Model 5 also estimated a two-factor higher-order structure. This model, however, specified higher-order Alphas and Betas across inventories. This was accomplished by allowing each first-order “Alpha” factor and the TCI “Gamma” factor to load freely on a higher order “Alpha” factor, and each of the first-order “Beta” factors to load on a higher-order “Beta” factor. Relative to the one-factor higher-order model this model had significantly improved fit (Table 4). The conceptual model and standardized coefficients are presented in Figure 2. Although this model converged, four error variances were negative and subsequently fixed to zero whereas three first-order factor variances were negative. Attempts to specify factors with non-negative variance resulted in models that would not converge. The overall model is probably untrustworthy but we note that the correlation between the alpha and beta factors was .28 (i.e., they share less than 8% of their variance). No single-factor third-order model was estimated as this would merely be a quantitative rearticulation of this correlation.
