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.

Increasing numbers of comparative survey datasets span multiple waves. Moving beyond purely cross-sectional analyses, multilevel longitudinal analyses of such datasets should generate substantively important insights into the political, social and economic correlates of many individual-level outcomes of interest (attitudes, behaviors, etc.). This article describes two simple techniques for extracting such insights, which allow change over time in y to be a function of change over time in x and/or of a time-invariant x. The article presents results from simulation studies that assess the techniques in the presence of complications that are likely to arise with real-world data, and concludes with applications to the issues of generalized social trust and postmaterialist values, using data from World/European Values Surveys.

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