Collinearity Issues in Autoregressive Models with Time-Varying Serially Dependent Covariates.

First-order autoregressive models are popular to assess the temporal dynamics of a univariate process. Researchers often extend these models to include time-varying covariates, such as contextual factors, to investigate how they moderate processes' dynamics. We demonstrate that doing so has implications for how well one can estimate the autoregressive and covariate effects, as serial dependence in the variables can imply predictor collinearity. This is a noteworthy contribution, since in current practice serial dependence in a time-varying covariate is rarely considered important. We first recapitulate the role of predictor collinearity for estimation precision in an ordinary least squares context, by discussing how it affects estimator variances, covariances and correlations. We then derive a general formula detailing how predictor collinearity in first-order autoregressive models is impacted by serial dependence in the covariate. We provide a simulation study to illustrate the implications of the formula for different types of covariates. The simulation results highlight when the collinearity issue becomes severe enough to hamper interpretation of the effects. We also show that the effect estimates can be biased in small samples (i.e., 50 time points). Implications for study design, the use of time as a predictor, and related model variants are discussed.

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

Much of recent affect research relies on intensive longitudinal studies to assess daily emotional experiences. The resulting data are analyzed with dynamic models to capture regulatory processes involved in emotional functioning. Daily contexts, however, are commonly ignored. This may not only result in biased parameter estimates and wrong conclusions, but also ignores the opportunity to investigate contextual effects on emotional dynamics. With fixed moderated time series analysis, we present an approach that resolves this problem by estimating context-dependent change in dynamic parameters in single-subject time series models. The approach examines parameter changes of known shape and thus addresses the problem of observed intra-individual heterogeneity (e.g., changes in emotional dynamics due to observed changes in daily stress). In comparison to existing approaches to unobserved heterogeneity, model estimation is facilitated and different forms of change can readily be accommodated. We demonstrate the approach's viability given relatively short time series by means of a simulation study. In addition, we present an empirical application, targeting the joint dynamics of affect and stress and how these co-vary with daily events. We discuss potentials and limitations of the approach and close with an outlook on the broader implications for understanding emotional adaption and development.

Optimal sampling rates for reliable continuous-time first-order autoregressive and vector autoregressive modeling.

Autoregressive and vector autoregressive models are a driving force in current psychological research. In affect research they are, for instance, frequently used to formalize affective processes and estimate affective dynamics. Discrete-time model variants are most commonly used, but continuous-time formulations are gaining popularity, because they can handle data from longitudinal studies in which the sampling rate varies within the study period, and yield results that can be compared across data sets from studies with different sampling rates. However, whether and how the sampling rate affects the quality with which such continuous-time models can be estimated, has largely been ignored in the literature. In the present article, we show how the sampling rate affects the estimation reliability (i.e., the standard errors of the parameter estimators, with smaller values indicating higher reliability) of continuous-time autoregressive and vector autoregressive models. Moreover, we determine which sampling rates are optimal in the sense that they lead to standard errors of minimal size (subject to the assumption that the models are correct). Our results are based on the theories of optimal design and maximum likelihood estimation. We illustrate them making use of data from the COGITO Study. We formulate recommendations for study planning, and elaborate on strengths and limitations of our approach. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Time series analysis of intensive longitudinal data in psychosomatic research: A methodological overview.

Time series analysis of intensive longitudinal data provides the psychological literature with a powerful tool for assessing how psychological processes evolve through time. Recent applications in the field of psychosomatic research have provided insights into the dynamical nature of the relationship between somatic symptoms, physiological measures, and emotional states. These promising results highlight the intrinsic value of employing time series analysis, although application comes with some important challenges. This paper aims to present an approachable, non-technical overview of the state of the art on these challenges and the solutions that have been proposed, with emphasis on application towards psychosomatic hypotheses. Specifically, we elaborate on issues related to measurement intervals, the number and nature of the variables used in the analysis, modeling stable and changing processes, concurrent relationships, and extending time series analysis to incorporate the data of multiple individuals. We also briefly discuss some general modeling issues, such as lag-specification, sample size and time series length, and the role of measurement errors. We hope to arm applied researchers with an overview from which to select appropriate techniques from the ever growing variety of time series analysis approaches.