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

• Published in: Psychometrika Vol. 87; no. 2; pp. 506 - 532
• Main Authors: Nestler, Steffen, Humberg, Sarah
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2022; Springer Nature B.V
• Subjects: Assessment; Behavioral Science and Psychology; Forecasting with Intensive Longitudinal Data; Humanities; Humans; Intelligence tests; Law; Likelihood Functions; Maximum Likelihood Statistics; Neural networks; Parameter estimation; Personality; Personality traits; Prediction models; Psychology; Psychometrics; Resistance (Psychology); Statistical Theory and Methods; Statistics for Social Sciences; Support vector machines; Teaching methods; Testing and Evaluation; Theory and Methods; Variables; lasso regression; regression trees; mixed-effect models; within-person variability; longitudinal data
• DOI: 10.1007/s11336-021-09787-w
• ISSN: 0033-3123; 1860-0980

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.