Dynamic Factor Analysis for Multivariate Time Series: An Application to Cognitive Trajectories

We propose a dynamic factor model appropriate for large epidemiological studies and develop an estimation algorithm which can handle datasets with large number of subjects and short temporal information. The algorithm uses a two cycle iterative approach for parameter estimation in such a large dataset. Each iteration consists of two distinct cycles, both following an EM algorithm approach. This iterative process will continue until convergence is achieved. We utilized a dataset from the National Alzheimer Coordinating Center (NACC) to estimate underlying measures of cognition based on a battery of observed neuropsychological tests. We assess the goodness of fit and the precision of the dynamic factor model estimators and compare it with a non-dynamic version in which temporal information is not used. The dynamic factor model is superior to a non-dynamic version with respect to fit statistics shown in simulation experiments. Moreover, it has increased power to detect differences in the rate of decline for a given sample size.