Abstract
This paper considers problems whether or not we can provide statistical evidence of the hypothesis “observed data is generated by orthogonal two factor models without correlated errors”, that is, the detection problems of orthogonal two factor models without correlated errors from statistical data. Regarding the detection criteria for single factor models without correlated errors, Spearman proposed the “Vanishing Tetrad Difference” in 1904, and Bekker and de Leeuw (1987) provided a necessary and sufficient condition that the observed covariance structure is equivalent to that from the single factor model. Regarding two factor models, although Kelley (1935) proposed the “Pentad Constraint” as a detection criterion for confirmatory orthogonal two factor models without correlated errors, the detailed discussion has not been provided. In this paper, we point out that our problem may not be solved by the Pentad Constraints, the Minor Constraints, or their combinations, and show that it is important to test the inequality constraints between the observed correlation coefficients in order to detect confirmatory orthogonal two factor models with correlated errors.
