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).

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).

Change in Australian Vitamin A Intakes over Time

BACKGROUND

The mean intake of vitamin A of Australians aged 2 y and older was 300 µg retinol equivalents lower in the 2011-2012 national nutrition survey than in 1995 and decreases preponderated in adults rather than young children.

OBJECTIVE

This aim of this study was to identify the foods associated with this change and to examine how the method used to adjust for within-person variability affects the estimated prevalence of inadequate intakes in both surveys.

METHODS

Foods contributing to vitamin A intake were calculated from the first day of data. The prevalence of inadequate intakes was calculated using a 2-d average, the Iowa State University method, and the National Cancer Institute (NCI) method and either taken from the published reports or calculated using Food Standards Australia New Zealand's in-house software.

RESULTS

In adults, lower consumption of liver, yellow fat spreads, milk products, and carrots and similar root vegetables accounted for most of the change in intake. Vitamin A intake data were less right-skewed in 2011-2012 than in 1995. The prevalence of inadequate vitamin A intake depended on the adjustment method chosen: for example, in 2011-2012 it ranged between 3% and 55% in men aged 19-30 y. The NCI method prevalence (21% for this group) is taken as the preferred estimate of inadequacy because the method adjusts around the mean and accounts for several other sources of variance. However, the NCI method could not be used to analyze the 1995 survey.

CONCLUSIONS

The lower vitamin A intake in Australia was related to changes in retinol intake rather than carotenoid intake and to lower consumption of several different types of food. The estimated prevalence of inadequate intake depends on the statistical method chosen for analysis. A direct measure of vitamin A status is needed to allow conclusions about the implications of the decreasing intake of this vitamin.

Estimation of the salt intake distribution of Dutch kidney transplant recipients using 24-h urinary sodium excretion: the potential of external within-person variance

BACKGROUND

There is growing interest in assessing a population's prevalence of inadequate nutrient intake using biomarkers. However, within-person variation is generally ignored because repeated data collections are considered costly and burdensome.

OBJECTIVES

The study aimed to show the importance of estimating, from repeated 24-h urine collections, a population's habitual salt intake and to explore the potential of using the ratio of within-person variance to total variance from an external source (W:T variance) with single 24-h urine collection.

METHODS

Salt intake was predicted from data for 24-h urinary sodium excretion in adult kidney transplant recipients in 1992-1997 (n = 432) and 2006-2011 (n = 1159). The salt intake distribution of single-day measurements was compared with estimates from multiple 24-h urine collections, which were statistically corrected for within-person variance. Habitual salt intake was also estimated using single-day measurements and external variance estimates. From each distribution, the proportion below specified cut-off values was estimated.

RESULTS

In 2006-2011 the average habitual salt intake was 10.6 g/d (men) and 8.5 g/d (women); in 1992-1997 these values were 8.6 g/d and 7.5 g/d, respectively. The proportion with salt intake <6 g/d was 5% and 13% in 2006-2011 and 22% and 28% in 1992-1997, respectively, for men and women. Correction for within-person variance significantly narrowed the salt intake distribution-the proportion with salt intake <6 g/d was overestimated by 3-13 percentage points using single-day data. Sensitivity analyses showed the importance of a sufficient sample size for estimating variance components. Variation of the W:T variance showed up to 40 percentage points deviation in the proportion with intakes below a specified cut-off value.

CONCLUSIONS

To estimate a population's salt intake distribution, it is important to correct 24-h urinary sodium excretion for within-person variance. Predicting habitual salt intake distribution using single-day measurements with external variances is promising; a sensitivity analysis is recommended to show the effect of different external variances.

Examining Population Differences in Within-Person Variability in Longitudinal Designs Using Latent Variable Modeling: An Application to the Study of Cognitive Functioning of Older Adults

Longitudinal studies have steadily grown in popularity across the educational and behavioral sciences, particularly with the increased availability of technological devices that allow the easy collection of repeated measures on multiple dimensions of substantive relevance. This article discusses a procedure that can be used to evaluate population differences in within-person (intraindividual) variability in such longitudinal investigations. The method is based on an application of the latent variable modeling methodology within a two-level modeling framework. The approach is used to obtain point and interval estimates of the differences in within-person variance and in the strength of correlative effects of repeated measures between normal and very mildly demented persons in a longitudinal study of a diagnostic cognitive test assessing verbal episodic memory.