Modeling Ability Differentiation in the Second-Order Factor Model
Structural Equation Modeling A Multidisciplinary JournalPublished 5 October 2011
Dylan Molenaar, Conor V. Dolan, Han L. J. van der Maas
Citations29
SJR quartileQ1
SJR score3.32
SNIP2.41
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Abstract
In this article we present factor models to test for ability differentiation. Ability differentiation predicts that the size of IQ subtest correlations decreases as a function of the general intelligence factor. In the Schmid-Leiman decomposition of the second-order factor model, we model differentiation by introducing heteroscedastic residuals, nonlinear factor loadings, and a skew-normal second-order factor distribution. Using marginal maximum likelihood, we fit this model to Spanish standardization data of the Wechsler Adult Intelligence Scale (3rd ed.) to test the differentiation hypothesis.
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Contemporary Sociology A Journal of ReviewsStructural Equations with Latent Variables.
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Padua Research Archive (University of Padua)A class of distributions which includes the normal ones
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Journal of the Royal Statistical Society Series B (Statistical Methodology)Statistical Applications of the Multivariate Skew Normal Distribution
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337 Citations1982A. Buse
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261 Citations1996Ian J. Deary, Vincent Egan +4 more
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140 Citations1994Gideon J. Mellenbergh
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