  High-dimensional multivariate longitudinal data, which arise when many
outcome variables are measured repeatedly over time, are becoming increasingly
common in social, behavioral and health sciences. We propose a latent variable
model for drawing statistical inferences on covariate effects and predicting
future outcomes based on high-dimensional multivariate longitudinal data. This
model introduces unobserved factors to account for the between-variable and
across-time dependence and assist the prediction. Statistical inference and
prediction tools are developed under a general setting that allows outcome
variables to be of mixed types and possibly unobserved for certain time points,
for example, due to right censoring. A central limit theorem is established for
drawing statistical inferences on regression coefficients. Additionally, an
information criterion is introduced to choose the number of factors. The
proposed model is applied to customer grocery shopping records to predict and
understand shopping behavior.
