We used standard covariance structure model estimation procedures in Mplus 5.1 29 for both biometric and hierarchical biometric-CFA models. Such procedures will be maximum likelihood if the raw data are multivariate normal. We compared nested models with the Satorra-Bentler scaled-difference (Δ) χ2 test, however, as that test is valid for large samples even if the data are skewed.30 We also used information-theoretic indices to compare the fit of alternative etiologic models underlying the observed phenotypic covariance matrices. Under normality, a Bayesian Information Criterion (BIC)31 can be computed for both biometric and CFA models, comparing each model to a “saturated” model in which each manifest variable has its own latent dimension. BIC includes a penalty for the number of parameters in the model, so that the alternative model with the lower BIC is preferred in the sense of balancing model parsimony with fidelity to the data in representing the observed covariances among the variables. The standardized root mean square residual (SRMR)32 quantifies the standardized difference between the observed predicted covariances, with 0 indicating a perfect fit and values < .08 conventionally
