scholarly journals A Mixed-Effects Location Scale Model for Dyadic Interactions

2018 ◽  
Author(s):  
Philippe Rast ◽  
Emilio Ferrer
Keyword(s):  
Monte Carlo ◽  
Random Effects ◽  
Monte Carlo Methods ◽  
Negative Emotions ◽  
Mixed Effects ◽  
Individual Variability ◽  
Scale Model ◽  
Dyadic Interactions ◽  
Scale Parameters ◽  
Mean Structures

We present a mixed-effects location scale model (MELSM) for examining thedaily dynamics of affect in dyads. The MELSM includes person and timevarying variables to predict the location, or individual means, and the scale,or within-person variances. It also incorporates a sub-model to account forbetween-person variances. The dyadic specification can accommodate individual and partner effects in both the location and the scale components,and allows random effects for all location and scale parameters. All covariances among the random effects, within and across the location and the scaleare also estimated. These covariances offer new insights into the interplayof individual mean structures, intra-individual variability, and the influenceof partner effects on such factors. To illustrate the model, we use data from274 couples who provided daily ratings on their positive and negative emotions toward their relationship – up to 90 consecutive days. The model is fitusing Hamiltonian Monte Carlo methods, and includes subsets of predictorsin order to demonstrate the flexibility of this approach. We conclude witha discussion on the usefulness and the limitations of the MELSM for dyadicresearch.

scholarly journals A Bayesian Nonlinear Mixed-Effects Location Scale Model for Learning

2018 ◽  
Author(s):  
Donald Ray Williams ◽  
Philippe Rast
Keyword(s):  
Random Effects ◽  
Verbal Memory ◽  
Predictive Accuracy ◽  
Age Groups ◽  
Nonlinear Function ◽  
Mixed Effects ◽  
Individual Variability ◽  
Scale Model ◽  
Nonlinear Mixed Effects ◽  
Context Of 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 while in the process learning. It incorporates a sub-model that can predictnonlinear parameters for the location and/or 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 because it provides the necessaryand 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 discussingthe usefulness, limitations, and future directions of the NL-MELSM.

scholarly journals A Mixed-Effects Location Scale Model for Dyadic Interactions

2018 ◽  
Vol 53 (5) ◽  
pp. 756-775 ◽  
Author(s):  
Philippe Rast ◽  
Emilio Ferrer
Keyword(s):  
Mixed Effects ◽  
Scale Model ◽  
Dyadic Interactions

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

2020 ◽  
Vol 36 (6) ◽  
pp. 981-997
Author(s):  
Donald R. Williams ◽  
Stephen R. Martin ◽  
Siwei Liu ◽  
Philippe Rast
Keyword(s):  
Physical Activity ◽  
Hypothesis Testing ◽  
Personality Traits ◽  
Random Effects ◽  
Mixed Effects ◽  
Scale Model ◽  
Affective Traits ◽  
Personality Research ◽  
Scale Modeling ◽  
Fully Bayesian

Abstract. 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.

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

2019 ◽  
Author(s):  
Donald Ray Williams ◽  
Siwei Liu ◽  
Stephen Ross Martin ◽  
Philippe Rast
Keyword(s):  
Hypothesis Testing ◽  
Personality Traits ◽  
Random Effects ◽  
Mixed Effects ◽  
Scale Model ◽  
Affective Traits ◽  
Personality Research ◽  
Scale Modeling ◽  
Fully Bayesian ◽  
Experience Sampling Methods

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 personality traits and the corresponding states. We take a \textit{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 psychical 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.

Modeling Intraindividual Variability in Three-Level Multilevel Models

Methodology ◽  
2018 ◽  
Vol 14 (3) ◽  
pp. 95-108 ◽  
Author(s):  
Steffen Nestler ◽  
Katharina Geukes ◽  
Mitja D. Back
Keyword(s):  
Multilevel Model ◽  
Multilevel Models ◽  
Mixed Effects ◽  
Repeated Measurements ◽  
Scale Model ◽  
Suggested Approach ◽  
Psychological Study ◽  
Level Data ◽  
Ecological Momentary ◽  
Momentary Assessment

Abstract. The mixed-effects location scale model is an extension of a multilevel model for longitudinal data. It allows covariates to affect both the within-subject variance and the between-subject variance (i.e., the intercept variance) beyond their influence on the means. Typically, the model is applied to two-level data (e.g., the repeated measurements of persons), although researchers are often faced with three-level data (e.g., the repeated measurements of persons within specific situations). Here, we describe an extension of the two-level mixed-effects location scale model to such three-level data. Furthermore, we show how the suggested model can be estimated with Bayesian software, and we present the results of a small simulation study that was conducted to investigate the statistical properties of the suggested approach. Finally, we illustrate the approach by presenting an example from a psychological study that employed ecological momentary assessment.

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