Interpreting the g loadings of intelligence test composite scores in light of Spearman's law of diminishing returns.

The linear loadings of intelligence test composite scores on a general factor (g) have been investigated recently in factor analytic studies. Spearman's law of diminishing returns (SLODR), however, implies that the g loadings of test scores likely decrease in magnitude as g increases, or they are nonlinear. The purpose of this study was to (a) investigate whether the g loadings of composite scores from the Differential Ability Scales (2nd ed.) (DAS-II, C. D. Elliott, 2007a, Differential Ability Scales (2nd ed.). San Antonio, TX: Pearson) were nonlinear and (b) if they were nonlinear, to compare them with linear g loadings to demonstrate how SLODR alters the interpretation of these loadings. Linear and nonlinear confirmatory factor analysis (CFA) models were used to model Nonverbal Reasoning, Verbal Ability, Visual Spatial Ability, Working Memory, and Processing Speed composite scores in four age groups (5-6, 7-8, 9-13, and 14-17) from the DAS-II norming sample. The nonlinear CFA models provided better fit to the data than did the linear models. In support of SLODR, estimates obtained from the nonlinear CFAs indicated that g loadings decreased as g level increased. The nonlinear portion for the nonverbal reasoning loading, however, was not statistically significant across the age groups. Knowledge of general ability level informs composite score interpretation because g is less likely to produce differences, or is measured less, in those scores at higher g levels. One implication is that it may be more important to examine the pattern of specific abilities at higher general ability levels.