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

First-interview response patterns of intensive longitudinal psychological and health data

Self-report data are essential in health psychology research where an individual's perception is critical to understanding one's health and psychological status. Intensive data collection over time, including daily diary assessments, is necessary in understanding within- and between-person variability in health and psychological processes over time. An "initial elevation or latent decline" (IELD) effect, inherent of self-report data, is increasingly acknowledged in the social psychology literature, but awareness of this effect in health psychology research is lacking, particularly in studies that emphasize within- and between-person variability in self-reports. The IELD effect is a pattern in which responses tend to be more extreme at the initial interview relative to subsequent responses. This paper illustrates the impact of IELD in applications of mixed-effects models based on observational self-reports and concludes that researchers take such effects into account in data analysis or in the research designing phase to help mitigate such effects.

A latent variable mixed-effects location scale model that also considers between-person differences in the autocorrelation

In public health research an increasing number of studies is conducted in which intensive longitudinal data is collected in an experience sampling or a daily diary design. Typically, the resulting data is analyzed with a mixed-effects model or mixed-effects location scale model because they allow one to examine a host of interesting longitudinal research questions. Here, we introduce an extension of the mixed-effects location scale model in which measurement error of the observed variables is considered by a latent factor model and in which-in addition to the mean-or location-related effects-the residual variance of the latent factor and the parameters of the autoregressive process of this latent factor can differ between persons. We show how to estimate the parameters of the model with a maximum likelihood approach, whose performance is also compared with a Bayesian approach in a small simulation study. We illustrate the models using a real data example and end with a discussion in which we suggest questions for future research.

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.

Random Effects Multinomial Processing Tree Models: A Maximum Likelihood Approach

The present article proposes and evaluates marginal maximum likelihood (ML) estimation methods for hierarchical multinomial processing tree (MPT) models with random and fixed effects. We assume that an identifiable MPT model with S parameters holds for each participant. Of these S parameters, R parameters are assumed to vary randomly between participants, and the remaining [Formula: see text] parameters are assumed to be fixed. We also propose an extended version of the model that includes effects of covariates on MPT model parameters. Because the likelihood functions of both versions of the model are too complex to be tractable, we propose three numerical methods to approximate the integrals that occur in the likelihood function, namely, the Laplace approximation (LA), adaptive Gauss-Hermite quadrature (AGHQ), and Quasi Monte Carlo (QMC) integration. We compare these three methods in a simulation study and show that AGHQ performs well in terms of both bias and coverage rate. QMC also performs well but the number of responses per participant must be sufficiently large. In contrast, LA fails quite often due to undefined standard errors. We also suggest ML-based methods to test the goodness of fit and to compare models taking model complexity into account. The article closes with an illustrative empirical application and an outlook on possible extensions and future applications of the proposed ML approach.

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 Lasso and a Regression Tree Mixed-Effect Model with Random Effects for the Level, the Residual Variance, and the Autocorrelation

Research in psychology is experiencing a rapid increase in the availability of intensive longitudinal data. To use such data for predicting feelings, beliefs, and behavior, recent methodological work suggested combinations of the longitudinal mixed-effect model with Lasso regression or with regression trees. The present article adds to this literature by suggesting an extension of these models that-in addition to a random effect for the mean level-also includes a random effect for the within-subject variance and a random effect for the autocorrelation. After introducing the extended mixed-effect location scale (E-MELS), the extended mixed-effect location-scale Lasso model (Lasso E-MELS), and the extended mixed-effect location-scale tree model (E-MELS trees), we show how its parameters can be estimated using a marginal maximum likelihood approach. Using real and simulated example data, we illustrate how to use E-MELS, Lasso E-MELS, and E-MELS trees for building prediction models to forecast individuals' daily nervousness. The article is accompanied by an R package (called mels) and functions that support users in the application of the suggested models.

Daily dynamics of grandiose narcissism: distribution, stability, and trait relations of admiration and rivalry states and state contingencies

On the basis of the Narcissistic Admiration and Rivalry Concept and recent theories on narcissistic pursuit of status, we provide a differentiated analysis of individual differences in the within-person dynamics of grandiose narcissism. In two daily diary studies (Sample 1: 56 days; Sample 2: 82 days; total participants: N = 198; total observations: N = 12,404), we investigated the degree, stability, and trait correlates of individual differences in average narcissism-relevant states (perceived status success, perceived admiration and rejection, positive and negative affect, and assertive and hostile behavior) as well as individual differences in within-person contingencies between these states. The results indicated substantial and stable between-person differences in averaged states that were related to their corresponding narcissism trait self-reports. State contingencies showed substantial strength, significant interindividual differences, and stability across the 56 and 82 days, respectively. We only found weak support for associations between state contingencies and trait narcissism self-reports. These findings support a differentiated approach to the conceptualization and assessment of grandiose state narcissism and call for even more comprehensive and fine-grained investigations.

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.

Gimme’s ability to recover group-level path coefficients and individual-level path coefficients

The growing availability of intensive longitudinal data has increased psychological researchers' interest in ideographic-statistical methods that, for example, reveal the contemporaneous or lagged associations between different variables for a specific individual. However, when researchers assess several individuals, the results of such models are difficult to generalize across individuals. Researchers recently suggested an algorithm called GIMME, which allows for the identification of coefficients that exist across all individuals (group-level coefficients) or are specific to one or a subgroup of individuals (individual-level coefficients). In three simulation studies we investigated GIMME's performance in recovering group-level and individual-level coefficients. For the former, we found that GIMME performed well when the magnitude of the parameters was moderate to high and when the number of measurements was sufficiently large. However, GIMME had problems detecting individual-level coefficients or coefficients that occurred for a subset of individuals from the whole sample.

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.