Comparative longitudinal structural analyses of the growth and decline of multiple intellectual abilities over the life span.

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Abstract
Latent growth curve techniques and longitudinal data are used to examine predictions from the theory of fluid and crystallized intelligence (Gf-Gc theory; J. L. Hom & R. B. Cartell, 1966, 1967). The data examined are from a sample (N similar to 1,200) measured on the Woodcock-Johnson Psycho-Educational Battery-Revised (WJ-R). The longitudinal structural equation models used are based on latent growth models of age using two-occasion "accelerated" data (e.g. J.J. McArdle & R. Q. Bell, 2000; J. J. McArdle & R W. Woodcock, 1997). Nonlinear mixed-effects growth models based on a dual exponential rate yield a reasonable fit to all life span cognitive data. These results suggest that most broad cognitive functions fit a generalized curve that rises and falls. Novel multilevel models directly comparing growth curves show that broad fluid reasoning (Gf) and acculturated crystallized knowledge (Gc) have different growth patterns. In all comparisons, any model of cognitive age changes with only a single g factor yields an overly simplistic view of growth and change over age.