Table 2.

Description of quantitative methods for intersectionality inquiry.

Method	Description	Sample size (range)	Number of social positions observed	Adjustment for confounders possible?	Connection to intersectionality	Strengths	Limitations
Regression with interaction terms
Linear and other models with identity link; multiplicative and other models with logit or log links (Barden et al., 2016; Berg, 2010; Cummings & Jackson, 2008; Harnois, 2015; Sen et al., 2009; Szmer et al., 2015; Velez et al., 2018; S.-L. L.; Williams et al., 2018)	This approach involves including an interaction term in a regression model. Both statistical scales (additive and multiplicative) were used by papers in this review. Some studies additionally used post-estimation to predict the marginal probabilities of the outcome for each intersectional position. Example equation: Y = B0 + B1*gender + B2*race + B3*gender*race + e Where Race: white/non-white Gender: male/female Y denotes the outcome variable of interest. B0 denotes the model intercept, e.g., the average outcome among white males. B1 denotes the effect of being female on the outcome among white individuals. B2 denotes the effect of being non-white among males. B3 denotes the additional effect of being non-white among females (or vice versa, the additional effect of being female among non-white individuals).	111–3,484,185	2–6	Yes	When an interaction term is introduced into a regression model, the interpretation of main effects must be in reference to a specific value of the other factor in the interaction. See example in description for more detail. Multiplicative scale: statistically significant interaction implies departure from statistical multiplicativity (i.e., the effect estimate for the interaction term is greater than the product of the main effects). Additive scale: statistically significant interaction implies departure from statistical additivity (i.e., the effect estimate for the interaction term is greater than the sum of the main effects) and can be used to further estimate the number of excess cases that are caused or presented because of the exposure(s).	Including an interaction term in a regression model is easy to implement. This method can provide a straightforward summary of effects across multiple exposure categories.	-Caution is needed to select the appropriate scale if investigators are evaluating intersectional hypotheses – assessing interaction on the additive scale is a more appropriate test for statistical multiplicativity. Additionally, additive scale interaction is more desirable from a public health perspective. -A relatively large sample size is needed in order to evaluate interaction using standard regression methods; -No significant interaction does not necessarily imply lack of intersectional effect -Statistical power is diminished with each dimension of interaction that is added -If causal inference is the goal of the study, confounders of both interaction factors must be adjusted for to yield valid causal estimates. However, even if causal inference is not the goal, appropriate covariate adjustment is needed to yield meaningful associational quantities. -When significant main effects (intersectional additive models) are used to inform the formation of intersectional multiplicative models, it's possible that interaction effects will be “missed” -- i.e., in the presence of qualitative interaction. -Evaluation of interaction terms must be done a priori rather than using a data driven approach.
Distributions by subgroups (Covarrubias, 2011; Covarrubias & Lara, 2014; Covarrubias & Liou, 2014; Goldstein et al., 2016)	The distribution of outcomes is presented based on categories defined by two or more intersectional positions.	13,773a	3–4	–	These exploratory analyses could provide insight into potential patterns in outcome variables between subgroups defined by intersectional categories.	These exploratory analyses are easy to implement and do not require any statistical assumptions to implement.	Distributions of the outcome by subgroups in the sample could be more reflective of who is represented in the sample.
ANOVA based methods (Fasoli et al., 2018; Friedman & Leaper, 2010; Greaves et al., 2017; Lefevor et al., 2018; Manzi et al., 2019; Moorman & Harrison, 2016; Quandt, 2019; Wilson et al., 2017)	ANOVA methods evaluate whether distributions of a continuous outcome differ between two or more groups. ANCOVA and MANCOVA allow for control of covariates. Factorial ANOVA allows for inclusion of interactions.	83–64,271	2–6	Yes, for ANCOVA and MANCOVA	ANOVA methods can be used to evaluate whether the distribution of a continuous outcome across intersectional subgroups differs significantly.	This method is robust even with small sample sizes.	If there are more than three groups of interest, one-way ANOVA only informs us that at least one pair of means is different but does not identify this comparison.
Chi-square (Bouris & Hill, 2017; Landstedt & Gådin, 2012; McGovern, 2017)	The chi-squared test evaluates whether two categorical variables are related to each other in the same population	163–1663	2	No	Chi-square analysis to evaluate an intersectionality hypothesis involves creation of a categorical variable combining 2 (or more) factors and evaluating whether this variable is predictive of a categorical outcome of interest.	Chi-square is robust to data distribution and can be useful when parametric assumptions of other tests cannot be fulfilled.	The validity of the chi-squared test is dependent on sample size, and may be unreliable for small sample sizes
T-tests (Budge et al., 2016; Gupta, 2019; Woodhams et al., 2015)	The t-test evaluates whether the distribution of a continuous outcome variable differs between two groups.	442–1,114,308	2–4	No	Statistically significant results for these tests suggest that the distribution of outcome differs between subgroups (i.e., intersectional positions).	This method is robust even with small sample sizes.	The distribution of data must be approximately normal to test the t-test hypothesis.
Categorization
Investigator-constructed intersectional variables (Bostwick et al., 2019; Cage et al., 2018; Chua et al., 2016; DuPont-Reyes et al., 2019; Hsieh & Ruther, 2016; Peck et al., 2014; Warner & Brown, 2011)	This approach involves the creation of a single “intersectional” variable containing all possible combinations of the social axes of interest as unique levels of the variable.	429-62,302	2–3	Yes, when combined with other analytic approaches (e.g., regression analysis) that allow for the control of confounders	This method serves as a preliminary step to setting up the data for an intersectional analysis (e.g., including the constructed intersectional variable in a regression model).	Once created, the intersectional variable can be employed across a variety of statistical methods (e.g., bivariate t-tests, regression, etc.)	-Depending on the number of categories, this method would require a large sample size. -Results may be less meaningful depending on the group specified to serve as the reference, which could be subjective. -If one social position being combined is measured poorly, this method could amplify measurement bias
Data reduction methods (latent class analysis, profile analysis) (Aguirre et al., 2016; Goodwin et al., 2018; Juan et al., 2016; Price et al., 2019; Taggart et al., 2019; Tomlinson et al., 2019; Whaley & Dubose, 2018)	This approach uses a data reduction method to create an “intersectional” variable, such as latent class analysis, principal components analysis, or profile analysis. In essence, all social factors of interest (i.e., gender, race, housing, etc.) will be reduced to a single variable, and labeled according to which factors contributed most to the categories created.	152-68,464	2–4	Yes, when combined with other analytic approaches (e.g., regression analysis) that allow for the control of confounders	This method classifies individuals into “profiles” or “classes” that are defined using the individual components – e.g., race, gender, sexual minority status. Subsequent class membership could be considered an “intersectional position”. The resulting classes can then be used in subsequent statistical techniques (e.g., including a categorical variable representing all classes into a regression model.).	-Data reduction methods could be particularly useful for hypothesis generation - When a large array of variables is of interest and it is not possible to include all in a regression model due to lack of statistical power/precision, data reduction strategies could be used to identify and group individuals in meaningful ways.	-Naming of categories/classes resulting from data reduction methods may be subjective. Though classes are often defined based on the variables that contributed most, there is still an element of subjectivity. -Group membership is based on probabilities (i.e., if LCA yields 5 classes, participant is assigned to the class that they have the highest probability of belonging). -Entirely data driven methods are agnostic to social hierarchies or processes that shape intersectional experiences. -There is a potential for systematic bias in sample recruitment and selection -These methods do not provide a clear reference group or appropriate comparison group.
Sum of marginalized identities (Lavaysse et al., 2018; Remedios & Snyder, 2018)	This approach collapses multiple social positions into a continuous variable by adding the number of marginalized identities an individual has (larger numbers imply a greater number of marginalized identities).	497–602	4–6	Yes, when combined with other analytic approaches (e.g., regression analysis) that allow for the control of confounders	When added to a regression model, the interpretation of this term in a regression model could be a test for whether adding more marginalized identities (i.e., having 5 versus 4 marginalized identities) increases the risk of an outcome.	This method could potentially be used for testing specific hypotheses related to multiple jeopardy.	-The summary variable equally weights all social positions, which could be an inaccurate reflection of an individual's lived experiences. -The summary variable is created without acknowledgement of the ways in which each of the factors used to create it are connected to one another (a concept central to intersectionality analyses).
Structural analyses and mediation approaches
Path analysis, structural equation modeling (Y. Kim & Calzada, 2019; Lewis et al., 2017; Toosi et al., 2019; Velez et al., 2018; Watson et al., 2016; M. G. Williams & Lewis, 2019)	This approach assesses the influence of a moderating variable on a hypothesized mediated relationship between a primary exposure and outcome of interest, i.e., a test of whether the indirect effect of a mediation analysis is modified by different levels of another variable. If the mediation analysis (first step) confirms an indirect pathway, then the moderation hypothesis (second step) is tested.	231–750	2–3	Yes	Statistically significant coefficient for the interaction term in the moderation model provides evidence for moderated mediation. If evaluating an intersectional variable as the primary exposure, both the mediation and moderation hypothesis could provide potential explanations regarding the mechanisms linking an intersectional position to an outcome of interest.	-Explicitly defines a proposed relationship between variables. -Can provide evidence for significant factors which could be the target of intervention. -Could be particularly useful to evaluate discrimination hypotheses (e.g., exposure as race, mediator as racial discrimination)	If testing a mediation hypothesis in which both the exposure and mediator are a social factor (e.g., the effect of gender on wage earning mediated through education), decomposition into indirect and direct effects (the mediation hypothesis) is not intuitively aligned with intersectionality theory (i.e., decomposition into effect of variable 1 mediated through variable 2 rather than the combined or additional effect of having both factors).
Three-way causal mediation decomposition (Bauer & Scheim, 2019b)	In contrast to the traditional Baron-Kenny mediation decomposition, three-way decomposition evolved from the causal inference literature and (1) allows for the assessment of exposure-mediator interaction and (2) defines direct and indirect effects within the counterfactual framework. There are four structural assumptions for causal mediation decomposition which need to be fulfilled in order to make valid causal inferences: (i) no mediator-exposure confounders, (ii) no mediator-outcome confounders, (iii) no exposure-outcome confounders, and (iv) no causal intermediates – i.e., confounders of the mediator-outcome relationship which occur downstream of the exposure.	2542a	2	Yes	-In the intersectionality context, the exposure of interest is a social factor (e.g., gender) and the mediator of interest is a discrimination factor (e.g., sexism). Estimates from this approach allow investigators to make conclusions about potential effects of interventions which equalize the mediator for all intersections to that of the most advantaged intersection. -One of the quantities that can be computed using this approach is the pure direct effect (PDE). This can be interpreted as the residual causal intersectional effect on the outcome that would persist if the mediator were set to the level it would take for the reference group. Additionally, a statistically significant pure indirect effect (PIE) would suggest that the mediator plays a causally mediating role.	-Provides potential evidence for factors which could be targeted for intervention to address disparities -If assumptions are satisfied, provides a rigorous approach to assess causality -This method could be a powerful tool for informing clear interventions, which is critical for intersectionality scholarship.	-Causal models require clear temporality, which will not always be clear in cross-sectional data. -Causal interpretation is dependent on confounding control and its sufficiency must always be considered. Additionally, the assumption that no mediator-outcome confounders (measured or unmeasured) are affected by the exposure must be fulfilled to make causal inferences. -This approach is computationally rigorous, and the interpretation can be complex and difficult for non-scientific audiences to understand, potentially limiting widespread utility and adoption.
Decomposition of inequality measures (see structural analysis and mediation approaches under “Three-way causal mediation decomposition”)
Decomposition of the general entropy class of measures (Chakraborty & Mukhopadhyay, 2017)	Broadly speaking, the general entropy class of measures are a tool to measure inequality in populations. General entropy measures vary between zero (representing perfect equality) and infinity (representing perfect inequality).	46,655a	2	Yes	Decomposing the general entropy measure of inequality allows one to examine the salience of the social factors (e.g., race, class, etc.) as grouping parameters. One can also explore whether adding additional grouping parameters will influence the between group components. This could potentially allow for exploration of potential social factors that may explain an observed inequality.	Does not allow for test of statistical significance for decomposed quantities.	-Decomposition of the general entropy class of measure is difficult to interpret.
Decomposition of the mutual information index (Guinea-Martin et al., 2015)	Like the general entropy class of measures, the mutual information index is a measure of inequality in a population. In relation to evaluating intersectionality, the first step is to develop the mutual information index, using data from the population (e.g., data on race and gender). The second step is to estimate the proportion of the index which is attributed exclusively to either factor (e.g., proportion attributed to either race or to gender). Finally, the last step is to compare the sum of the proportions attributed to either factor to a proportion attributed to the joint inequality.	22,200,000a	2	Yes	By comparing the sum of the proportions that are attributed to each individual factor exclusively to a proportion of the inequality that is attributed to the factors jointly, one can effectively test an interaction hypothesis. This can be a direct assessment of the multiple jeopardy hypothesis.	The mutual information index has strong group decomposition properties.	-The mutual information index does not completely separate groups unless they are completely mutually exclusive and have identical demographic characteristics. -The M index is sensitive to changes in the shares of each subgroup in the population and in the overall outcome mix.
Oaxaca-Blinder decomposition (Y.-M. Kim, 2017)	Oaxaca-Blinder decomposition is a method used to explain differences in an inequality variable by decomposing the component that is due to an “explained” and “unexplained” component. The “explained” part is the proportion of the gap in outcome that could be explained by observable characteristics, and the “unexplained” part.	4224a	2	Yes	Though the interpretation of the unexplained component is controversial, in its historical introduction, this component was thought to represent either discrimination or systemic processes which were inherent to the inequality. In the intersectionality scholarship, this could potentially represent a structural or political force that enacts inequality beyond what can be explained by the variables included in the decomposition.	Oaxaca-Blinder decomposition is simple to implement and only requires effect estimates from regression models and summary data for any independent variables used.	When variables in the Oaxaca-Blinder decomposition are discrete, the decomposition effects are sensitive to reference category choice.
Prediction
Multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) (Evans & Erickson, 2019; Evans C.R. et al., 2019)	The first step of the MAIHDA approach involves creating a “social strata” variable that corresponds to every social position of interest. Example, if interested in gender (male/female) and race (White, Black, Latino), the MAIHDA analysis would create a social strata variable with six unique categories. The multilevel MAIHDA model nests individuals (level 1) within their social strata (level 2). There are several MAIHDA models with corresponding interpretations. In a null model, the total variation between social strata is represented by the between-stratum variance parameter. In a MAIHDA model adjusting for main effects, the stratum specific residual can be interpreted as the remaining total “interaction effect” that remains unexplained by the main effects.	15,388–32,788	3–4	Yes	The variance partition coefficient (VPC), calculated following each MAIHDA model, is interpreted as the percent of the total variation in the outcome that is attributable to the between-strata level after adjustment for any variables (including main effects and covariates). The VPC is a measure of discriminatory accuracy, i.e., the ability of the model to correctly discriminate between people with/without the outcome of interest. The proportional change in variance (PCV), calculated following each MAIHDA model, indicates the total between stratum variance from the null model that is explained after adjustment for additive main effects and covariates. Differences between the total predicted effect and the predicted effect based only on the additive main effects allows for the examination of intersectionality for all strata of the dimensions of interest.	-Hierarchical models typically function best when more level 2 units are included in the analysis. Therefore, in contrast to fixed effects models, it is better in MAIHDA models to include more dimensions of social position/process and/or more categories within each dimension. -MAIHDA models are more scalable and parsimonious. -Automatically adjusts estimates based on the observed sample size, providing more conservative and reliable estimates for strata with small N. -Simulation analyses suggest that MAIHDA models provide more reliable estimates and are less likely to erroneously detect interactions of statistical significance due to chance alone than their conventional single-level counterparts.	-Estimates using a MAIHDA approach are inherently more conservative in cases where a stratum has few respondents. -Using mixed models forces the explicit and appropriate modeling of the random effects (level 2), which could potentially leave more room for error. -This method assumes that stratum specific residuals are normally distributed, which is less likely for highly marginalized groups
Area under the receiver operating curve (AUROC) (Wemrell et al., 2017)	This approach involves developing models of increasing complexity and using the AUROC to compare the discriminatory ability of each model. The regression models to be compared (using AUROC) could include one variable, followed by a model adjusting for all other social factors of interest, and finally a model including an “intersectional variable”.	3,600,000a	4	Yes	-Comparison of the AUROC between the separate models provides a measure of the increased ability to discriminate between outcome/no outcome. -This method could provide evidence that adding additional aspects of social position could lead to stronger prediction of outcome. This could imply that social identities themselves should be evaluated in combination with others.	This method could capture accurate risk exposure between groups indicative of power relationships	Not necessarily a limitation, but this method should be used in prediction settings rather than seen as a way of quantifying intersectional effects.
Classification and regression trees (CART) (Cairney et al., 2014; Greene et al., 2019)	Broadly speaking, CART is a method that includes two different types of decision trees: classification trees (for categorical outcomes) and regression trees (for continuous outcomes). Ultimately, the goal of CART analysis is to develop a classification structure which seeks to best predict an outcome variable. These classification structures are developed based on recursive procedures, which split the tree based on values of variables that best differentiate observations on the outcome of interest.	691-1213	4–5	Yes	Sensitivity, specificity, positive predictive value, and negative predictive value of the CART model are interpretable as the model's predictive accuracy. Good accuracy in individual terminal nodes allows for the identification of specific subgroups of the sample that are more/less likely to have the outcome. The final CART model reveals how individual predictor variables intersect to predict an outcome, which maps directly onto intersectionality theory	-No assumptions about variable distributions or relationships. -Capable of identifying complex and unsuspected interactions. -Can identify complex interactions in studies that are unable to use linear models for interactions. -Nonparametric -Method facilitates hypothesis generation	-One concern about CART is that this method is obligated to select specific cut-points, so doesn't work well with continuous predictors -- making replication of results difficult. -Classifications can be determined by covariates that do not reflect social categories of marginalization or hierarchies of power
Exhaustive chi-square automatic interaction detection (CHAID) (Shaw et al., 2012)	This approach investigates possible interactions across a large number of categorical data. Classification trees are used to test predictor variables one at a time and detect the strongest associations between predictors and outcomes. The goal is to identify the classification which best differentiates the outcome variable. This approach divides the sample into subgroups characterized by different combinations of the predictor variables and assigns an index score to each group, representing the proportion of outcomes observed in that group.	211,736a	4	No	Using this method, a wide variety of data are distilled into groups that are more or less predictive of the outcome of interest. One can evaluate the compositions of groups (i.e., which combinations of factors) that are more or less predictive of the outcome as a means of evaluating how combinations of factors influence the ability to predict outcome risk.	-Each of the subgroups represents a combination of different predictor variables and intrinsically acknowledges the interconnectedness of different social positions -Exhaustive CHAID does not require distributional assumptions of traditional analyses; -Could identify intersections that were not previously theorized; could be useful for hypothesis generation -Decision tree method could be used to rank variables and identify social categories that are “most” important for explaining the outcome.	-Predictors in CHAID models must be measured on either the nominal or ordinal scale
Regression stratified by subgroups
Regression stratified by subgroups (Parent et al., 2018; Rodriguez-Seijas et al., 2019; Rosenfield, 2012; Sen & Iyer, 2012; Veenstra & Patterson, 2016)	This approach has been used in studies in which more than two intersectional positions were of interest. Rather than including a three-way interaction term, which is difficult to interpret, this method assesses the association between a 2-way interaction term between two axes of interest by strata of a third axis of social position. Effectively, this is an evaluation of effect modification. Formal assessment of differences between strata can be evaluated using the Chow test.	237-1,065,110	2–5	Yes	The Chow test compares whether a stratified model explains more variance than a pooled model. Statistically significant results for the Chow test suggest that the interaction effect differs significantly between strata of a third variable of interest. In relation to intersectionality, this method provides evidence of differences in outcomes at intersectional subgroups.	This approach provides similar information as including a three-way interaction term in a regression model. However, interpretation may be easier as parameter estimates are interpreted within levels of the stratifying variable.	This approach would require a large enough sample for each stratum in order to detect intersections.
Geographically weighted regression (Jang & Kim, 2018)	Geographically weighted regression is an extension of ordinary least squares regression that allows for the association between predictor and outcome variables to differ based on location. In other words, it allows for the modeling of predictors and outcomes at the local level. This method implements a regression model for each location in a dataset, specifying bandwidths around each location.	1164a	2	Yes	When implementing this method for intersectionality research, one could examine whether the association between intersectional social categories and an outcome of interest differs based on setting. This could potentially facilitate the identification of particularly vulnerable neighborhoods which could be targets for intervention.	For outcomes that are particularly localized (e.g., anti-bullying policies implemented at the school district level, access to food or health care), geographically weighted regression could complement traditional OLS techniques by allowing for potential special nuances.	This method is sensitive to the choice of bandwidth (i.e., distance band for each “neighborhood” defined).
Surrogate measures of additive interaction. The below are measure of additive interaction that are calculated using effect estimates from a multiplicative model. Equations below are for risk ratios. Similar measures exist for odds ratios, which have been described elsewhere (VanderWeele & Knol, 2014).
Relative Excess Risk due to Interaction, RERI (Jackson et al., 2016; Kanchi et al., 2018; Tejera et al., 2019)	The relative excess risk of interaction (RERI) represents a ratio between the excess intersectional disparity and the mean outcome in the non-marginalized group. RERIRR = RR11 – RR01 – RR10 +1	1527–10,386	2	Yes	•In the absence of interaction, RERI = 0. RERI>0 provides evidence of positive additive interaction, and RERI<0 provides evidence for negative additive interaction.	Statistically significant additive interaction maps directly onto the concept of intersectional multiplicativity.	Surrogate measures provide a way to directly translate multiplicative measures of interaction into additive measures. Requires additional post-estimation following multiplicative regression analysis, potential for error in coding. In order for interaction effects to have a causal interpretation, must adjust for confounders of both interaction factors. Significant surrogate measures of additive interaction can only provide direction and presence of interactive effect, but not magnitude.
Attributable Proportion, AP (Jackson et al., 2016; Kanchi et al., 2018; Tejera et al., 2019)	The attributable proportion (AP) is the proportion of the mean outcome in a doubly marginalized group that is explained by the excess intersectional disparity. AP = $\frac{RR11-RR10-RR01}{RR11}$	1527–10,386	2	Yes	•In the absence of interaction, AP = 1. AP is interpreted as the proportion of disease that is due to the interaction among people who are doubly exposed.
Synergy Index, SI (Jackson et al., 2016; Kanchi et al., 2018; Tejera et al., 2019)	The synergy index (SI) is a ratio of the observed joint disparity that would have been expected if there was no excess intersectionality disparity. SI = $\frac{RR11-1}{\left(RR10-1\right)+(RR01-1)}$	1527–10,386	2	Yes	•SI is interpreted as the excess risk of double exposure in the presence of interaction relative to the risk from exposure with no interaction. In the absence of interaction, SI = 1
Ratio of Observed and Expected Joint Effects, RJE (Jackson et al., 2016; Kanchi et al., 2018; Tejera et al., 2019)	The ratio of observed versus expected joint effects on the relative scale (RJE) compares the observed mean outcome in the multiply marginalized group versus the expected mean if one axis alone could explain the mean outcome RJE = $\frac{observedRR11}{ExoectedRR11}$ Expected RR11 = RR10 + RR01 -1 RJE = 1/(1-AP)	1527–10,386	2	Yes	-RJE>1 implies positive additive interaction, RJE<1 implies negative additive interaction.
Block/set regression
Block/set regression (Reisen et al., 2013, Reisen et al., 2013; Ro & Loya, 2015)	Block/set regression is a hierarchical modeling approach which adds sets of characteristics to a model one at a time and evaluates the variance in the outcome explained.	301-5017	2	Yes	The variance in the outcome after adding a new set of characteristics is compared to a model without that set of characteristics.	If there are complicated constructs of social position comprised of highly correlated factors (such as sexual minority status, which typically comprises three domains: attraction, behavior, and identity), this approach may be useful for model building.	Adding characteristics as sets of variables does not allow for the evaluation of potential relationships that exist between variables across sets, thus not allowing for the evaluation of mutual constitutions of intersectional positions that may be important for a given outcome of interest.

^aSample size is from a single study.