A tutorial for conducting intersectional multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA).

Intersectional multilevel analysis of individual heterogeneity and discriminatory accuracy (I-MAIHDA) is an innovative approach for investigating inequalities, including intersectional inequalities in health, disease, psychosocial, socioeconomic, and other outcomes. I-MAIHDA and related MAIHDA approaches have conceptual and methodological advantages over conventional single-level regression analysis. By enabling the study of inequalities produced by numerous interlocking systems of marginalization and oppression, and by addressing many of the limitations of studying interactions in conventional analyses, intersectional MAIHDA provides a valuable analytical tool in social epidemiology, health psychology, precision medicine and public health, environmental justice, and beyond. The approach allows for estimation of average differences between intersectional strata (stratum inequalities), in-depth exploration of interaction effects, as well as decomposition of the total individual variation (heterogeneity) in individual outcomes within and between strata. Specific advice for conducting and interpreting MAIHDA models has been scattered across a burgeoning literature. We consolidate this knowledge into an accessible conceptual and applied tutorial for studying both continuous and binary individual outcomes. We emphasize I-MAIHDA in our illustration, however this tutorial is also informative for understanding related approaches, such as multicategorical MAIHDA, which has been proposed for use in clinical research and beyond. The tutorial will support readers who wish to perform their own analyses and those interested in expanding their understanding of the approach. To demonstrate the methodology, we provide step-by-step analytical advice and present an illustrative health application using simulated data. We provide the data and syntax to replicate all our analyses.

Clarifications on the intersectional MAIHDA approach: A conceptual guide and response to Wilkes and Karimi (2024).

Intersectional Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy (MAIHDA) has been welcomed as a new gold standard for quantitative evaluation of intersectional inequalities, and it is being rapidly adopted across the health and social sciences. In their commentary "What does the MAIHDA method explain?", Wilkes and Karimi (2024) raise methodological concerns with this approach, leading them to advocate for the continued use of conventional single-level linear regression models with fixed-effects interaction parameters for quantitative intersectional analysis. In this response, we systematically address these concerns, and ultimately find them to be unfounded, arising from a series of subtle but important misunderstandings of the MAIHDA approach and literature. Since readers new to MAIHDA may share confusion on these points, we take this opportunity to provide clarifications. Our response is organized around four important clarifications: (1) At what level are the additive main effect variables defined in intersectional MAIHDA models? (2) Do MAIHDA models have problems with collinearity? (3) Why does the Variance Partitioning Coefficient (VPC) tend to be small, and the Proportional Change in Variance (PCV) tend to be large in MAIHDA? and (4) What are the goals of MAIHDA analysis?

Overcoming combination fatigue: Addressing high-dimensional effect measure modification and interaction in clinical, biomedical, and epidemiologic research using multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA).

Growing interest in precision medicine, gene-environment interactions, health equity, expanding diversity in research, and the generalizability results, requires researchers to evaluate how the effects of treatments or exposures differ across numerous subgroups. Evaluating combination complexity, in the form of effect measure modification and interaction, is therefore a common study aim in the biomedical, clinical, and epidemiologic sciences. There is also substantial interest in expanding the combinations of factors analyzed to include complex treatment protocols (e.g., multiple study arms or factorial randomization), comorbid medical conditions or risk factors, and sociodemographic and other subgroup identifiers. However, expanding the number of subgroup category combinations creates combination fatigue problems, including concerns over small sample size, reduced power, multiple testing, spurious results, and design and analytic complexity. Creative new approaches for managing combination fatigue and evaluating high-dimensional effect measure modification and interaction are needed. Intersectional MAIHDA (multilevel analysis of individual heterogeneity and discriminatory accuracy) has already attracted substantial interest in social epidemiology, and has been hailed as the new gold standard for investigating health inequities across complex intersections of social identity. Leveraging the inherent advantages of multilevel models, a more general multicategorical MAIHDA can be used to study statistical interactions and predict effects across high-dimensional combinations of conditions, with important advantages over alternative approaches. Though it has primarily been used thus far as an analytic approach, MAIHDA should also be used as a framework for study design. In this article, I introduce MAIHDA to the broader health sciences research community, discuss its advantages over conventional approaches, and provide an overview of potential applications in clinical, biomedical, and epidemiologic research.

Intersectional inequities in the birthweight gap between twin and singleton births: A random effects MAIHDA analysis of 2012-2018 New York City birth data.

Birthweight is a widely-used biomarker of infant health, with inequities patterned intersectionally by maternal age, race/ethnicity, nativity/immigration status, and socioeconomic status in the United States. However, studies of birthweight inequities almost exclusively focus on singleton births, neglecting high-risk twin births. We address this gap using a large sample (N = 753,180) of birth records, obtained from the 2012-2018 New York City (NYC) Department of Health and Mental Hygiene, Bureau of Vital Statistics, representing 99% of all births registered in NYC, and a novel random coefficients intersectional MAIHDA (Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy) model. Our results show evidence of intersectional inequities in birthweight outcomes for both twin and singleton births by maternal age, race/ethnicity, education, and nativity status. Twins have considerably lower predicted birthweights than singletons overall (-930 g on average), and this is especially true for babies born to mothers who are younger (11-19 years), older (40+), racial/ethnic minoritized, foreign-born, and have lower education. However, the magnitude of this birthweight 'gap' between twins and singletons varies considerably across social identity strata, ranging between 830.8 g (observed among 40+ year old Black foreign-born mothers with high school degrees) and 1013.7 g (observed among 30-39 year old Hispanic/Latina foreign-born mothers with less than high school degrees). This study underscored the needs of a high-risk population and the need for aggressive social policies to address health inequities and dismantle intersectional systems of marginalization, oppression, and socioeconomic inequality. In addition to our substantive contributions, we add to the growing methods literature on intersectional quantitative analysis by demonstrating how to apply intersectional MAIHDA with random coefficients and random slopes. We conclude with a discussion of the significant potential for this methodological extension in future research on inequities.

The application of intersectional multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) to examine birthweight inequities in New York City.

Exploring the intersection of dimensions of social identity is critical for understanding drivers of health inequities. We used multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) to examine the intersection of age, race/ethnicity, education, and nativity status on infant birthweight among singleton births in New York City from 2012 to 2018 (N = 725,875). We found evidence of intersectional effects of various systems of oppression on birthweight inequities and identified U.S.-born Black women as having infants of lower-than-expected birthweights. The MAIHDA approach should be used to identify intersectional causes of health inequities and individuals affected most to develop policies and interventions redressing inequities.

An Intercategorical Ecology of Lead Exposure: Complex Environmental Health Vulnerabilities in the Flint Water Crisis.

In 2014, city and state officials channeled toxic water into Flint, Michigan and its unevenly distributed and corroding lead service lines (LSLs). The resulting Flint water crisis is a tragic example of environmental racism against a majority Black city and enduring racial and spatial disparities in environmental lead exposures in the United States. Important questions remain about how race intersected with other established environmental health vulnerabilities of gender and single-parent family structure to create unequal toxic exposures within Flint. We address this question with (1) an "intercategorical ecology" framework that extends the "racial ecology" lens into the complex spatial and demographic dimensions of environmental health vulnerabilities and (2) a multivariate analysis using block-level data from the 2010 U.S. decennial census and a key dataset estimating the LSL connections for 56,038 land parcels in Flint. We found that blocks exposed to LSLs had, on average, higher concentrations of single-parent white, Black, and Latinx families. However, logistic regression results indicate that the likelihood of block exposure to LSLs was most consistently and positively associated with the percentage of single-father Black and single-mother Latina families, net of other racialized and gendered single-parent family structures, socioeconomic status, and the spatial concentration of LSL exposure.

Cross-classified multilevel models (CCMM) in health research: A systematic review of published empirical studies and recommendations for best practices.

Recognizing that health outcomes are influenced by and occur within multiple social and physical contexts, researchers have used multilevel modeling techniques for decades to analyze hierarchical or nested data. Cross-Classified Multilevel Models (CCMM) are a statistical technique proposed in the 1990s that extend standard multilevel modeling and enable the simultaneous analysis of non-nested multilevel data. Though use of CCMM in empirical health studies has become increasingly popular, there has not yet been a review summarizing how CCMM are used in the health literature. To address this gap, we performed a scoping review of empirical health studies using CCMM to: (a) evaluate the extent to which this statistical approach has been adopted; (b) assess the rationale and procedures for using CCMM; and (c) provide concrete recommendations for the future use of CCMM. We identified 118 CCMM papers published in English-language literature between 1994 and 2018. Our results reveal a steady growth in empirical health studies using CCMM to address a wide variety of health outcomes in clustered non-hierarchical data. Health researchers use CCMM primarily for five reasons: (1) to statistically account for non-independence in clustered data structures; out of substantive interest in the variance explained by (2) concurrent contexts, (3) contexts over time, and (4) age-period-cohort effects; and (5) to apply CCMM alongside other techniques within a joint model. We conclude by proposing a set of recommendations for use of CCMM with the aim of improved clarity and standardization of reporting in future research using this statistical approach.

Multilevel versus single-level regression for the analysis of multilevel information: The case of quantitative intersectional analysis.

Intersectional MAIHDA involves applying multilevel models in order to estimate intercategorical inequalities. The approach has been validated thus far using both simulations and empirical applications, and has numerous methodological and theoretical advantages over single-level approaches, including parsimony and reliability for analyzing high-dimensional interactions. In this issue of SSM, Lizotte, Mahendran, Churchill and Bauer (hereafter "LMCB") assert that there has been insufficient clarity on the interpretation of fixed effects regression coefficients in intersectional MAIHDA, and that stratum-level residuals in intersectional MAIHDA are not interpretable as interaction effects. We disagree with their second assertion; however, the authors are right to call for greater clarity. For this purpose, in this response we have three main objectives. (1) In their commentary, LMCB incorrectly describe model predictions based on MAIHDA fixed effects as estimates of "grand means" (or the mean of means), when they are actually "precision-weighted grand means." We clarify the differences between average predicted values obtained by different models, and argue that predictions obtained by MAIHDA are more suitable to serve as reference points for residual/interaction effects. This further enables us to clarify the interpretation of residual/interaction effects in MAIHDA and conventional models. Using simple simulations, we demonstrate conditions under which the precision-weighted grand mean resembles a grand mean, and when it resembles a population mean (or the mean of all individual observations) obtained using single-level regression, explaining the results obtained by LMCB and informing future research. (2) We construct a modification to MAIHDA that constrains the fixed effects so that the resulting model predictions provide estimates of population means, which we use to demonstrate the robustness of results reported by Evans et al. (2018). We find that stratum-specific residuals obtained using the two approaches are highly correlated (Pearson corr = 0.98, p < 0.0001) and no substantive conclusions would have been affected if the preference had been for estimating population means. However, we advise researchers to use the original, unconstrained MAIHDA. (3) Finally, we outline the extent to which single-level and MAIHDA approaches address the fundamental goals of quantitative intersectional analyses and conclude that intersectional MAIHDA remains a promising new approach for the examination of inequalities.

Reintegrating contexts into quantitative intersectional analyses of health inequalities.

Quantitative intersectional analyses often overlook the roles of contexts in shaping intersectional experiences and outcomes. This study advances a novel approach for integrating quantitative intersectional methods with models of contextual-level determinants of health inequalities. Building on recent methodological advancements, I propose an adaptation of intersectional MAIHDA (multilevel analysis of individual heterogeneity and discriminatory accuracy) where respondents are nested hierarchically in social strata defined by gender, race/ethnicity and socioeconomic classifications interacted with contextual classifications. To demonstrate this approach I examine past-month adolescent cigarette use intersectionally by school- and neighborhood-poverty status in Wave 1 of the National Longitudinal Study of Adolescent to Adult Health (N = 17,234). I conclude by discussing the adaptability of this approach to a variety of research questions, including intersectional effects that vary by contextual exposures over time, positions in social networks, and exposures to social policies.

Adolescent Sexual Initiation: A Cross-Classified Multilevel Analysis of Peer Group-, School-, and Neighborhood-Level Influences.

PURPOSE: This study examines the simultaneous roles of neighborhood, school, and peer group contexts on variation in age of U.S. adolescent sexual initiation (coitarche). All three contexts have been shown to be important determinants of adolescent sexual and reproductive health outcomes but are typically examined separately, leaving a large gap in our understanding of their relative and joint importance. Furthermore, little is known about whether these contexts matter differently for boys and girls. METHODS: Using sociocentric network data from the National Longitudinal Study of Adolescent to Adult Health, we combine gender-stratified analyses, social network community detection (to identify teens' social cliques), and cross-classified multilevel modeling to simultaneously analyze gender, neighborhood, school, and peer group effects. These results are compared against results from traditional multilevel models (MLMs), which analyze the contexts individually. RESULTS: Evaluated separately in MLM, peer groups accounted for 6.79% of the total variation in coitarche, schools for 3.56%, and neighborhoods for 4.11%. Under simultaneous cross-classified multilevel modeling analysis, a different story emerges: peer groups and schools accounted for 3.66% and 3.19% of the total variation in coitarche, respectively, whereas neighborhood explained only 1.16% of the total variation. Stratified analyses indicate that gender modifies these associations. CONCLUSIONS: Results demonstrate that omitting any one of these contexts may lead to an overestimation of the importance of contexts included in models. When modeled simultaneously with neighborhoods, our findings suggest that peer groups and schools are meaningful contributing contexts to the variance in sexual initiation, and that these contexts matter differently for boys and girls.

Modeling the intersectionality of processes in the social production of health inequalities.

BACKGROUND: The recent pair of studies by Bauer and Scheim make substantial contributions to the literature on intersectionality and health: a validation study of the Intersectional Discrimination Index and a study outlining a promising analytic approach to intersectionality that explicitly considers the roles of social processes in the production of health inequalities. RATIONALE: In this commentary, I situate Bauer and Scheim's contribution within the wider landscape of intersectional scholarship. I also respond to emerging concerns about the value of descriptive intersectional approaches, in particular the critique that such approaches blunt the critical edge and transformative aims of intersectionality. Finally, I outline important future directions for intersectional scholarship modeling social processes, in particular, the need for addressing structural determinants of inequalities intersectionally. CONCLUSIONS: Whether a study is descriptive or analytic, engagement with theory is essential in order to maintain the critical and transformative edge of intersectionality. Theories of population health such as fundamental causes, social production, and ecosocial theory, should be framed and applied in explicitly intersectional terms. As the field moves toward intersectional evaluations of social processes, attention should be given to all ecological levels but especially the structural/institutional level. This attention includes considering interactions between intersectional social strata and contexts and considering the roles of structural-level discrimination in shaping population health outcomes intersectionally.

Intersectionality and depression in adolescence and early adulthood: A MAIHDA analysis of the national longitudinal study of adolescent to adult health, 1995-2008.

Depression in adolescents and young adults remains a pressing public health concern and there is increasing interest in evaluating population-level inequalities in depression intersectionally. A recent advancement in quantitative methods-multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA)-has many practical and theoretical advantages over conventional models of intercategorical intersectionality, including the ability to more easily evaluate numerous points of intersection between axes of marginalization. This study is the first to apply the MAIHDA approach to investigate mental health outcomes intersectionally in any population. We examine intersectionality and depression among adolescents and young adults in the U.S. along dimensions of gender, race/ethnicity, immigration status, and family income using a large, nationally representative sample-the National Longitudinal Study of Adolescent to Adult Health. We find evidence of considerable inequalities between social strata, with women, racial/ethnic minorities, immigrants, and low income strata experiencing elevated depression scores. Importantly, the majority of between-strata variation is explained by additive main effects, with no strata experiencing statistically significant residual "interaction" effects. We compare these findings to previous intersectional research on depression and discuss possible sources of differences between MAIHDA and conventional intersectional models.

Adding interactions to models of intersectional health inequalities: Comparing multilevel and conventional methods.

Examining health inequalities intersectionally is gaining in popularity and recent quantitative innovations, such as the development of intersectional multilevel methods, have enabled researchers to expand the number of dimensions of inequality evaluated while avoiding many of the theoretical and methodological limitations of the conventional fixed effects approach. Yet there remains substantial uncertainty about the effects of integrating numerous additional interactions into models: will doing so reveal statistically significant interactions that were previously hidden or explain away interactions seen when fewer dimensions were considered? Furthermore, how does the multilevel approach compare empirically to the conventional approach across a range of conditions? These questions are essential to informing our understanding of population-level health inequalities. I address these gaps using data from the National Longitudinal Study of Adolescent to Adult Health by evaluating conventional and multilevel intersectional models across a range of interaction conditions (ranging from six points of interaction to more than ninety, interacting gender, race/ethnicity/immigration status, parent education, family income, and sexual identification), different model types (linear and logistic), and seven diverse dependent variables commonly examined by health researchers: body mass index, depression, general self-rated health, binge drinking, cigarette use, marijuana use, and other illegal drug use. Findings suggest that adding categories to intersectional analyses will tend to reveal new points of interaction. Stratum-level results from the multilevel approach are robust to cross-classification by school context. Conventional and multilevel approaches differ substantially when tested empirically. I conclude with a detailed consideration of the origin of these differences and provide recommendations for future scholarship of intersectional health inequalities.

Does an uneven sample size distribution across settings matter in cross-classified multilevel modeling? Results of a simulation study.

BACKGROUND: Recent advances in multilevel modeling allow for modeling non-hierarchical levels (e.g., youth in non-nested schools and neighborhoods) using cross-classified multilevel models (CCMM). Current practice is to cluster samples from one context (e.g., schools) and utilize the observations however they are distributed from the second context (e.g., neighborhoods). However, it is unknown whether an uneven distribution of sample size across these contexts leads to incorrect estimates of random effects in CCMMs. METHODS: Using the school and neighborhood data structure in Add Health, we examined the effect of neighborhood sample size imbalance on the estimation of variance parameters in models predicting BMI. We differentially assigned students from a given school to neighborhoods within that school's catchment area using three scenarios of (im)balance. 1000 random datasets were simulated for each of five combinations of school- and neighborhood-level variance and imbalance scenarios, for a total of 15,000 simulated data sets. For each simulation, we calculated 95% CIs for the variance parameters to determine whether the true simulated variance fell within the interval. RESULTS: Across all simulations, the "true" school and neighborhood variance parameters were estimated 93-96% of the time. Only 5% of models failed to capture neighborhood variance; 6% failed to capture school variance. CONCLUSIONS: These results suggest that there is no systematic bias in the ability of CCMM to capture the true variance parameters regardless of the distribution of students across neighborhoods. Ongoing efforts to use CCMM are warranted and can proceed without concern for the sample imbalance across contexts.

A multilevel approach to modeling health inequalities at the intersection of multiple social identities.

RATIONALE: Examining interactions between numerous interlocking social identities and the systems of oppression and privilege that shape them is central to health inequalities research. Multilevel models are an alternative and novel approach to examining health inequalities at the intersection of multiple social identities. This approach draws attention to the heterogeneity within and between intersectional social strata by partitioning the total variance across two levels. METHOD: Utilizing a familiar empirical example from social epidemiology-body mass index among U.S. adults (N = 32,788)-we compare the application of multilevel models to the conventional fixed effects approach to studying high-dimension interactions. Researchers are often confronted with the need to explore numerous interactions of identities and social processes. We explore the interactions of five dimensions of social identity and position-gender, race/ethnicity, income, education, and age-for a total of 384 unique intersectional social strata. RESULTS: We find that the multilevel approach provides advantages over conventional models, including scalability for higher dimensions, adjustment for sample size of social strata, model parsimony, and ease of interpretation. CONCLUSION: Considerable variation is attributable to the within-strata level, indicating the low discriminatory accuracy of these intersectional identities and the high within-strata heterogeneity of risk that remains unexplained. Multilevel modeling is an innovative and valuable tool for evaluating the intersectionality of health inequalities.

Contextual Effects of Neighborhoods and Schools on Adolescent and Young Adult Marijuana Use in the United States.

Little is known about the unique contribution of schools vs neighborhoods in driving adolescent marijuana use. This study examined the relative contribution of each setting and the influence of school and neighborhood socioeconomic status on use. We performed a series of cross-classified multilevel logistic models predicting past 30-day adolescent (N = 18 329) and young adult (N = 13 908) marijuana use using data from Add Health. Marijuana use differed by age, sex, race/ethnicity, and public assistance in adjusted models. Variance parameters indicated a high degree of clustering by school (σ2 = 0.30) and less pronounced clustering by neighborhood (σ2 = 0.06) in adolescence when accounting for both levels simultaneously in a cross-classified multilevel model. Clustering by school persisted into young adulthood (σ2 = 0.08). Parental receipt of public assistance increased the likelihood of use during adolescence (odds ratio = 1.39; 95% confidence interval: 1.19-1.59), and higher parental education was associated with increased likelihood of use in young adulthood. These findings indicate that both contexts may be promising locations for intervention.

Multiple contexts and adolescent body mass index: Schools, neighborhoods, and social networks.

Adolescent health and behaviors are influenced by multiple contexts, including schools, neighborhoods, and social networks, yet these contexts are rarely considered simultaneously. In this study we combine social network community detection analysis and cross-classified multilevel modeling in order to compare the contributions of each of these three contexts to the total variation in adolescent body mass index (BMI). Wave 1 of the National Longitudinal Study of Adolescent to Adult Health is used, and for robustness we conduct the analysis in both the core sample (122 schools; N = 14,144) and a sub-set of the sample (16 schools; N = 3335), known as the saturated sample due to its completeness of neighborhood data. After adjusting for relevant covariates, we find that the school-level and neighborhood-level contributions to the variance are modest compared with the network community-level (σ(2)school = 0.069, σ(2)neighborhood = 0.144, σ(2)network = 0.463). These results are robust to two alternative algorithms for specifying network communities, and to analysis in the saturated sample. While this study does not determine whether network effects are attributable to social influence or selection, it does highlight the salience of adolescent social networks and indicates that they may be a promising context to address in the design of health promotion programs.

Disentangling the relative influence of schools and neighborhoods on adolescents' risk for depressive symptoms.

OBJECTIVES: Although schools and neighborhoods influence health, little is known about their relative importance, or the influence of one context after the influence of the other has been taken into account. We simultaneously examined the influence of each setting on depression among adolescents. METHODS: Analyzing data from wave 1 (1994-1995) of the National Longitudinal Study of Adolescent Health, we used cross-classified multilevel modeling to examine between-level variation and individual-, school-, and neighborhood-level predictors of adolescent depressive symptoms. Also, we compared the results of our cross-classified multilevel models (CCMMs) with those of a multilevel model wherein either school or neighborhood was excluded. RESULTS: In CCMMs, the school-level random effect was significant and more than 3 times the neighborhood-level random effect, even after individual-level characteristics had been taken into account. Individual-level indicators (e.g., race/ethnicity, socioeconomic status) were associated with depressive symptoms, but there was no association with either school- or neighborhood-level fixed effects. The between-level variance in depressive symptoms was driven largely by schools as opposed to neighborhoods. CONCLUSIONS: Schools appear to be more salient than neighborhoods in explaining variation in depressive symptoms. Future work incorporating cross-classified multilevel modeling is needed to understand the relative effects of schools and neighborhoods.