“Longitudinal” or “panel” data includes some repeated surveys of the same people over time. Sharon Lohr’s book describes examples such as the CPS:
Once a household is recruited to be in a panel survey such as the U.S. Current Population Survey, which measures characteristics related to employment, it stays in the survey for subsequent interviews.
The new-in-the-third-edition chapter on nonprobability samples also describes online web panels:
An online panel is a group of persons who have been recruited by a survey organization for the purpose of taking surveys. Then, when a topic comes up for which polling is desired, the organization asks a sample of persons from the panel who meet the survey criteria to take the poll.
The panel data structure can be incorporated into models in various ways. For example, a hierarchical (i.e. multilevel) model can include an unobserved person-level effect. As Gelman et al. write in BDA p.21:
In general, we prefer to model complexity with a hierarchical structure using additional variables rather than with complicated marginal distributions, even when the additional variables are unobserved or even unobservable; this theme underlies mixture models…
But as Antonelli et al. (2016) and Fitzmaurice et al. p.39 write:
For linear mixed-effect models … deviations from the normality assumptions for the random effects have very little impact on the estimation of the fixed-effects parameters…For non-linear and generalized linear mixed models, misspecification of the random-effects distribution can lead to seriously biased estimates for the fixed-effects parameters.
In much of survey research, variables of interest are discrete, e.g. vote choice. So we would fit non-linear models, where the cautions above apply. How do most survey practitioners analyze longitudinal binary data ?
(I asked about this in stan discourse back in 2022 but could use more guidance.)
