What to do Without a Control Group: You have to go latent, but not all latents are equal

Analyzing within-group change in an experimental context, where the same group of people is measured before and after some event, can be fraught with statistical problems and issues with causal inference. Still, these designs are common from political science to developmental neuropsychology to economics. In cases with cognitive data, it has long been known that a second administration, with no treatment or an ineffective manipulation between testings, leads to increased scores at time 2 without an increase in the underlying latent ability. We investigate several analytic approaches involving both manifest and latent variable modeling to see which methods are able to accurately model manifest score changes with no latent change. Using data from 760 schoolchildren given an intelligence test twice, with no intervention between, we show using manifest test scores, either directly or through univariate latent change score analysis, falsely leads one to believe an underlying increase has occurred. Second-order latent change score models also show a spurious significant effect on the underlying latent ability. Longitudinal structural equation modeling with measurement invariance correctly shows no change at the latent level when measurement invariance is tested, imposed, and model fit tested. When analyzing within-group change in an experiment, analyses must occur at the latent level, measurement invariance tested, and change parameters explicitly tested. Otherwise, one may see change where none exists.