First, Model 3 was estimated in which Alpha and Beta, or Alpha, Beta, and Gamma in the case of the TCI (see Rushton & Irwing, 2009a), were specified for each omnibus inventory. This model had eleven higher order factors (Alphas and Betas for all 5 inventories and 1 Gamma for the TCI) which were freed to correlate. This model seemed to fit the underlying data better than Models 1 and 2 (see Table 4). However, there were a number of inadmissible values (i.e., greater than 1) in the factor correlations. Estimating a second-order general factor in Model 4 resulted in a notably worse fit across all indices (Table 4). Additionally, this model demonstrated clear misspecification in the form of two negative first-order factor variances and two negative error variances (TCI Cooperativeness and NEO-PI-R Neuroticism). The fit of Model 4 presented in Table 4 is from a modified model with these error variances fixed to 0. Figure 13 provides a conceptual diagram along with the standardized factor loadings and error variances.
