Use of Composites in Analysis of Individual Time Series: Implications for Person-Specific Dynamic Parameters

A new frontier for studying within-person variability: Bayesian multivariate generalized autoregressive conditional heteroskedasticity models

Research on individual variation has received increased attention. The bulk of the models discussed in psychological research so far, focus mainly on the temporal development of the mean structure. We expand the view on within-person residual variability and present a new model parameterization derived from classic multivariate GARCH models used to predict and forecast volatility in financial time-series. We propose a new pdBEKK and a modified dynamic conditional correlation (DCC) model that accommodate external time-varying predictors for the within-person variance. The main goal of this work is to evaluate the potential usefulness of MGARCH models for research in within-person variability. MGARCH models partition the within-person variance into, at least, 3 components: An overall constant and unconditional baseline variance, a process that introduces variance conditional on previous innovations, or random shocks, and a process that governs the carry-over effects of previous conditional variance, similar to an AR model. These models allow for variance spillover effects from one time-series to another. We illustrate the pdBEKK- and the DCC-MGARCH on two individuals who have rated their daily positive and negative affect over 100 consecutive days. The full models comprised a multivariate ARMA(1,1) model for the means and included physical activity as moderator of the overall baseline variance. Overall, the pdBEKK seems to result in a more straightforward psychological interpretation, but the DCC is generally easier to estimate and can accommodate more simultaneous time-series. Both models require rather large amounts of datapoints to detect nonzero parameters. We provide an R-package bmgarch that facilitates the estimation of these types of models. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Treating random effects as observed versus latent predictors: The bias-variance tradeoff in small samples

Random effects in longitudinal multilevel models represent individuals' deviations from population means and are indicators of individual differences. Researchers are often interested in examining how these random effects predict outcome variables that vary across individuals. This can be done via a two-step approach in which empirical Bayes (EB) estimates of the random effects are extracted and then treated as observed predictor variables in follow-up regression analyses. This approach ignores the unreliability of EB estimates, leading to underestimation of regression coefficients. As such, previous studies have recommended a multilevel structural equation modeling (ML-SEM) approach that treats random effects as latent variables. The current study uses simulation and empirical data to show that a bias-variance tradeoff exists when selecting between the two approaches. ML-SEM produces generally unbiased regression coefficient estimates but also larger standard errors, which can lead to lower power than the two-step approach. Implications of the results for model selection and alternative solutions are discussed.

Dynamic Mixture Modeling with dynr

Mixture modeling is commonly used to model sample heterogeneity by identifying unobserved classes of individuals with similar characteristics. Despite abundance of evidence in the literature suggesting that individuals are often characterized by different dynamic processes underlying their physiological, cognitive, psychological, and behavioral states, applications of dynamic mixture modeling are surprisingly lacking. We present here a proof-of-concept example of dynamic mixture modeling, where latent groups of individuals were identified based on different dynamic patterns in their time series. Our sample consists of 192 men who were in a heterosexual relationship. They were asked to complete a daily questionnaire involving emotions related to their relationship. Two latent groups were identified based on the strength of association between positive (e.g., loving) and negative (e.g., doubtful) affect. Men in the group characterized by a strong negative association (β=-.67) tended to be younger and had higher levels of anxiety toward their relationship than men in the other group, which was characterized by a weaker negative association (β=-.31). We illustrate the specification and estimation of dynamic mixture model using "dynr," an R package capable of handling a broad class of linear and nonlinear discrete- and continuous-time models with regime-switching properties.