Author: Hamid Bulut
Date: 2026-05-16

# Introduction to MAIHDA

#### Hamid Bulut

#### 2026-05-16

## 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("hdbt/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 & 2: Create Intersectional Strata and Fit a Null MAIHDA Model

Use `fit_maihda()` to combine multiple social categories directly in the random effect formula. Providing the variables in the random effect combined with `:` allows the function to automatically build the intersectional strata on the fly and fit the multilevel model.

    library(MAIHDA)

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

    # PVC compares variance across models, so both models must use the same
    # analytic sample. Keep complete cases for all variables used below.
    health_complete <- maihda_health_data[complete.cases(
      maihda_health_data[, c("BMI", "Age", "Gender", "Race", "Education", "Poverty")]
    ), ]

    # Fit the initial Null model with auto-generated strata
    model_null <- fit_maihda(
      BMI ~ 1 + (1 | Gender:Race:Education),
      data = health_complete,
      engine = "lme4"
    )

    # Summarize the variance components (VPC)
    summary_null <- summary(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 | Gender:Race:Education),
      data = health_complete
    )

    # 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 using the prepared data with strata
    stepwise_results <- stepwise_pcv(
      data = model_null$original_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, advanced visualization options for checking your model estimates natively mirroring the Shiny application logic:

    # Predicted stratum values with 95% CIs
    plot(model_adj, type = "predicted")

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

    # Bivariate risk against stratum-level intersectional effect
    plot(model_adj, type = "risk_vs_effect")

    # Additive versus Intersectional Effect decomposition
    plot(model_adj, type = "effect_decomp")

    # Ternary Plot of Variances
    plot(model_adj, type = "ternary")

    # Individual Prediction Deviance Dashboard
    plot(model_adj, type = "prediction_deviation")

## 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.