understanding how joint social categories (e.g., Race x Gender x Education) influence individual outcomes.

By utilizing multilevel mixed-effects models (via `lme4` or `brms`), MAIHDA allows researchers to: 1. Automatically construct intersectional strata. 2. Estimate between-stratum variance and Variance Partition Coefficients (VPC). 3. Evaluate the Proportional Change in Variance (PCV) to understand how much inequalities are driven by additive main effects versus unique intersectional effects. 4. Launch an interactive Shiny Dashboard for code-free analysis.

## Installation

You can install the development version of MAIHDA from GitHub:

    install.packages("MAIHDA")
    # Or for the latest development version:
    # install.packages("remotes")
    # remotes::install_github("hamidbulut/MAIHDA")

## Real-World Example Analysis

The package includes a pedagogical subset of the National Health and Nutrition Examination Survey (`maihda_health_data`). We will use this to examine how Body Mass Index (BMI) varies across intersectional demographic groups.

### Step 1: Create Intersectional Strata

First, use `make_strata()` to combine multiple social categories into a single Random Effect grouping variable:

    library(MAIHDA)

    # Load the built-in NHANES dataset
    data("maihda_health_data")

    # Create strata from Gender, Race, and Education
    strata_result <- make_strata(maihda_health_data, vars = c("Gender", "Race", "Education"))

    # View the strata structural information
    print(strata_result)

### Step 2: Fit a Null MAIHDA Model

Fit a multilevel model using the generated strata. A “Null” model contains only the intercept and the strata random effect.

    # Fit the initial Null model
    model_null <- fit_maihda(
      BMI ~ 1 + (1 | stratum),
      data = strata_result$data,
      engine = "lme4"
    )

    # Summarize the variance components (VPC)
    summary_null <- summary_maihda(model_null)
    print(summary_null)

Interpretation: The resulting Variance Partition Coefficient (VPC or ICC) tells us what percentage of the total variance in BMI in the population lies between the intersectional social groups, rather than just within them.

### Step 3: Evaluate Proportional Change in Variance (PCV)

To understand if these intersectional inequalities are simply the sum of their parts (additive), we evaluate how much variance is explained by adding main-effects to the model.

If the variance drops significantly (High PCV), the inequalities are largely explained by the additive characteristics. If the variance remains or even increases (Negative PCV), it signifies strong, unique intersectional interactions that cannot be explained away by simple main effects.

    # Fit an adjusted model
    model_adj <- fit_maihda(
      BMI ~ Age + Gender + Race + Education + Poverty + (1 | stratum),
      data = strata_result$data
    )

    # Calculate PCV with Parametric Bootstrap Confidence Intervals
    pcv_result <- calculate_pvc(model_null, model_adj, bootstrap = TRUE, n_boot = 500)
    print(pcv_result)

### Step 4: Stepwise PCV Decomposition

Often, researchers want to know exactly which variable explained the variance. Use the `stepwise_pcv()` function to add covariates one-by-one and track the variance dynamically.

    # Run a stepwise variance decomposition
    stepwise_results <- stepwise_pcv(
      data = strata_result$data,
      outcome = "BMI",
      vars = c("Age", "Gender", "Race", "Education", "Poverty")
    )

    print(stepwise_results)

Negative step PCVs in this table highlight “unmasking” or suppression effects: adding a variable caused the intersectional groups to push further apart mathematically, revealing hidden structural inequalities.

### Step 5: Visualizations

The package provides multiple pre-configured visualization options for checking your model estimates (using `plot_maihda()`):

    # Caterpillar plot of stratum random effects (with 95% CIs)
    plot_maihda(model_adj, type = "caterpillar")

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

## Interactive Shiny App

The MAIHDA package ships with a fully-featured, interactive Shiny Dashboard.

You can upload your own data (CSV, SPSS `.sav`, Stata `.dta`), dynamically select variables, and compute Stepwise PCV tables and prediction plots.

    # Launch the interactive interface
    run_maihda_app()

## 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.