Fixed and random effects models: making an informed choice

By Andrew Bell, Malcolm Fairbrother, Kelvyn Jones. Quality & Quantity: International Journal of Methodology, 2018

934 citations recorded by the source corpus.

This paper assesses the options available to researchers analysing multilevel (including longitudinal) data, with the aim of supporting good methodological decision-making. Given the confusion in the literature about the key properties of fixed and random effects (FE and RE) models, we present these models’ capabilities and limitations. We also discuss the within-between RE model, sometimes misleadingly labelled a ‘hybrid’ model, showing that it is the most general of the three, with all the strengths of the other two. As such, and because it allows for important extensions—notably random slopes—we argue it should be used (as a starting point at least) in all multilevel analyses. We develop the argument through simulations, evaluating how these models cope with some likely mis-specifications. These simulations reveal that (1) failing to include random slopes can generate anti-conservative standard errors, and (2) assuming random intercepts are Normally distributed, when they are not, introduces only modest biases. These results strengthen the case for the use of, and need for, these models.

Subfields: Health, Sociology and Political Science, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2b52796d2fe248a1b19837f65b103f3c330c630e

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Citations in the corpus

Interactions in Fixed Effects Regression Models (2020, background): “However, the complete elimination of effect heterogeneity from the FE error term through FEIS is accompanied by inferential benefits (see, e.g., Bell et al. 2018).”
Feeling Authentic on Social Media: Subjective Authenticity Across Instagram Stories and Posts (2021, methodology): “In all models, Level 1 predictors were centered around their respective person means and the person means were reintroduced as sample-mean-centered Level 2 variables, to compare within-person and between-person effects of predictors on outcomes (Bell et al., 2019).”
Why You Should Always Include a Random Slope for the Lower-Level Variable Involved in a Cross-Level Interaction (2019, background): “Against the background of the preceding discussion, one may wonder if the incorporation of random slopes is also important for achieving correct inference on the coefficients of lower-level variables that are not involved in a cross-level interaction term, that is, on ‘pure’ lower-level effects (cf.”