Longitudinal studies of achievement growth using latent variable modeling

Abstract

This article gives a pedagogical description of growth modeling of longitudinal data using latent variable methods. The growth modeling is described using an example of mathematics achievement developing over grades 7 to 10 in two cohorts of students. The article describes the basic idea behind growth modeling of individual differences in growth over time and applies it to mathematics achievement development as a function of background variables such as gender, mother's education, and home resources. The modeling ideas are described in words, diagrams, and formulas. The discussion covers modeling that assesses the form of the growth, the influence of background variables on the growth, multiple-cohort analysis, analysis with missing data, and multiple-group analysis of males and females. A corresponding set of analyses are performed on the mathematics data to illustrate the modeling ideas.