Longitudinal studies of achievement growth using latent variable modeling

This article gives a pedagogical description of growth modeling of longitud inal data using latent variable methods. The growth modeling is described u sing an example of mathematics achievement developing over grades 7 to 10 i n two cohorts of students. The article describes the basic idea behind grow th 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 model ing that assesses the form of the growth, the influence of background varia bles on the growth, multiple-cohort analysis, analysis with missing data, a nd multiple-group analysis of males and females. A corresponding set of ana lyses are performed on the mathematics data to illustrate the modeling idea s.