Chapter 9 Longitudinal regression
We describe how to perform inference in longitudinal/panel models using a Bayesian framework. In this context, multiple cross-sectional units are observed repeatedly over time, a structure referred to as panel data by econometricians and longitudinal data by statisticians. Specifically, we present models for continuous (normal), binary (logit), and count (Poisson) responses. Applications and exercises illustrate the potential of these models.
In longitudinal/panel data sets, we have yit where i=1,2,…,N and t=1,2,…,Ti. If Ti=T for all i, the dataset is balanced; otherwise, it is unbalanced. Longitudinal data typically involves by far more cross-sectional units than time periods, this is called typically a short panel. It assumes that cross-sectional units are independent, though serial correlation exists within each unit over time, and unobserved heterogeneity for each unit must be accounted for. We can treat this unobserved heterogeneity as random variables, assuming it is either independent or dependent on control variables. Econometricians refer to these cases as random effects and fixed effects, respectively. The Bayesian literature takes a different approach, modeling the panel structure hierarchically, where the unobserved heterogeneity may or may not depend on other controls.51.
Remember that we can run our GUI typing shiny::runGitHub("besmarter/BSTApp", launch.browser=T) in the R console or any R code editor and execute it. However, users should see Chapter 5 for details.