How is Autoregressive Model used in longitudinal data analysis?

Question

I know that in the analysis of time series, Auto-regressive Model such as AR(1) is frequently used. In the context of time series, there is no covariate (or the only covariate is time). In the context of longitudinal data analysis, covariate and response are given. I am just wondering if the technique in time series analysis such as AR(1) are used in longitudinal data analysis.

Answer 1

$AR(1)$ is one the most common models in longitudinal data, as unlike in time series where you have a lot realizations of the same process, in longitudinal data you usually have very few realization of multiple processes. Therefore, you don't have enough repeated measurements in order to perform valuable estimation of complex $ARMA(p,q)$ structures (large $p$ and $q$). In econometric analysis it us pretty common to find models like $$ y_{t+1}=\beta_0 + \beta_1y_{t} + \beta_2x+\epsilon_t, $$
that is, you have $AR(1)$ process as a part of the regression.