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.

Lost Dynamics and the Dynamics of Loss: Longitudinal Compression of Brain Signal Variability is Coupled with Declines in Functional Integration and Cognitive Performance.

Reduced moment-to-moment blood oxygen level-dependent (BOLD) signal variability has been consistently linked to advanced age and poorer cognitive performance, showing potential as a functional marker of brain aging. To date, however, this promise has rested exclusively on cross-sectional comparisons. In a sample of 74 healthy adults, we provide the first longitudinal evidence linking individual differences in BOLD variability, age, and performance across multiple cognitive domains over an average period of 2.5 years. As expected, those expressing greater loss of BOLD variability also exhibited greater decline in cognition. The fronto-striato-thalamic system emerged as a core neural substrate for these change-change associations. Preservation of signal variability within regions of the fronto-striato-thalamic system also cohered with preservation of functional integration across regions of this system, suggesting that longitudinal maintenance of "local" dynamics may require across-region communication. We therefore propose this neural system as a primary target in future longitudinal studies on the neural substrates of cognitive aging. Given that longitudinal change-change associations between brain and cognition are notoriously difficult to detect, the presence of such an association within a relatively short follow-up period bolsters the promise of brain signal variability as a viable, experimentally sensitive probe for studying individual differences in human cognitive aging.

: An R Package for performing kernel change point detection on the running statistics of multivariate time series.

In many scientific disciplines, researchers are interested in discovering when complex systems such as stock markets, the weather or the human body display abrupt changes. Essentially, this often comes down to detecting whether a multivariate time series contains abrupt changes in one or more statistics, such as means, variances or pairwise correlations. To assist researchers in this endeavor, this paper presents the package for performing kernel change point (KCP) detection on user-selected running statistics of multivariate time series. The running statistics are extracted by sliding a window across the time series and computing the value of the statistic(s) of interest in each window. Next, the similarities of the running values are assessed using a Gaussian kernel, and change points that segment the time series into maximally homogeneous phases are located by minimizing a within-phase variance criterion. To decide on the number of change points, a combination of a permutation-based significance test and a grid search is provided. stands out among the variety of change point detection packages available in because it can be easily adapted to uncover changes in any user-selected statistic without imposing any distribution on the data. To exhibit the usefulness of the package, two empirical examples are provided pertaining to two types of physiological data.

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.

Detecting long-lived autodependency changes in a multivariate system via change point detection and regime switching models.

Long-lived simultaneous changes in the autodependency of dynamic system variables characterize crucial events as epileptic seizures and volcanic eruptions and are expected to precede psychiatric conditions. To understand and predict such phenomena, methods are needed that detect such changes in multivariate time series. We put forward two methods: First, we propose KCP-AR, a novel adaptation of the general-purpose KCP (Kernel Change Point) method. Whereas KCP is implemented on the raw data and does not shed light on which parameter changed, KCP-AR is applied to the running autocorrelations, allowing to focus on changes in this parameter. Second, we revisit the regime switching AR(1) approach and propose to fit models wherein only the parameters capturing autodependency differ across the regimes. We perform a simulation study comparing both methods: KCP-AR outperforms regime switching AR(1) when variables are uncorrelated, while the latter is more reliable when multicolinearity is severe. Regime switching AR(1), however, may yield recurrent switches even when the change is long-lived. We discuss an application to psychopathology data where we investigate whether emotional inertia -the autodependency of affective states- changes before a relapse into depression.

Measurement invariance within and between individuals: a distinct problem in testing the equivalence of intra- and inter-individual model structures.

We address the question of equivalence between modeling results obtained on intra-individual and inter-individual levels of psychometric analysis. Our focus is on the concept of measurement invariance and the role it may play in this context. We discuss this in general against the background of the latent variable paradigm, complemented by an operational demonstration in terms of a linear state-space model, i.e., a time series model with latent variables. Implemented in a multiple-occasion and multiple-subject setting, the model simultaneously accounts for intra-individual and inter-individual differences. We consider the conditions-in terms of invariance constraints-under which modeling results are generalizable (a) over time within subjects, (b) over subjects within occasions, and (c) over time and subjects simultaneously thus implying an equivalence-relationship between both dimensions. Since we distinguish the measurement model from the structural model governing relations between the latent variables of interest, we decompose the invariance constraints into those that involve structural parameters and those that involve measurement parameters and relate to measurement invariance. Within the resulting taxonomy of models, we show that, under the condition of measurement invariance over time and subjects, there exists a form of structural equivalence between levels of analysis that is distinct from full structural equivalence, i.e., ergodicity. We demonstrate how measurement invariance between and within subjects can be tested in the context of high-frequency repeated measures in personality research. Finally, we relate problems of measurement variance to problems of non-ergodicity as currently discussed and approached in the literature.