Simultaneous Growth Curve Models and Their Use for Intervention Evaluation: A Practical Instruction to Model Fitting and Parameter Interpretation

This is the authors' abstract. We don't add key points for this paper.

Understanding how an intervention unfolds its effects is as important for its further development as establishing whether it works. This article introduces Simultaneous Growth Curve Models (SGCM) for longitudinal intervention data: separate latent growth curves fitted simultaneously to several repeatedly measured variables and connected by a structural model. It focuses on the multigroup formulation, in which every model matrix is estimated per group. The central argument is that the invariance testing sequence and the decomposition of group differences in expected growth are not two exercises but two views of one analysis: each constraint removes an identifiable component from the decomposition, so the surviving components define the effect structure. We derive this correspondence algebraically and illustrate it with a constructed example containing every type of group difference and with a cluster-randomized classroom intervention in mathematics. Guidance on unequally spaced time scores, control variables, diagnostics, and causal interpretation is given throughout.