Catching Up on Multilevel Modeling

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.

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

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.

The Role of Sex and Age on Pre-drinking: An Exploratory International Comparison of 27 Countries

Aims This exploratory study aims to model the impact of sex and age on the percentage of pre-drinking in 27 countries, presenting a single model of pre-drinking behaviour for all countries and then comparing the role of sex and age on pre-drinking behaviour between countries. Methods Using data from the Global Drug Survey, the percentages of pre-drinkers were estimated for 27 countries from 64,485 respondents. Bivariate and multivariate multilevel models were used to investigate and compare the percentage of pre-drinking by sex (male and female) and age (16–35 years) between countries. Results The estimated percentage of pre-drinkers per country ranged from 17.8% (Greece) to 85.6% (Ireland). The influence of sex and age on pre-drinking showed large variation between the 27 countries. With the exception of Canada and Denmark, higher percentages of males engaged in pre-drinking compared to females, at all ages. While we noted a decline in pre-drinking probability among respondents in all countries after 21 years of age, after the age of 30 this probability remained constant in some countries, or even increased in Brazil, Canada, England, Ireland, New Zealand and the United States. Conclusions Pre-drinking is a worldwide phenomenon, but varies substantially by sex and age between countries. These variations suggest that policy-makers would benefit from increased understanding of the particularities of pre-drinking in their own country to efficiently target harmful pre-drinking behaviours.

Mind the step: A more insightful and robust analysis of the sentencing process in England and Wales under the new sentencing guidelines

The ‘England and Wales Sentencing Guidelines’ aim to promote consistency by organizing the sentencing process as a sequence of steps, with initial judicial assessments subsequently adjusted to reflect relevant case characteristics. Yet, existing evaluations of the guidelines have failed to incorporate this structure adequately, instead concentrating solely on sentence outcomes. We use multivariate multilevel models to offer new insights into the decisions made throughout the sentencing process. Focusing on cases of assault sentenced at the Crown Court we show that the level of compliance with the guidelines is high. However, we also show that some case characteristics are being unduly considered at more than one stage of the sentencing process, meaning existing studies may be underestimating their true influence.