A Mixed-Effects Location Scale Model for Dyadic Interactions

A Mixed-Effects Model in Which the Parameters of the Autocorrelated Error Structure Can Differ between Individuals

Research in psychology has seen a rapid increase in the usage of experience sampling methods and daily diary methods. The data that result from using these methods are typically analyzed with a mixed-effects or a multilevel model because it allows testing hypotheses about the time course of the longitudinally assessed variable or the influence of time-varying predictors in a simple way. Here, we describe an extension of this model that does not only allow to include random effects for the mean structure but also for the residual variance, for the parameter of an autoregressive process of order 1 and/or the parameter of a moving average process of order 1. After we have introduced this extension, we show how to estimate the parameters with maximum likelihood. Because the likelihood function contains complex integrals, we suggest using adaptive Gauss-Hermite quadrature and Quasi-Monte Carlo integration to approximate it. We illustrate the models using a real data example and also report the results of a small simulation study in which the two integral approximation methods are compared.

Infant-directed speech does not always involve exaggerated vowel distinctions: Evidence from Danish

This study compared the acoustic properties of 26 (100% female, 100% monolingual) Danish caregivers' spontaneous speech addressed to their 11- to 24-month-old infants (infant-directed speech, IDS) and an adult experimenter (adult-directed speech, ADS). The data were collected between 2016 and 2018 in Aarhus, Denmark. Prosodic properties of Danish IDS conformed to cross-linguistic patterns, with a higher pitch, greater pitch variability, and slower articulation rate than ADS. However, an acoustic analysis of vocalic properties revealed that Danish IDS had a reduced or similar vowel space, higher within-vowel variability, raised formants, and lower degree of vowel discriminability compared to ADS. None of the measures, except articulation rate, showed age-related differences. These results push for future research to conduct theory-driven comparisons across languages with distinct phonological systems.

Emotional (in)stability: Neuroticism is associated with increased variability in negative emotion after all

The personality trait neuroticism is tightly linked to mental health, and neurotic people experience stronger negative emotions in everyday life. But, do their negative emotions also show greater fluctuation? This commonsensical notion was recently questioned by [Kalokerinos et al. Proc Natl Acad Sci USA 112, 15838-15843 (2020)], who suggested that the associations found in previous studies were spurious. Less neurotic people often report very low levels of negative emotion, which is usually measured with bounded rating scales. Therefore, they often pick the lowest possible response option, which severely constrains the amount of emotional variability that can be observed in principle. Applying a multistep statistical procedure that is supposed to correct for this dependency, [Kalokerinos et al. Proc Natl Acad Sci USA 112, 15838-15843 (2020)] no longer found an association between neuroticism and emotional variability. However, like other common approaches for controlling for undesirable effects due to bounded scales, this method is opaque with respect to the assumed mechanism of data generation and might not result in a successful correction. We thus suggest an alternative approach that a) takes into account that emotional states outside of the scale bounds can occur and b) models associations between neuroticism and both the mean and variability of emotion in a single step with the help of Bayesian censored location-scale models. Simulations supported this model over alternative approaches. We analyzed 13 longitudinal datasets (2,518 individuals and 11,170 measurements in total) and found clear evidence that more neurotic people experience greater variability in negative emotion.

The Reliability Factor: Modeling Individual Reliability with Multiple Items from a Single Assessment

Reliability is a crucial concept in psychometrics. Although it is typically estimated as a single fixed quantity, previous work suggests that reliability can vary across persons, groups, and covariates. We propose a novel method for estimating and modeling case-specific reliability without repeated measurements or parallel tests. The proposed method employs a "Reliability Factor" that models the error variance of each case across multiple indicators, thereby producing case-specific reliability estimates. Additionally, we use Gaussian process modeling to estimate a nonlinear, non-monotonic function between the latent factor itself and the reliability of the measure, providing an analogue to test information functions in item response theory. The reliability factor model is a new tool for examining latent regions with poor conditional reliability, and correlates thereof, in a classical test theory framework.

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).

A systematic review and Bayesian meta-analysis of the development of turn taking in adult-child vocal interactions

Fluent conversation requires temporal organization between conversational exchanges. By performing a systematic review and Bayesian multi-level meta-analysis, we map the trajectory of infants' turn-taking abilities over the course of early development (0 to 70 months). We synthesize the evidence from 26 studies (78 estimates from 429 unique infants, of which at least 152 are female) reporting response latencies in infant-adult dyadic interactions. The data were collected between 1975 and 2019, exclusively in North America and Europe. Infants took on average circa 1 s to respond, and the evidence of changes in response over time was inconclusive. Infants' response latencies are related to those of their adult conversational partners: an increase of 1 s in adult response latency (e.g., 400 to 1400 ms) would be related to an increase of over 1 s in infant response latency (from 600 to 1857 ms). These results highlight the dynamic reciprocity involved in the temporal organization of turn-taking. Based on these results, we provide recommendations for future avenues of enquiry: studies should analyze how turn-by-turn exchanges develop on a longitudinal timescale, with rich assessment of infants' linguistic and social development.

Catching Up on Multilevel Modeling

This review focuses on the use of multilevel models in psychology and other social sciences. We target readers who are catching up on current best practices and sources of controversy in the specification of multilevel models. We first describe common use cases for clustered, longitudinal, and cross-classified designs, as well as their combinations. Using examples from both clustered and longitudinal designs, we then address issues of centering for observed predictor variables: its use in creating interpretable fixed and random effects of predictors, its relationship to endogeneity problems (correlations between predictors and model error terms), and its translation into multivariate multilevel models (using latent-centering within multilevel structural equation models). Finally, we describe novel extensions—mixed-effects location–scale models—designed for predicting differential amounts of variability.

An extension of the mixed-effects growth model that considers between-person differences in the within-subject variance and the autocorrelation

Experience sampling methods have led to a significant increase in the availability of intensive longitudinal data. Typically, this type of data is analyzed with a mixed-effects model that allows to examine hypotheses concerning between-person differences in the mean structure by including multiple random effects per individual (eg, random intercept and random slopes). Here, we describe an extension of this model that-in addition to the random effects for the mean structure-also includes a random effect for the within-subject variance and a random effect for the autocorrelation. After the description of the model, we show how its parameters can be efficiently estimated using a marginal maximum likelihood (ML) approach. We then illustrate the model using a real data example. We also present the results of a small simulation study in which we compare the ML approach with a Bayesian estimation approach.

Beneath the surface: Unearthing within-person variability and mean relations with Bayesian mixed models

Mixed-effects models are becoming common in psychological science. Although they have many desirable features, there is still untapped potential. It is customary to view homogeneous variance as an assumption to satisfy. We argue to move beyond that perspective, and to view modeling within-person variance as an opportunity to gain a richer understanding of psychological processes. The technique to do so is based on the mixed-effects location scale model that can simultaneously estimate mixed-effects submodels to both the mean (location) and within-person variance (scale). We develop a framework that goes beyond assessing the submodels in isolation of one another and introduce a novel Bayesian hypothesis test for mean-variance correlations in the distribution of random effects. We first present a motivating example, which makes clear how the model can characterize mean-variance relations. We then apply the method to reaction times (RTs) gathered from 2 cognitive inhibition tasks. We find there are more individual differences in the within-person variance than the mean structure, as well as a complex web of structural mean-variance relations. This stands in contrast to the dominant view of within-person variance (i.e., "noise"). The results also point toward paradoxical within-person, as opposed to between-person, effects: several people had slower and less variable incongruent responses. This contradicts the typical pattern, wherein larger means tend to be associated with more variability. We conclude with future directions, spanning from methodological to theoretical inquires, that can be answered with the presented methodology. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Modelling inter-individual differences in latent within-person variation: The confirmatory factor level variability model

Psychological theories often produce hypotheses that pertain to individual differences in within-person variability. To empirically test the predictions entailed by such hypotheses with longitudinal data, researchers often use multilevel approaches that allow them to model between-person differences in the mean level of a certain variable and the residual within-person variance. Currently, these approaches can be applied only when the data stem from a single variable. However, it is common practice in psychology to assess not just a single measure but rather several measures of a construct. In this paper we describe a model in which we combine the single-indicator model with confirmatory factor analysis. The new model allows individual differences in latent mean-level factors and latent within-person variability factors to be estimated. Furthermore, we show how the model's parameters can be estimated with a maximum likelihood estimator, and we illustrate the approach using an example that involves intensive longitudinal data.

Bayesian Multivariate Mixed-Effects Location Scale Modeling of Longitudinal Relations Among Affective Traits, States, and Physical Activity

Intensive longitudinal studies and experience sampling methods are becoming more common in psychology. While they provide a unique opportunity to ask novel questions about within-person processes relating to personality, there is a lack of methods specifically built to characterize the interplay between traits and states. We thus introduce a Bayesian multivariate mixed-effects location scale model (M-MELSM). The formulation can simultaneously model both personality traits (the location) and states (the scale) for multivariate data common to personality research. Variables can be included to predict either (or both) the traits and states, in addition to estimating random effects therein. This provides correlations between location and scale random effects, both across and within each outcome, which allows for characterizing relations between any number of personality traits and the corresponding states. We take a fully Bayesian approach, not only to make estimation possible, but also because it provides the necessary information for use in psychological applications such as hypothesis testing. To illustrate the model we use data from 194 individuals that provided daily ratings of negative and positive affect, as well as their physical activity in the form of step counts over 100 consecutive days. We describe the fitted model, where we emphasize, with visualization, the richness of information provided by the M-MELSM. We demonstrate Bayesian hypothesis testing for the correlations between the random effects. We conclude by discussing limitations of the MELSM in general and extensions to the M-MELSM specifically for personality research.

A Bayesian nonlinear mixed-effects location scale model for learning

We present a Bayesian nonlinear mixed-effects location scale model (NL-MELSM). The NL-MELSM allows for fitting nonlinear functions to the location, or individual means, and the scale, or within-person variance. Specifically, in the context of learning, this model allows the within-person variance to follow a nonlinear trajectory, where it can be determined whether variability reduces during learning. It incorporates a sub-model that can predict nonlinear parameters for both the location and scale. This specification estimates random effects for all nonlinear location and scale parameters that are drawn from a common multivariate distribution. This allows estimation of covariances among the random effects, within and across the location and the scale. These covariances offer new insights into the interplay between individual mean structures and intra-individual variability in nonlinear parameters. We take a fully Bayesian approach, not only for ease of estimation but also for inference because it provides the necessary and consistent information for use in psychological applications, such as model selection and hypothesis testing. To illustrate the model, we use data from 333 individuals, consisting of three age groups, who participated in five learning trials that assessed verbal memory. In an exploratory context, we demonstrate that fitting a nonlinear function to the within-person variance, and allowing for individual variation therein, improves predictive accuracy compared to customary modeling techniques (e.g., assuming constant variance). We conclude by discussing the usefulness, limitations, and future directions of the NL-MELSM.