This article challenges Fixed Effects (FE) modeling as the ‘default’ for time-series-cross-sectional and panel data. Understanding different within and between effects is crucial when choosing modeling strategies. The downside of Random Effects (RE) modeling—correlated lower-level covariates and higher-level residuals—is omitted-variable bias, solvable with Mundlak's (1978a) formulation. Consequently, RE can provide everything that FE promises and more, as confirmed by Monte-Carlo simulations, which additionally show problems with Plümper and Troeger's FE Vector Decomposition method when data are unbalanced. As well as incorporating time-invariant variables, RE models are readily extendable, with random coefficients, cross-level interactions and complex variance functions. We argue not simply for technical solutions to endogeneity, but for the substantive importance of context/heterogeneity, modeled using RE. The implications extend beyond political science to all multilevel datasets. However, omitted variables could still bias estimated higher-level variable effects; as with any model, care is required in interpretation.

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 anticonservative 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.

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Research Highlights Age, period and cohort (APC) trends cannot be disentangled mechanically  Explicit assumptions must be made for APC models to be identified  Imposing arbitrary assumptions leads to arbitrary model results  Assumptions should be based on strong theory and be stated explicitly AbstractThis commentary discusses the age-period-cohort identification problem. It shows that, despite a plethora of proposed solutions in the literature, no model is able to solve the identification problem because the identification problem is inherent to the real-world processes being modelled. As such, we cast doubt on the conclusions of a number of papers, including one presented here (Page et al., this issue). We conclude with some recommendations for those wanting to model age, period and cohort in a compelling way.3