Catching Up on Multilevel Modeling

2022 ◽  
Vol 73 (1) ◽  
pp. 659-689
Author(s):  
Lesa Hoffman ◽  
Ryan W. Walters
Keyword(s):  
Best Practices ◽  
Structural Equation ◽  
Multilevel Models ◽  
Structural Equation Models ◽  
Catching Up ◽  
Scale Models ◽  
Fixed And Random Effects ◽  
Error Terms ◽  
Multilevel Structural Equation ◽  
Multivariate Multilevel Models

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.

scholarly journals Catching Up on Multilevel Modeling (in press, Annual Review of Psychology)

2021 ◽  
Author(s):  
Lesa Hoffman ◽  
Ryan W. Walters
Keyword(s):  
Multilevel Modeling ◽  
Structural Equation ◽  
Multilevel Models ◽  
Structural Equation Models ◽  
Annual Review ◽  
Catching Up ◽  
Scale Models ◽  
Fixed And Random Effects ◽  
Error Terms ◽  
Introductory Textbooks

The present review focuses on the use of multilevel models in psychology and other social sciences. We target readers aiming to get up to speed 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, 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 online supplement provides suggested introductory textbooks for getting started with multilevel modeling.

scholarly journals On the Interpretation of Parameters in Multivariate Multilevel Models Across Different Combinations of Model Specification and Estimation

2019 ◽  
Vol 2 (3) ◽  
pp. 288-311 ◽  
Author(s):  
Lesa Hoffman
Keyword(s):  
Latent Variables ◽  
Structural Equation ◽  
Multilevel Models ◽  
Structural Equation Models ◽  
Simulated Data ◽  
Recent Change ◽  
Model Specification ◽  
Predictor Variables ◽  
Random Slopes ◽  
Multivariate Multilevel Models

The increasing availability of software with which to estimate multivariate multilevel models (also called multilevel structural equation models) makes it easier than ever before to leverage these powerful techniques to answer research questions at multiple levels of analysis simultaneously. However, interpretation can be tricky given that different choices for centering model predictors can lead to different versions of what appear to be the same parameters; this is especially the case when the predictors are latent variables created through model-estimated variance components. A further complication is a recent change to Mplus (Version 8.1), a popular software program for estimating multivariate multilevel models, in which the selection of Bayesian estimation instead of maximum likelihood results in different lower-level predictors when random slopes are requested. This article provides a detailed explication of how the parameters of multilevel models differ as a function of the analyst’s decisions regarding centering and the form of lower-level predictors (i.e., observed or latent), the method of estimation, and the variant of program syntax used. After explaining how different methods of centering lower-level observed predictor variables result in different higher-level effects within univariate multilevel models, this article uses simulated data to demonstrate how these same concepts apply in specifying multivariate multilevel models with latent lower-level predictor variables. Complete data, input, and output files for all of the example models have been made available online to further aid readers in accurately translating these central tenets of multivariate multilevel modeling into practice.

A Between- and Within-Person Analysis of Parenting and Time Spent in Criminogenic Settings During Adolescence: The Role of Self-Control and Delinquent Attitudes

2016 ◽  
Vol 50 (2) ◽  
pp. 229-254 ◽  
Author(s):  
Heleen J. Janssen ◽  
Gerben J. N. Bruinsma ◽  
Maja Deković ◽  
Veroni I. Eichelsheim
Keyword(s):  
Panel Data ◽  
Indirect Effects ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Physical Characteristics ◽  
Self Control ◽  
Adolescent Delinquency ◽  
Multilevel Structural Equation

Although spending time in criminogenic settings is increasingly recognized as an explanation for adolescent delinquency, little is known about its determinants. The current study aims to examine the extent to which (change in) self-control and (change in) delinquent attitudes relate to (change in) time spent in criminogenic settings, and the extent to which they mediate the effects of (change in) parenting. Time spent in criminogenic settings was measured comprehensively, by including social and physical characteristics of micro settings (200 × 200 meters). Multilevel structural equation models on two waves of panel data on 603 adolescents (aged 12-19) showed that self-control and delinquent attitudes contributed to between-person differences in time spent in criminogenic settings. Within-person increases in time spent in such settings were predicted by increased delinquent attitudes. For indirect effects, self-control partially mediated between-person effects of parenting, whereas delinquent attitudes partially mediated both between- and within-person effects.

scholarly journals The Impact of Intraclass Correlation on the Effectiveness of Level-Specific Fit Indices in Multilevel Structural Equation Modeling

2016 ◽  
Vol 77 (1) ◽  
pp. 5-31 ◽  
Author(s):  
Hsien-Yuan Hsu ◽  
Jr-Hung Lin ◽  
Oi-Man Kwok ◽  
Sandra Acosta ◽  
Victor Willson
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Intraclass Correlation ◽  
Monte Carlo Study ◽  
Multilevel Structural Equation Modeling ◽  
Equation Modeling ◽  
Saturated Model ◽  
Fit Indices ◽  
The Impact ◽  
Multilevel Structural Equation

Several researchers have recommended that level-specific fit indices should be applied to detect the lack of model fit at any level in multilevel structural equation models. Although we concur with their view, we note that these studies did not sufficiently consider the impact of intraclass correlation (ICC) on the performance of level-specific fit indices. Our study proposed to fill this gap in the methodological literature. A Monte Carlo study was conducted to investigate the performance of (a) level-specific fit indices derived by a partially saturated model method (e.g., [Formula: see text] and [Formula: see text]) and (b) [Formula: see text] and [Formula: see text] in terms of their performance in multilevel structural equation models across varying ICCs. The design factors included intraclass correlation (ICC: ICC1 = 0.091 to ICC6 = 0.500), numbers of groups in between-level models (NG: 50, 100, 200, and 1,000), group size (GS: 30, 50, and 100), and type of misspecification (no misspecification, between-level misspecification, and within-level misspecification). Our simulation findings raise a concern regarding the performance of between-level-specific partial saturated fit indices in low ICC conditions: the performances of both [Formula: see text] and [Formula: see text] were more influenced by ICC compared with [Formula: see text] and SRMRB. However, when traditional cutoff values ( RMSEA≤ 0.06; CFI, TLI≥ 0.95; SRMR≤ 0.08) were applied, [Formula: see text] and [Formula: see text] were still able to detect misspecified between-level models even when ICC was as low as 0.091 (ICC1). On the other hand, both [Formula: see text] and [Formula: see text] were not recommended under low ICC conditions.

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