Accounting for the Relationship Between Initial Status and Growth in Regression Models

Educational analysts studying achievement and other educational outcomes frequently encounter an association between initial status and growth, which has important implications for the analysis of covariate effects, including group differences in growth. As explicated by Allison (1990 Allison, P. D. (1990). Change scores as dependent variables in regression analyses. Sociological Methodology, 20, 93–114.[Crossref] , [Google Scholar]), where only two time points of data are available, identifying a preferred model can be difficult or impossible. In this paper we extend Allison's inquiry by considering multiple sources of the association between initial status and growth simultaneously, including measurement error but also intrinsic associations between initial status and growth. We illustrate the potential trade-offs between the change-score model specifications (models without a control for initial status) and regressor-variable specifications (with a control for initial status) using simulated data.