New approaches to studying problem behaviors: a comparison of methods for modeling longitudinal, categorical adolescent drinking data

Abstract

Analyzing problem-behavior trajectories can be difficult. The data are generally categorical and often quite skewed, violating distributional assumptions of standard normal-theory statistical models. In this article, the authors present several currently available modeling options, all of which make appropriate distributional assumptions for the observed categorical data. Three are based on the generalized linear model: a hierarchical generalized linear model, a growth mixture model, and a latent class growth analysis. They also describe a longitudinal latent class analysis, which requires fewer assumptions than the first 3. Finally, they illustrate all of the models using actual longitudinal adolescent alcohol-use data. They guide the reader through the model-selection process, comparing the results in terms of convergence properties, fit and residuals, parsimony, and interpretability. Advances in computing and statistical software have made the tools for these types of analyses readily accessible to most researchers. Using appropriate models for categorical data will lead to more accurate and reliable results, and their application in real data settings could contribute to substantive advancements in the field of development and the science of prevention.

Figure 1

Pictorial representation of how thresholds (τ's) in an underlying, continuous latent response variable correspond to the categories in an ordinal variable.

Figure 2

Path diagram of a hierarchical generalized linear model (HGLM) with a covariate, X. Model is shown with fixed times of measurement, but individual times of measurement may be specified in the model.

Figures 3a and 3b

A skewed univariate distribution characterized by a mixture of normal distributions on top (generalized linear growth mixture model; GMM), or mass points on the bottom (generalized linear latent class growth analysis; LCGA).

Figure 4a and 4b

Path diagrams for growth mixture model (GMM) and latent class growth analysis (LCGA) on the top. Solid lines are parameters present in both models and dashed lines represent parameters that, if present, define the model as GMM. Bottom shows the path diagram of longitudinal latent class analysis (LLCA). Both models are shown with covariate, X.

Figure 5

Observed drinking category probabilities by gender and grade.

Figure 6

Estimated mean trajectories for 3-class generalized linear growth mixture model (GMM) and generalized linear latent class growth analysis (LCGA). GMM plot includes standard deviation bars at each time and, in both plots, thresholds are shown by dashed lines.

Figure 7

Plots of predicted category proportions for 3-class models: generalized linear growth mixture model (GMM; top), generalized linear latent class growth analysis (LCGA; middle), and longitudinal latent class analysis (LLCA; bottom).

Figure 8

Plots of predicted category proportions for 4-class generalized linear latent class growth analysis (LCGA).

Figure 9

Plot of predicted hierarchical generalized linear model (HGLM) trajectories by levels of the covariate, target's report of the number of alcohol-using friends in 7^th grade (range of scale: 0 = none to 4 = all of them).