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Mixed-effects models are an analytic technique for modeling repeated measurement or nested data. This paper explains the logic of mixed-effects modeling and describes two examples of mixed-effects analyses using R. The intended audience of the paper is psychologists who specialize in cognitive development research. Therefore, the concepts and examples covered will focus primarily on repeated-measurement data resulting from studies in which participants respond to multiple items or trials. However, many of the concepts and examples we cover will likely be of use to readers outside this area of psychology. Finally, we discuss recommendations for dealing with practical challenges, suggest approaches for troubleshooting, and provide guidance on reporting results from mixed-effects models.

Background: Women and people of color continue to be underrepresented in many STEM fields and careers. Many studies have linked societal biases against the mathematical abilities of women and people of color to this underrepresentation, as well as to earlier measures of mathematical confidence and performance. Recent studies have shown that teachers may unintentionally have biases that reflect those in broader society. Yet, many studies on teachers' reports of students' abilities use data in the field--not experimental data--and thus often cannot say if the findings reflect bias or actual differences. The few experimental studies conducted suggest bias against the abilities of girls and students of color, but the prior work has limitations, which we seek to address (e.g., local samples, no exploration of moderators, no preregistration). Methods: In this preregistered experiment of 458 teachers across the U.S., we randomly assigned gender- and race-specific names to solutions to math problems, then asked teachers to rate the correctness of the solution, as well as the student's math ability and effort. Teachers also completed scales reflecting their own beliefs and dispositions, which we then assessed how those beliefs/dispositions moderated their biases. We used multilevel modeling to account for the nested data structure. Results: Consistent with our preregistered hypotheses, when the solution was not fully correct, findings suggest teachers thought boys had higher ability, even though the same teachers did not report differences in the correctness of the solution or perceived effort. Moreover, teachers who reported that gender disparities no longer exist in society were particularly likely to underestimate girls' abilities. Although findings revealed no evidence of racial bias on average, teachers' math anxiety moderated their ability judgments of students from different races, albeit with only marginal significance; teachers with high math anxiety tended to assume that White students had higher math ability than students of color. Conclusions: The present research identifies teachers' beliefs and dispositions that moderate their gender and racial biases. This experimental evidence sheds new light on why even low-performing boys consistently report higher math confidence and pursue STEM--namely, their teachers believe they have higher mathematical ability.

In a Registered Report, the authors propose a new survey‐bias‐mitigation method—incorporating inverse probability weighting via boosted regression—to better understand lesbian, gay, bisexual, or questioning (LGBQ)‐heterosexual youth risk disparities. This method is tested using the 2019 US Centers for Disease Control and Prevention‐collected Youth Risk Behavior Survey (YRBS) national data, which contain 12,847 observations (ages 12–18 [M = 16, SD = 1.25]; 49.1% male [8.7% LGBQ] and 50.9% female [22.4% LGBQ]; nationally representative regarding race and ethnicity). Looking across 44 outcomes, the authors found that the YRBS contains responses that are potentially biased against LGBQ youth in systematic ways, inflating perceived risk for this group in some outcomes. This potential bias is more pronounced among reported males than among reported females, and it is more pronounced for low‐incidence outcomes. For example, the steroid‐use disparity estimate among reported males reduced by 67%, while the reduction in bullying victimization was small and not statistically significant. The authors discuss robustness of results, the new method, and data policy implications. [ABSTRACT FROM AUTHOR]