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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.

Although using random digit dialing (RDD) telephone samples was the preferred method for conducting surveys of households for many years, declining response and coverage rates have led researchers to explore alternative approaches. The use of address-based sampling (ABS) has been examined for sampling the general population and subgroups, most often using mail or invitations to web surveys. For surveying rare groups, these studies often involve multiple phases to identify eligible population members and then collect responses. We describe a new approach for surveying rare subgroups using ABS with a single-phase mail survey. The study incorporates a new method for using a list frame with the ABS frame to increase the yield of the subgroup of interest while avoiding a potential bias inherent in many dual-frame survey designs. The findings suggest that the new approach is both efficient and effective for identifying and measuring a rare population.