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Multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) is a new approach to quantitative intersectional modelling. Along with an outcome of interest, MAIHDA entails the use of two sets of independent variables. These include group demographics such as race, gender, and poverty status as well as strata which are constructs such as Black female poor, Black female wealthy, and White female poor. These constructs represent the combination of the demographic variables. To operationalize the approach, an initial random intercepts model with strata as a level 2 context is specified. Then, another model is specified that includes the strata as well as the demographic variables as level 1 fixed effects. As such, it is argued that MAIHDA uniquely identifies the additive and intersectional effects for any given outcome. In this paper we show that MAIHDA falls short of this promise: the strata are an individual-level composite variable not a level 2 context. Rather than being analogous to neighborhoods as contexts, strata are analogous to socio-economic status which is a combination of individual-level demographic variables, albeit often presented as a group-level characteristic. The result is that the demographic variables are inserted in both level 2 and 1. This duplication across the levels in MAIHDA means that there is a built-in collinearity across the levels and that the models are mis-specified and, therefore, redundant. We conclude that single-level models with the demographic variables and interactions or with the strata as fixed effects are still the more accurate models for quantitative intersectional analyses. • There has been limited analysis of the MAIHDA method. • We compare MAIHDA to traditional HLM. • We show that strata are a level 1 composite variable not a level 2 context. • We identify duplication and collinearity in this approach. • We advocate for single level models in quantitative intersectionality. [ABSTRACT FROM AUTHOR]