Abstract
Longitudinal data are becoming increasingly common in social science research. In this chapter, we discuss methods for exploiting the features of longitudinal data to study causal effects. The methods we discuss are broadly termed fixed effects and random effects models. We begin by discussing some of the advantages of fixed effects models over traditional regression approaches and then present a basic notation for the fixed effects model. This notation serves also as a baseline for introducing the random effects model, a common alternative to the fixed effects approach. After comparing fixed effects and random effects models – paying particular attention to their underlying assumptions – we describe hybrid models that combine attractive features of each. To provide a deeper understanding of these models, and to help researchers determine the most appropriate approach to use when analyzing longitudinal data, we provide three empirical examples. We also briefly discuss several extensions of fixed/random effects models. We conclude by suggesting additional literature that readers may find helpful.
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- 1.
Because time is nested in the units, it might seem more natural to use the notation Y ti instead, as in Raudenbush (2009). We nonetheless follow convention in the fixed effects literature and place the subscript “i” before the “t.”
- 2.
To adjust for inflation across the 10 years of data collection, all wages are standardized using the consumer price index to obtain wages in 1983 dollars.
- 3.
Because our purpose is to compare the results for the fixed effects, random effects, and hybrid models to a simple OLS baseline model, we do not adjust the OLS standard errors for clustering. In any case, adjusting the standard errors scarcely affects the results.
- 4.
A subject-specific coefficient estimates the change in Y for a particular individual if the predictor variable were increased by one unit. A population-averaged coefficient estimates the change in Y for the whole population if the predictor variable were increased by one unit for everyone. The two estimates are equivalent for linear models, but not for nonlinear models, such as logistic regression models (see Allison 2005, chapter 3).
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Firebaugh, G., Warner, C., Massoglia, M. (2013). Fixed Effects, Random Effects, and Hybrid Models for Causal Analysis. In: Morgan, S. (eds) Handbook of Causal Analysis for Social Research. Handbooks of Sociology and Social Research. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6094-3_7
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