Triangulating on Developmental Models With a Combination of Experimental and Nonexperimental Estimates

Plausible competing developmental models show similar or identical structural equation modeling model fit indices, despite making very different causal predictions. One way to help address this problem is incorporating outside information into selecting among models. This study attempted to select among developmental models of children's early mathematical skills by incorporating information about the extent to which models forecast the longitudinal pattern of causal impacts of early math interventions. We tested for the usefulness and validity of the approach by applying it to data from three randomized controlled trials of early math interventions with longitudinal follow-up assessments in the United States (Ns = 1,375, 591, 744; baseline age 4.3, 6.5, 4.4; 17%-69% Black). We found that, across data sets, (a) some models consistently outperformed other models at forecasting later experimental impacts, (b) traditional statistical fit indices were not strongly related to causal fit as indexed by models' accuracy at forecasting later experimental impacts, and (c) models showed consistent patterns of similarity and discrepancy between statistical fit and models' effectiveness at forecasting experimental impacts. We highlight the importance of triangulation and call for more comparisons of experimental and nonexperimental estimates for choosing among developmental models. Public Significance Statement When analyzing data from experiments with longer term follow-up assessments, sometimes researchers publish experimental impacts and longitudinal associations in separate articles. However, we argue that more can be learned from analyses that attempt to compare and contrast these experimental and nonexperimental estimates than from separate analyses that do not treat the experimental and nonexperimental analyses as potentially mutually informative.