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

Key takeaways

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Reading notes

Imported on 2025-04-27 17:42

⭐ Important

• & 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. (p. 1)
• & McCall (2005) identified three distinct methodological approaches for applying the concept of intersectionality: the anticategorical, intracategorical, and intercategorical approach. (p. 5)
• & The anticategorical approach engages in the critique and deconstruction of categories. In this approach, intersectionality is not studied with social categories because social life is considered too complex for fixed categories to adequately represent it. (p. 5)
• & The intracategorical approach acknowledges the relevance of social categories for studying intersectionality, but maintains a critical stance toward them by emphasizing the heterogeneity within social categories. (p. 5)
• Gender non-conforming groups?:
  • & Intersectional research, which takes an intracategorical approach, typically focuses on specific social groups at neglected intersections to reveal the complexity of lived experiences within those groups. (p. 5)
• & in the intercategorical approach, analytical categories are provisionally adopted to analyze inequalities between social groups as well as interactions between different social categories. The intercategorical approach addresses the complexity of social life with multigroup studies and systematic comparisons (McCall, 2005). (p. 5)
• & However, it has been argued that quantitative methods are also suitable for conducting intersectionality research (Bauer, 2014; Bowleg, 2008; Codiroli Mcmaster & Cook, 2019; Cole, 2009; Else-Quest & Hyde, 2016a; Gross et al., 2016a; McCall, 2005). (p. 5)
• & “When Black + lesbian + woman≠ Black lesbian woman: The methodological challenges of qualitative and quantitative intersectionality research” (Bowleg, 2008). However, it is important to note that whereas quantitative (educational) research distinguishes between additive effects and interaction effects, with interaction effects referring to effects that go beyond additive effects (i.e., the observed effect is greater than the sum of the additive components), the meaning of these terms is different in the intersectional theoretical framework. The meaning of “interaction” in this context is similar to the meaning of “intersection,” and examining the multiplicative interaction of gender and race, for example, does not imply a multiplicative statistical interaction model. This terminological distinction is important for implementing intersectional research with quantitative methods sensibly (Bauer, 2014). (p. 6)
• & However, the traditional regression approach comes with several methodological limitations. As discussed by Evans et al. (2018), one limitation concerns scalability. The more social categories are considered, the higher the number of parameters that would have to be accounted for in the traditional regression approach to represent all possible interaction effects (Figure S1). (p. 6)
• & “Main effects” can be also referred to as “first-order effects” and “interaction effects” as “higher-order effects” (Cohen et al., 2003). (p. 6)
• & Following this idea, the MAIHDA approach models individuals at the first level of analysis and combinations of multiple social categories at the second level of analysis. (p. 7)
• & Importantly, the MAIHDA approach disentangles variance between and within intersectional strata to assess the extent to which (a) intersectionality is relevant overall, taking into account heterogeneity within and between social strata (i.e., providing global measures of intersectionality), (b) specific strata have higher or lower educational outcomes than expected based on individuals’ simultaneous membership in multiple social categories (i.e., providing a specific measure of intersectionality; Bell et al., 2019), and (c) strata membership predicts individuals’ educational outcomes (i.e., the discriminatory accuracy of the strata). In addition, MAIHDA can be used to predict educational outcomes for each intersectional stratum, providing another specific measure of intersectionality. (p. 7)
• & The first step in the approach is to assign each individual i (i = 1, ..., N) to a certain intersectional stratum j (j = 1, ..., J; see Fig. 1). The intersectional strata are defined by forming all possible combinations from a set of social categories for a group of individuals that share intersecting social categories (e.g., Evans et  al., 2018). (p. 10)
• & Importantly, very large and diverse samples are required to apply the intersectional MAIHDA approach for reliably estimating effects. The larger the sample, the more likely it is that more strata with sufficient sample sizes can be created. In addition, it is important to find meaningful cut points for the creation of social categories when (a) continuous variables need to be transformed into categorical ones or (b) categories need to be collapsed to reduce the number of resulting strata, if the sample size would not be sufficient for all possible strata. (p. 10)
• & For instance, in our empirical example, we collapsed the variable “parental education” from seven categories into the categories “below university entrance certificate” and “at least university entrance certificate.” We chose these categories because they reflect socially significant distinctions in educational achievement in Germany (Fend, 2013; McElvany et  al., 2009) and partitioned the sample into sufficiently large groups. (p. 10)
• & To transform continuous variables into categorical variables, they can also be divided into quantiles. (p. 10)
• & The simple intersectional model decomposes the total variance in the outcome y (i.e., reading achievement) into variance that can be attributed to (a) mean-level differences between intersectional strata (𝜎2 strata) and (b) interindividual differences within intersectional strata (𝜎2 e0). Using the notation by Raudenbush and Bryk (2002), the simple intersectional model is specified as a two-level model that contains a residual term e0ij to represent the within-strata random residual at the individual level (Eq.  2) and a random-coefficient 𝜇0j that represents how the mean level of a certain stratum deviates from the grand mean 𝛾00 of the outcome (Eq.  3). The residual terms e0ij and the random effects 𝜇0j are assumed to be uncorrelated and to follow a normal distribution with variances 𝜎2 e0 and 𝜎2 st r at a, respectively. The simple intersectional model depicts the important intersectional idea that social categories may interact simultaneously and multidirectionally, given that the reading achievement mean levels of intersectional strata 𝜇0j may freely vary around the grand mean 𝛾00. (p. 11)
• & The purpose of the simple intersectional model is to (a) calculate the variance partition coefficient (VPC; a global measure of intersectionality) and (b) map the averages of the intersectional strata to identify inequalities in education (as specific measures of intersectionality). The VPC represents the proportion of the total variance in educational outcomes (𝜎2 strata + 𝜎2 e0) that is located at the strata level (Merlo, 2018; Eq. 5) and thus serves as a global measure of intersectionality (together with the VPC from the main effects model and the proportional change in the betweenstrata variance [PCV]). (p. 11)
• & In the simple intersectional model, the VPC is identical to the intra-class correlation coefficient (ICC), which can be interpreted as the correlation between two randomly selected individuals from the same intersectional stratum (Goldstein, 2010). (p. 11)
• & As a result, the VPC from the simple intersectional model is also a measure of similarity or clustering, which is analogous to a measure of discriminatory accuracy. (p. 11)
• & For binary outcomes (e.g., school dropout), this measure is similar to the area under the receiver operating characteristic (ROC) curve (AUC). (p. 11)
• & In sum, the VPC from the simple intersectional model quantifies the intersectional general contextual effect (GCE), that is, the influence of being a member of an intersectional stratum on educational outcomes alone (Merlo, 2018). (p. 12)
• & A high VPC indicates that intersectional strata are useful for understanding individual differences in, for example, students’ reading achievement. By contrast, a VPC of 0 would indicate that intersectional strata resemble random samples from the student body and are not relevant for understanding differences in educational inequalities (Merlo, 2018). (p. 12)
• & In addition, the simple intersectional model provides a detailed map of educational inequalities by predicting the average educational outcomes for each intersectional stratum. The predicted average strata-specific educational outcomes can therefore be understood as a specific measure of intersectionality. In sum, this analysis helps to identify specific strata with particularly positive or negative educational outcomes. In our example, the strata-specific predicted values for reading achievement help to improve our understanding of the gendered, socioeconomic, and immigration-related patterned distribution of reading achievement (p. 12)
• & The purpose of the second model, the main effects model (or intersectional interaction model), is threefold: to calculate two additional global measures of intersectionality (i.e., the adjusted VPC and the PCV) and one additional specific measure of intersectionality (i.e., the strata-level residuals). The adjusted VPC indicates what percentage of the total variance is explained by the interaction effects at the strata level after controlling for the additive main effects that are associated with the social categories. (p. 12)
• & In our example, a total of M = 7 main effect predictor variables are included. (p. 13)
• & In the intersectional interaction model, the strata-level residual 𝜇0j.adj (i.e., the random effect) now represents the difference between the average reading achievement y in stratum j and the reading achievement y that is expected by the main effects of the social categories for that particular stratum. The values of 𝜇0j.adj are assumed to be normally distributed with mean 0 and variance 𝜎2 strata.res. As in the simple intersectional model, the adjusted reading achievement mean levels of the intersectional strata 𝜇0j.adj may freely vary around the grand mean 𝛾00.adj. Thus, the extended model also reflects the intersectional idea that social categories may interact simultaneously and multidirectionally. (p. 13)
• & While the VPC of the simple intersectional model represents the upper bound of the explanatory power of the intersectional strata and includes both the additive and potential interaction effects of the variables that define the strata, the adjusted VPC in the intersectional interaction model represents the strata-level variance that is due to interaction effects only, at least in relation to the included variables (Axelsson Fisk et al., 2018). Thus, the adjusted VPC can be understood as a global measure of intersectionality. (p. 13)
• & To calculate the adjusted VPC, the between-strata variance is divided by the total variance (i.e., the sum of the between- and within-strata variance) in the intersectional interaction model. (p. 13)
• & The third global measure of intersectionality is the PCV. The PCV measures how much between-strata variance observed in the simple intersectional model is explained by additive main effects vs. interaction effects (Axelsson Fisk et al., 2018; Evans, 2019b). To calculate the PCV, the strata-level variance in the intersectional interaction model is first subtracted from the strata-level variance in the simple intersectional model and then divided by the strata-level variance in the simple intersectional model (see Eq. 10). PCVs are usually multiplied by 100 and reported as percentages. Subtracting the PCV from 100% yields the percentage of the strata-level variance that cannot be explained by the main effects, and is therefore likely due to the interaction effects. (p. 13)
• & Low PCV values imply that the main effects cannot fully explain the variation in the outcome and that the remaining between-strata variance is due to the existence of interaction effects between the social categories defining the intersectional strata. In contrast, high PCV values indicate that the main effects explain a large proportion of the mean-level differences between intersectional strata in the outcome. In sum, by calculating the adjusted VPC and PCV, the intersectional interaction model decomposes the intersectional GCE into an additive and an interaction component, which allows for the identification of the portion of the intersectional GCE attributable to each component. (p. 14)
• & A specific measure of intersectionality is the strata-level residual 𝜇0j.adj (i.e., the random effects of the intersectional interaction model). It indicates the unique intersectional effect of each stratum after controlling for the main effects of being a member in a certain social category. (p. 14)