Keep Calm and Learn Multilevel Logistic Modeling: A Simplified Three-Step Procedure Using Stata, R, Mplus, and SPSS

Abstract

This paper aims to introduce multilevel logistic regression analysis in a simple and practical way. First, we introduce the basic principles of logistic regression analysis (conditional probability, logit transformation, odds ratio). Second, we discuss the two fundamental implications of running this kind of analysis with a nested data structure: In multilevel logistic regression, the odds that the outcome variable equals one (rather than zero) may vary from one cluster to another (i.e. the intercept may vary) and the effect of a lower-level variable may also vary from one cluster to another (i.e. the slope may vary). Third and finally, we provide a simplified three-step “turnkey” procedure for multilevel logistic regression modeling: -Preliminary phase: Cluster- or grand-mean centering variables-Step #1: Running an empty model and calculating the intraclass correlation coefficient (ICC)-Step #2: Running a constrained and an augmented intermediate model and performing a likelihood ratio test to determine whether considering the cluster-based variation of the effect of the lower-level variable improves the model fit-Step #3 Running a final model and interpreting the odds ratio and confidence intervals to determine whether data support your hypothesis Command syntax for Stata, R, Mplus, and SPSS are included. These steps will be applied to a study on Justin Bieber, because everybody likes Justin Bieber.1

Keywords

• Logistic regression
• multilevel logistic modeling
• grand-mean centering and cluster-mean centering
• intraclass correlation coefficient
• likelihood ratio test and random random slope variance
• three-step simplified procedure
• Justin Bieber