Bayesian Structural Equation Modeling of the WISC-IV with a Large Referred US Sample

When investigating the structure of cognitive ability measures like the WISC-IV, subtest scores theoretically associated with one latent variable could also be related to other factors. The objective of this study was to determine whether secondary interpretation of the 10 WISC-IV core subtests in a large referred US sample could be justified or whether a simple and unambiguous interpretation was more appropriate. To achieve this goal, the influence of each latent factor on subtest scores was estimated using Bayesian structural equation modeling (BSEM). A major drawback of classical confirmatory factor analysis (CFA) is that the majority of factor loadings needs to be fixed to zero to estimate the model parameters. This unnecessary strict parameterization can lead to model rejection and cause researchers to perform many exploratory modifications to achieve acceptable model fit. BSEM overcomes this limitation by replacing fixed-to-zero-loadings with “approximate” zeros that translates into small, but not necessary zero, cross-loadings. Because all relationships between factors and subtest scores are estimated, both the number of models to be tested and the risk of capitalizing on the chance characteristics of the data are decreased. WISC-IV data were obtained from 1,130 US children (ages 6-0 to 16-11) who were assessed for learning difficulties and subjected to BSEM. Two substantive cross-loadings were found with a higher order 4-factor model suggesting that secondary interpretation of some subtest scores could be adequate. However, a bi-factor alternative (with four first-order factors and one general factor) compared favorably to the higher order model. With the bi-factor model, no secondary interpretation of the subtest scores was supported by these data. Results suggested a simple and parsimonious interpretation of WISC-IV subtest scores. Results also indicated that the four WISC-IV factor index scores did not necessarily provide additional and separate information from the Full Scale IQ score.