CHC Theory, Cognitive Assessment, Tutorial

Factor Analysis of the WISC-IV Integrated with a Schmid-Leiman Transformation

On the IAPCHC listserv, the question of what the WISC-IV Integrated Spatial Span measures came up recently. I obtained permission from Pearson to use Tables 5.1, 10.1, and 10.2 to construct a correlation matrix of the subtests in the WISC-IV Integrated. I removed the process scores that have to do with time bonuses. I also removed subtests that are the sum of two, more basic subtests (e.g., Digit Span is the sum of Digits Forward and Digits Backward). This was necessary because the correlation matrix is not positive definite if the parts and the sum are included. A matrix that is not positive definite is impossible to factor analyze.

I used the correlation matrix to extract 5 principal factors with promax rotation. I played around with other factor extractions but a variety of concerns led me to settle on 5 factors. I used the Cattell-Horn-Carroll names for the factors (Gc, Gv, Gsm, Gq, and Gs). I then applied a Schmid-Leiman transformation to the analysis so that it would be parallel to Carroll’s analyses.

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Note the absence of Gf. I think that Picture Concepts is not a strong enough Gf measure to team up with Matrix Reasoning for it to emerge. Gf often does not emerge anyway because it is so correlated with g.

I used the reliability estimates (averaged across all ages) to estimate how much of the variance in each subtest is error, specific, and shared by g and the 5 smaller factors.