A primer on fixed effects and fixed-effects panel modeling using R, Stata, and SPSS

Fixed-effects modeling is a powerful tool for estimating within-clusters associations in cross-sectional data and within-participants associations in longitudinal data. Although commonly used by other social scientists, this tool remains largely unknown to psychologists. To address this issue, we offer a pedagogical primer tailored for this audience, complete with R, Stata, and SPSS scripts. This primer is organized into three parts. In Part 1, we show how fixed-effects modeling applies to clustered cross-sectional data. We introduce the concepts of “cluster dummies” and “demeaning” and provide scripts to estimate the within-schools association between sports and depression in a fictional data set. In Part 2, we show how fixed-effects modeling applies to longitudinal data and provide scripts to estimate the within-participants association between sports and depression over time in a fictional four-wave data set. In this part, we cover three additional topics. First, we explain how to calculate effect sizes and offer simulation-based sample-size guidelines to detect within-participants effects of plausible magnitude with sufficient power. Second, we show how to test two possible interactions: between a time-invariant and a time-varying predictor and between two time-varying predictors. Third, we introduce three relevant extensions: first-difference modeling (estimating changes from one wave to the next), time-distributed fixed-effects modeling (estimating changes before, during, and after an individual event), and within-between multilevel modeling (estimating both within- and between-participants associations). In Part 3, we discuss two limitations of fixed-effects modeling: time-varying confounders and reverse causation. We conclude with reflections on causality in nonexperimental data.