Exploratory Bifactor Analysis of the WJ-III Achievement at School Age via the Schmid–Leiman Orthogonalization Procedure

Abstract

The structure of academic achievement measures has been rarely investigated in the literature apart from that which appears in the instruments’ technical manuals. This is concerning, given the widespread use of academic achievement instruments when making educational decisions about children. The Woodcock–Johnson III (WJ-III) Achievement for school-aged children (age 9-19) was investigated using exploratory bifactor analysis via the Schmid–Leiman (SL) orthogonalization procedure. This is the first time the SL has been applied to an academic achievement measure. The results revealed a unidimensional model of academic achievement across the standard 11 subtest battery, a two- or three-factor model at age 9 to 13 in the extended battery, and a two-factor model at age 14 to 19 across the extended battery. Forcing the four-factor fit in the standard battery required extracting eigenvalues as low as 0.67 and yielded areas of both convergence with and divergence from the structure posited in the Technical Manual. Forcing the six-factor fit across the extended battery yielded Heywood Cases, a lack of convergence of the factor solution, and the need to truncate iterations at 2 to force the fit. The results of this study indicate that the WJ-III Achievement is a solid model of general achievement across the 9 to 19 age range. Examination of omega coefficients, the divergent factor structure, and the small amount of variance accounted for by the lower order factors suggest caution when interpreting beyond this level (i.e., the academic clusters). Implications for interpretation of the WJ-III Achievement at age 9 to 19 are discussed.