Real longitudinal data analysis for real people: building a good enough mixed model

Abstract

Mixed effects models have become very popular, especially for the analysis of longitudinal data. One challenge is how to build a good enough mixed effects model. In this paper, we suggest a systematic strategy for addressing this challenge and introduce easily implemented practical advice to build mixed effects models. A general discussion of the scientific strategies motivates the recommended five-step procedure for model fitting. The need to model both the mean structure (the fixed effects) and the covariance structure (the random effects and residual error) creates the fundamental flexibility and complexity. Some very practical recommendations help to conquer the complexity. Centering, scaling, and full-rank coding of all the predictor variables radically improve the chances of convergence, computing speed, and numerical accuracy. Applying computational and assumption diagnostics from univariate linear models to mixed model data greatly helps to detect and solve the related computational problems. Applying computational and assumption diagnostics from the univariate linear models to the mixed model data can radically improve the chances of convergence, computing speed, and numerical accuracy. The approach helps to fit more general covariance models, a crucial step in selecting a credible covariance model needed for defensible inference. A detailed demonstration of the recommended strategy is based on data from a published study of a randomized trial of a multicomponent intervention to prevent young adolescents' alcohol use. The discussion highlights a need for additional covariance and inference tools for mixed models. The discussion also highlights the need for improving how scientists and statisticians teach and review the process of finding a good enough mixed model.

Figure 1

The average number of alcohol use in the last 30 days over time.

Figure 2

The OLS residual versus time.

Figure 3

The Jackknifed studentized residual histogram from the linear mixed effect model with the original outcome at 1.5 years.

Figure 4

The Jackknifed studentized residual histogram from the linear mixed effect model with the Box-Cox (power = 16) transformed outcome at 1.5 years.

Figure 5

Predicted value versus Jackknifed studentized residual from the linear mixed effect model with the Box-Cox (power = 16) transformed outcome at 1.5 years.