Dynamic Factor Analysis Models With Time-Varying Parameters

Dynamic factor analysis models with time-varying parameters offer a valuable tool for evaluating multivariate time series data with time-varying dynamics and/or measurement properties. We use the Dynamic Model of Activation proposed by Zautra and colleagues (Zautra, Potter, Reich, 1997) as a motivating example to construct a dynamic factor model with vector autoregressive relations and time-varying cross-regression parameters at the factor level. Using techniques drawn from the state-space literature, the model was fitted to a set of daily affect data (over 71 days) from 10 participants who had been diagnosed with Parkinson's disease. Our empirical results lend partial support and some potential refinement to the Dynamic Model of Activation with regard to how the time dependencies between positive and negative affects change over time. A simulation study is conducted to examine the performance of the proposed techniques when (a) changes in the time-varying parameters are represented using the true model of change, (b) supposedly time-invariant parameters are represented as time-varying, and (c) the time-varying parameters show discrete shifts that are approximated using an autoregressive model of differences.