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?

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.

Mapping socio-geographical disparities in the occurrence of teenage maternity in Colombia using multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA)

BACKGROUND

The prevalence of teenage pregnancy in Colombia is higher than the worldwide average. The identification of socio-geographical disparities might help to prioritize public health interventions.

AIM

To describe variation in the probability of teenage maternity across geopolitical departments and socio-geographical intersectional strata in Colombia.

METHODS

A cross-sectional study based on live birth certificates in Colombia. Teenage maternity was defined as a woman giving birth aged 19 or younger. Multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) was applied using multilevel Poisson and logistic regression. Two different approaches were used: (1) intersectional: using strata defined by the combination of health insurance, region, area of residency, and ethnicity as the second level (2) geographical: using geopolitical departments as the second level. Null, partial, and full models were obtained. General contextual effect (GCE) based on the variance partition coefficient (VPC) was considered as the measure of disparity. Proportional change in variance (PCV) was used to identify the contribution of each variable to the between-strata variation and to identify whether this variation, if any, was due to additive or interaction effects. Residuals were used to identify strata with potential higher-order interactions.

RESULTS

The prevalence of teenage mothers in Colombia was 18.30% (95% CI 18.20-18.40). The highest prevalence was observed in Vichada, 25.65% (95% CI: 23.71-27.78), and in the stratum containing mothers with Subsidized/Unaffiliated healthcare insurance, Mestizo, Rural area in the Caribbean region, 29.08% (95% CI 28.55-29.61). The VPC from the null model was 1.70% and 9.16% using the geographical and socio-geographical intersectional approaches, respectively. The higher PCV for the intersectional model was attributed to health insurance. Positive and negative interactions of effects were observed.

CONCLUSION

Disparities were observed between intersectional socio-geographical strata but not between geo-political departments. Our results indicate that if resources for prevention are limited, using an intersectional socio-geographical approach would be more effective than focusing on geopolitical departments especially when focusing resources on those groups which show the highest prevalence. MAIHDA could potentially be applied to many other health outcomes where resource decisions must be made.

Intersectional inequalities in the transition to grandparenthood and cognitive functioning: A longitudinal Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy (MAIHDA)

Objectives

With aging societies, more people become vulnerable to experiencing cognitive decline. While normal aging is associated with a deterioration in certain cognitive abilities, little is known about how social determinants intersect to create late-life cognitive functioning inequalities. Simultaneously, the role of grandparenthood is central for older adults and their families. There are indications that social determinants intersect to modulate the effect of the transition to grandparenthood, but further evidence is needed. Our study investigates the relation of transition to grandparenthood with cognitive functioning and explores differences across intersectional strata.

Methods

Using longitudinal data from the Survey of Health, Ageing and Retirement in Europe, we analyzed a sample of 19,953 individuals aged 50-85 without grandchildren at the baseline. We applied Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy to investigate cognitive functioning differences across 48 intersectional strata, defined by sex/gender, migration, education, and occupation. We allowed the impact of becoming a grandparent to vary across strata by including random slopes.

Results

Intersectional strata accounted for 17.43% of the overall variance in cognitive functioning, with most of the stratum-level variation explained by additive effects of the stratum-defining characteristics. Transition to grandparenthood was associated with higher cognitive functioning, with a stronger effect for women. Stratum-level variation in the grandparenthood effect was modest.

Discussion

This study highlights the importance of social determinants for understanding heterogeneities in the association of transition to grandparenthood with cognitive functioning. Adopting an intersectional lens is useful to decompose inequalities and derive tailored interventions to promote equal healthy aging.

Educational Inequalities at the Intersection of Multiple Social Categories: An Introduction and Systematic Review of the Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy (MAIHDA) Approach

Intersectional approaches have become increasingly important for explaining educational inequalities because they help to improve our understanding of how individual experiences are shaped by simultaneous membership in multiple social categories that are associated with interconnected systems of power, privilege, and oppression. For years, there has been a call in psychological and educational research for quantitative approaches that can account for the intersection of multiple social categories. The present paper introduces the Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy (MAIHDA) approach, a novel intersectional approach from epidemiology, to study educational inequalities. The MAIHDA approach uses a multilevel model as the statistical framework to define intersectional strata that represent individuals’ membership in multiple social categories. By partitioning the variance within and between intersectional strata, the MAIHDA approach allows identifying intersectional effects at the strata level as well as obtaining information on the discriminatory accuracy of these strata for predicting individual educational outcomes. Compared to conventional quantitative intersectional approaches, MAIHDA analyses have several advantages, including better scalability for higher dimensions, model parsimony, and precision-weighted estimates of strata with small sample sizes. We provide a systematic review of its past application and illustrate its use by analyzing inequalities in reading achievement across 40 unique intersectional strata (combining the social categories of gender, immigrant background, parental education, and parental occupational status) using data from 15-year-old students in Germany (N = 5451). We conclude that the MAIHDA approach is a valuable intersectional tool to study inequalities in educational contexts.

Assessment of heterogeneous Head Start treatment effects on cognitive and social-emotional outcomes

Head Start is a federally funded, nation-wide program in the U.S. for enhancing school readiness of children aged 3–5 from low-income families. Understanding heterogeneity in treatment effects (HTE) is an important task when evaluating programs, but most attempts to explore HTE in Head Start have been limited to subgroup analyses that rely on average treatment effects by subgroups. This study applies an extension of multilevel modelling, complex variance modelling, to data from a randomized controlled trial of Head Start, Head Start Impact Study (HSIS). The treatment effects on the variance, in addition to the mean, of nine cognitive and social-emotional outcomes were assessed for 4,442 children aged 3–4 years who were followed until their 3rd grade year. Head Start had positive short-term effects on the means of multiple cognitive outcomes while having no effect on the means of social-emotional outcomes. Head Start reduced the variances of multiple cognitive and one social-emotional outcomes, meaning that substantial HTE exists. In particular, the increased mean and decreased variance reflect the ability of Head Start to improve the outcomes and reduce their variability. Exploratory secondary analyses suggested that larger benefits for children with Spanish as a primary language and low parental educational level partly explained the reduced variability, but the HTE remained and the variability was reduced even within these subgroups. Routinely monitoring the treatment effects on the variance, in addition to the mean, would lead to a more comprehensive program evaluation that describes how a program performs on average and on the entire distribution.

Mapping mental health inequalities: The intersecting effects of gender, race, class, and ethnicity on ADHD diagnosis

While the effects of social stratification by gender, race, class, and ethnicity on health inequalities are well-documented, our understanding of the intersecting consequences of these social dimensions on diagnosis remains limited. This is particularly the case in studies of mental health, where "paradoxical" patterns of stratification have been identified. Using a Bayesian multi-level random-effects Poisson model and a nationally representative random sample of 138,009 households from the National Survey of Children's Health, this study updates and extends the literature on mental health inequalities through an intersectional investigation of one of the most commonly diagnosed psychiatric conditions of childhood/adolescence: attention-deficit hyperactivity disorder (ADHD). Findings indicate that gender, race, class, and ethnicity combine in mutually constitutive ways to explain between-group variation in ADHD diagnosis. Observed effects underscore the importance and feasibility of an intersectional, multi-level modelling approach and data mapping technique to advance our understanding of social subgroups more/less likely to be diagnosed with mental health conditions.

Understanding unequal ageing: towards a synthesis of intersectionality and life course analyses

Intersectionality has received an increasing amount of attention in health inequalities research in recent years. It suggests that treating social characteristics separately—mainly age, gender, ethnicity, and socio-economic position—does not match the reality that people simultaneously embody multiple characteristics and are therefore potentially subject to multiple forms of discrimination. Yet the intersectionality literature has paid very little attention to the nature of ageing or the life course, and gerontology has rarely incorporated insights from intersectionality. In this paper, we aim to illustrate how intersectionality might be synthesised with a life course perspective to deliver novel insights into unequal ageing, especially with respect to health. First we provide an overview of how intersectionality can be used in research on inequality, focusing on intersectional subgroups, discrimination, categorisation, and individual heterogeneity. We cover two key approaches—the use of interaction terms in conventional models and multilevel models which are particularly focussed on granular subgroup differences. In advancing a conceptual dialogue with the life course perspective, we discuss the concepts of roles, life stages, transitions, age/cohort, cumulative disadvantage/advantage, and trajectories. We conclude that the synergies between intersectionality and the life course hold exciting opportunities to bring new insights to unequal ageing and its attendant health inequalities.

Mapping intersectional inequalities in biomarkers of healthy ageing and chronic disease in older English adults

Chronic diseases and their inequalities amongst older adults are a significant public health challenge. Prevention and treatment of chronic diseases will benefit from insight into which population groups show greatest risk. Biomarkers are indicators of the biological mechanisms underlying health and disease. We analysed disparities in a common set of biomarkers at the population level using English national data (n = 16,437). Blood-based biomarkers were HbA1c, total cholesterol and C-reactive protein. Non-blood biomarkers were systolic blood pressure, resting heart rate and body mass index. We employed an intersectionality perspective which is concerned with how socioeconomic, gender and ethnic disparities combine to lead to varied health outcomes. We find granular intersectional disparities, which vary by biomarker, with total cholesterol and HbA1c showing the greatest intersectional variation. These disparities were additive rather than multiplicative. Each intersectional subgroup has its own profile of biomarkers. Whilst the majority of variation in biomarkers is at the individual rather than intersectional level (i.e. intersections exhibit high heterogeneity), the average differences are potentially associated with important clinical outcomes. An intersectional perspective helps to shed light on how socio-demographic factors combine to result in differential risk for disease or potential for healthy ageing.

Geographical and sociodemographic differences in discontinuation of medication for Chronic Obstructive Pulmonary Disease - A Cross-Classified Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy (MAIHDA)

BACKGROUND

While discontinuation of COPD maintenance medication is a known problem, the proportion of patients with discontinuation and its geographical and sociodemographic distribution are so far unknown in Sweden. Therefore, we analyse this question by applying an innovative approach called multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA).

PATIENTS AND METHODS

We analysed 49,019 patients categorized into 18 sociodemographic contexts and 21 counties of residence. All patients had a hospital COPD diagnosis and had been on inhaled maintenance medication during the 5 years before the study baseline in 2010. We defined "discontinuation" as the absolute lack of retrieval from a pharmacy of any inhaled maintenance medication during 2011. We performed a cross-classified MAIHDA and obtained the average proportion of discontinuation, as well as county and sociodemographic absolute risks, and compared them with a proposed benchmark value of 10%. We calculated the variance partition coefficient (VPC) and the area under the receiver operating characteristics curve (AUC) to quantify county and sociodemographic differences. To summarize the results, we used a framework with 15 scenarios defined by the size of the differences and the level of achievement in relation to the benchmark value.

RESULTS

Around 18% of COPD patients in Sweden discontinued maintenance medication, so the benchmark value was not achieved. There were very small county differences (VPC=0.35%, AUC=0.54). The sociodemographic differences were small (VPC=4.98%, AUC=0.57).

CONCLUSION

Continuity of maintenance medication among COPD patients in Sweden could be improved by reducing the unjustifiably high prevalence of discontinuation. The very small county and small sociodemographic differences should motivate universal interventions across all counties and sociodemographic groups. Geographical analyses should be combined with sociodemographic analyses, and the cross-classified MAIHDA is an appropriate tool to assess health-care quality.

Intersectionality and Adolescent Mental Well-being: A Cross-Nationally Comparative Analysis of the Interplay Between Immigration Background, Socioeconomic Status and Gender

PURPOSE

Intersectionality theory highlights the importance of the interplay of multiple social group memberships in shaping individual mental well-being. This article investigates elements of adolescent mental well-being (life dissatisfaction and psychosomatic complaints) from an intersectional perspective. It tests mental well-being consequences of membership in combinations of multiple social groups and examines to what extent such intersectional effects depend on the national context (immigration and integration policies, national-level income, and gender equality).

METHODS

Using Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy, we assessed the role of the national context in shaping the interplay between immigration background, socioeconomic status, and gender, using data from 33 countries from the 2017/2018 Health Behaviour in School-aged Children survey.

RESULTS

We found no uniform intersectionality effects across all countries. However, when allowing the interplay to vary by national context, results did point toward some intersectional effects. Some aggravated negative effects were found for members of multiple disadvantaged social groups in countries with low levels of income equality and restrictive migration policies, whereas enhanced positive effects were found for members of multiple advantaged groups in these countries. Similarly, mitigated negative effects of membership in multiple disadvantaged groups were shown in countries with higher levels of income equality and more inclusive migration policies, whereas mitigated positive effects were found for multiply advantaged individuals. Although for national-level gender equality results pointed in a similar direction, girls' scores were counterintuitive. High national-level gender equality disproportionately benefitted groups of disadvantaged boys, whereas advantaged girls were doing worse than expected, and reversed effects were found for countries with low gender equality.

CONCLUSIONS

To fully understand social inequalities in adolescent mental well-being, the interplay between individual-level and national-level indicators must be explored.

International migration and health: it is time to go beyond conventional theoretical frameworks

The large-scale international migration in the 21st century has emerged as a major threat to the global health equity movement. Not only has the volume of migration substantially increased but also the patterns of migration have become more complex. This paper began by focusing on the drivers of international migration and how health inequalities are linked to migration. Situating migration within the broader structural contexts, the paper calls for using the unharnessed potential of the intersectionality framework to advance immigrant health research. Despite coming from poorer socioeconomic backgrounds and facing disparities in the host society, the immigrants are often paradoxically shown to be healthier than the native population, although this health advantage diminishes over time. Studies on immigrant health, however, are traditionally informed by the acculturation framework which holds the assimilation of unhealthy lifestyles primarily responsible for immigrant health deterioration, diverting the attention away from the structural factors. Although the alternative structural framework came up with the promise to explore the structural factors, it is criticised for an overwhelming focus on access to healthcare and inadequate attention to institutional and societal contexts. However, the heterogeneity of the immigrant population across multiple dimensions of vulnerability demands a novel approach that can bring to the fore both premigratory and postmigratory contextual factors and adequately capture the picture of immigrant health. The paper concludes by questioning the acculturation perspective and pushing the structural paradigm to embrace the intersectionality framework which has the potential to address a wide range of vulnerabilities that intersect to produce health inequalities among the immigrants.

Precision public health: Mapping socioeconomic disparities in opioid dispensations at Swedish pharmacies by Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy (MAIHDA)

BACKGROUND

In light of the opioid epidemic in the United States, there is growing concern about the use of opioids in Sweden as it may lead to misuse and overuse and, in turn, severe public health problems. However, little is known about the distribution of opioid use across different demographic and socioeconomic dimensions in the Swedish general population. Therefore, we applied an intersectional Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy (MAIHDA), to obtain an improved mapping of the risk heterogeneity of and socioeconomic inequalities in opioid prescription receipt.

METHODS AND FINDINGS

Using data from 6,846,106 residents in Sweden aged 18 and above, we constructed 72 intersectional strata from combinations of gender, age, income, cohabitation status, and presence or absence of psychological distress. We modelled the absolute risk (AR) of opioid prescription receipt in a series of multilevel logistic regression models distinguishing between additive and interaction effects. By means of the Variance Partitioning Coefficient (VPC) and the area under the receiver operating characteristic curve (AUC), we quantified the discriminatory accuracy (DA) of the intersectional strata for discerning those who received opioid prescriptions from those who did not. The AR of opioid prescription receipt ranged from 2.77% (95% CI 2.69-2.86) among low-income men aged 18-34, living alone, without psychological distress, to 28.25% (95% CI 27.95-28.56) among medium-income women aged 65 and older, living alone, with psychological distress. In a model that conflated both additive and interaction effects, the intersectional strata had a fair DA for discerning opioid users from non-users (VPC = 13.2%, AUC = 0.68). However, in the model that decomposed total effects into additive and interaction effects, the VPC was very low (0.42%) indicating the existence of small interaction effects for a number of the intersectional strata.

CONCLUSIONS

The intersectional MAIHDA approach aligns with the aims of precision public health, through improving the evidence base for health policy by increasing understanding of both health inequalities and individual heterogeneity. This approach is particularly relevant for socioeconomically conditioned outcomes such as opioid prescription receipt. We have identified intersections of social position within the Swedish population at greater risk for opioid prescription receipt.

Using Shrinkage in Multilevel Models to Understand Intersectionality

Abstract. Multilevel models have recently been used to empirically investigate the idea that social characteristics are intersectional such as age, sex, ethnicity, and socioeconomic position interact with each other to drive outcomes. Some argue this approach solves the multiple-testing problem found in standard dummy-variable (fixed-effects) regression, because intersectional effects are automatically shrunk toward their mean. The hope is intersections appearing statistically significant by chance in a fixed-effects regression will not appear so in a multilevel model. However, this requires assumptions that are likely to be broken. We use simulations to show the effect of breaking these assumptions: when there are true main effects/interactions, unmodeled in the fixed part of the model. We show, while the multilevel approach outperforms the fixed-effects approach, shrinkage is less than is desired, and some intersectional effects are likely to appear erroneously statistically significant by chance. We conclude with advice to make this promising method work robustly.

Socioeconomic differences in body mass index in Spain: An intersectional multilevel analysis of individual heterogeneity and discriminatory accuracy

Many studies have demonstrated the existence of simple, unidimensional socioeconomic gradients in body mass index (BMI). However, in the present paper we move beyond such traditional analyses by simultaneously considering multiple demographic and socioeconomic dimensions. Using the Spanish National Health Survey 2011–2012, we apply intersectionality theory and multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) to analyze 14,190 adults nested within 108 intersectional strata defined by combining categories of gender, age, income, educational achievement and living situation. We develop two multilevel models to obtain information on stratum-specific BMI averages and the degree of clustering of BMI within strata expressed by the intra-class correlation coefficient (ICC). The first model is a simple variance components analysis that provides a detailed mapping of the BMI disparities in the population and measures the accuracy of stratum membership to predict individual BMI. The second model includes the variables used to define the intersectional strata as a way to identify stratum-specific interactions. The first model suggests moderate but meaningful clustering of individual BMI within the intersectional strata (ICC = 12.4%). Compared with the population average (BMI = 26.07 Kg/m2), the stratum of cohabiting 18-35-year-old females with medium income and high education presents the lowest BMI (-3.7 Kg/m2), while cohabiting 36-64-year-old females with low income and low education show the highest BMI (+2.6 Kg/m2). In the second model, the ICC falls to 1.9%, suggesting the existence of only very small stratum specific interaction effects. We confirm the existence of a socioeconomic gradient in BMI. Compared with traditional analyses, the intersectional MAIHDA approach provides a better mapping of socioeconomic and demographic inequalities in BMI. Because of the moderate clustering, public health policies aiming to reduce BMI in Spain should not solely focus on the intersectional strata with the highest BMI, but should also consider whole population polices.

Chronic Obstructive Pulmonary Disease in Sweden: An intersectional multilevel analysis of individual heterogeneity and discriminatory accuracy

Socioeconomic, ethnic and gender disparities in Chronic Obstructive Pulmonary Disease (COPD) risk are well established but no studies have applied multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) within an intersectional framework to study this outcome. We study individuals at the first level of analysis and combinations of multiple social and demographic categorizations (i.e., intersectional strata) at the second level of analysis. Here we used MAIHDA to assess to what extent individual differences in the propensity of developing COPD are at the intersectional strata level. We also used MAIHDA to determine the degree of similarity in COPD incidence of individuals in the same intersectional stratum. This leads to an improved understanding of risk heterogeneity and of the social dynamics driving socioeconomic and demographic disparities in COPD incidence. Using data from 2,445,501 residents in Sweden aged 45–65, we constructed 96 intersectional strata combining categories of age, gender, income, education, civil- and migration status. The incidences of COPD ranged from 0.02% for young, native males with high income and high education who cohabited to 0.98% for older native females with low income and low education who lived alone. We calculated the intra-class correlation coefficient (ICC) that informs on the discriminatory accuracy of the categorizations. In a model that conflated additive and interaction effects, the ICC was good (20.0%). In contrast, in a model that measured only interaction effects, the ICC was poor (1.1%) suggesting that most of the observed differences in COPD incidence across strata are due to the main effects of the categories used to construct the intersectional matrix while only a minor share of the differences are attributable to intersectional interactions. We found conclusive interaction effects. The intersectional MAIHDA approach offers improved information to guide public health policies in COPD prevention, and such policies should adopt an intersectional perspective.

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We use multilevel analysis of individual heterogeneity and discriminatory accuracy.

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There is a clear difference in COPD incidence between intersectional strata.

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Intersectionality improves mapping of socioeconomic differences in COPD incidence.

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Preventive measures should be based on intersectional rather than classic analyses.