This investigation examines the efficacy of multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) over fixed-effects models when performing intersectional studies. The research questions are as follows: (1) What are typical strata representation rates and outcomes on physics research-based assessments? (2) To what extent do MAIHDA models create more accurate predicted strata outcomes than fixed-effects models? and (3) To what extent do MAIHDA models allow the modeling of smaller strata sample sizes? We simulated 3,000 data sets based on real-world data from 5,955 students on the LASSO platform. We found that MAIHDA created more accurate and precise predictions than fixed-effects models. We also found that using MAIHDA could allow researchers to disaggregate their data further, creating smaller group sample sizes while maintaining more accurate findings than fixed-effects models. We recommend using MAIHDA over fixed-effects models for intersectional investigations.