Modeling Relations Among Discrete Developmental Processes: A General Approach to Associative Latent Transition Analysis

Abstract

To understand one developmental process, it is often helpful to investigate its relations with other developmental processes. Statistical methods that model development in multiple processes simultaneously over time include latent growth curve models with time-varying covariates, multivariate latent growth curve models, and dual trajectory models. These models are designed for growth represented by continuous, unidimensional trajectories. The purpose of this article is to present a flexible approach to modeling relations in development among two or more discrete, multidimensional latent variables based on the general framework of loglinear modeling with latent variables called associative latent transition analysis (ALTA). Focus is given to the substantive interpretation of different associative latent transition models, and exactly what hypotheses are expressed in each model. An empirical demonstration of ALTA is presented to examine the association between the development of alcohol use and sexual risk behavior during adolescence.

Figure 1

Graphical representations of ALTA Models 1–7. A₁ refers to alcohol use at time 1; A₂ refers to alcohol use at time 2; S₁ refers to sexual behavior at time 1; S₂ refers to sexual behavior at time 2. The loglinear notation for each model is shown below its graphical representation. Note that only the structural relations among variables are included in the graphical representations and loglinear notations. A latent class measurement model is assumed for each discrete latent variable.

Figure 2

Relative nesting of ALTA Models 1–7. A line between two models indicates that the lower numbered model is statistically nested within the higher numbered model, as well as all other models within which the higher numbered model is itself nested.