Search for a common factor model to describe a cross-lagged correlation difference

Abstract

This study describes the development of a common factor model for a cross-lagged difference involving a measure of aural comprehension and an intellectual composite. The direction of the difference was that the Listening Test predicted the composite more accurately than the composite predicted the Listening Test. A complex model which allowed seemingly identical common factors appearing at different ages to be highly, but imperfectly, correlated fit the 32 x 32 table of intercorrelations of 16 variables measured at each of two time periods. The model also described quite accurately the multiple correlations on which the cross-lagged difference was based. Aural comprehension at grade 5 was equidistant from the vectors of the two general factors at grades 5 and 11; but aural comprehension at grade 11, while close to the general factor at grade 11, was outside the space created by the two general factor vectors. Individual differences in aural comprehension anticipated by several years changes in rank on the general factor as defined by standard tests.