Dynamic Factor Analysis Models With Time-Varying Parameters

Abstract

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

Toward a Unified Framework for the Study of Between-Person and Within-Person Structures: Building a Bridge Between Two Research Paradigms

“…Although this is possible with current SEM software, for T ≥ 80 and with several thousand models to be estimated, SEM is no viable alternative for reasons outlined earlier. This is an active field of research and we are optimistic that future software and/or estimation procedures will overcome these limitations (e.g., see Molenaar, 1994;Molenaar, Sinclair, Rovine, Ram, & Corneal, 2009;Chow, Zu, Shifren, & Zhang, 2011, for work on time-varying parameters). For the time being and for the purpose of this article, however, a work-around is needed.…”

Don’t blame the model: Reconsidering the network approach to psychopathology.

“…However, also in this respect the latent variable model as such should not be seen as the root of the problem, as the important contrast is between dynamic and static approaches, not between network and latent variable models. This can be seen in the fact that latent variable models can also account for dynamics in the form of, for example, a dynamic factor model, which can take time dependencies and thus interactions between variables or symptoms over time into account (Chow, Zu, Shifren, & Zhang, 2011;Ferrer & Nesselroade, 2003;Ferrer, Widaman, Card, Selig, & Little, 2008;Molenaar, 1985;Molenaar, De Gooijer, & Schmitz, 1992). Therefore, we propose that instead of the contrast between latent variable models and network models, or the contrast between medical and mental disorders, the focus in psychopathological modeling should be on other contrasts: Most importantly, static vs. dynamic models and symptom-oriented vs. syndrome-oriented approaches.…”

Capturing Context-Related Change in Emotional Dynamics via Fixed Moderated Time Series Analysis

“…Regime-switching models thus allow investigating discontinuous and abrupt changes in model parameters. Other models, on the contrary, evoke a continuous-valued parameter process, for instance a Gaussian AR process, to account for gradual changes in process parameters over time (e.g., Boker, 2015;Chow, Ferrer, & Nesselroade, 2007;Chow et al, 2011;Molenaar, Beltz, Gates, & Wilson, 2016;.…”

“…Complex and changing environments as well as ongoing developmental processes likely relate to variability and change in how we function and, thus, how psychological processes evolve over time (e.g., Hollenstein, LichtwarckAschoff, & Potworowski, 2013;Molenaar, 2004;Nesselroade, 1991). For instance, an individual's emotional dynamics may fluctuate within a certain range (Chow, Zu, Shifren, & Zhang, 2011;Koval & Kuppens, 2011;Ram et al, 2014;Sliwinski, Almeida, Smyth, & Stawski, 2009;Zautra et al, 2002), possibly reflecting "state-dependent regulation" (De Haan-Rietdijk, Gottman, Bergeman, & Hamaker, 2016, p. 217). Furthermore, the possibility of temporal trends in the variability and predictability of affect has received interest in the context of forecasting major regime shifts such as transitions into depression (Scheffer et al, 2009;van de Leemput et al, 2014).…”