Congruence coefficient

Abstract: All attempts to study the stability of factors depend on having some useful statistic that measures the degree of similarity between factors. This study attempts to provide some normative data about the distribution of one measure of similarity, the congruence coefficient, through a Monte Carlo technique. The matching of “chance” factor patterns was done by the method of Tucker. Statistical tests of the results, based on similarities of the method to canonical and multiple correlation, seemed satisfactory. The tabled results can be used as guides to the significance of congruence coefficients for some cases. The consistencies of the data indicate that a functional resolution may be possible, but none was found.

Abstract: Four types of metric scales are distinguished: the absolute scale, the ratio scale, the difference scale and the interval scale. A general coefficient of association for two variables of the same metric scale type is developed. Some properties of this general coefficient are discussed. It is shown that the matrix containing these coefficients between any number of variables is Gramian. The general coefficient reduces to specific coefficients of association for each of the four metric scales. Two of these coefficients are well known, the product-moment correlation and Tucker's congruence coefficient. Applications of the new coefficients are discussed.

Abstract: Procrustes methods of factor rotation have been criticized for producing excessively high coefficients of congruence when attempting to fit one factor pattern matrix into the space of a targeted pattern. A Monte Carlo study was designed to evaluate some of the conditions contributing to this problem when using Schonemann's orthogonal Procrustes transformation. It was found that the expected size of the factor congruence coefficient varied with (a) the number of variables in the analysis, (b) the number of salient variables defining a factor, and (c) the size of the salient variables' factor pattern coefficients. The number of factors extracted also had some influence on congruence but only in interaction with the size of the salient pattern values. The results of this simulation study, which include a prediction equation, can be used by researchers to appraise levels of factor congruence they find with real data.

Abstract: BackgroundNormative and pathological personality traits have rarely been integrated into a joint large-scale structural analysis with psychiatric disorders, although a recent study suggested they entail a common individual differences continuum.MethodsWe explored the joint factor structure of 11 psychiatric disorders, five personality-disorder trait domains (DSM-5 Section III), and five normative personality trait domains (the ‘Big Five’) in a population-based sample of 2796 Norwegian twins, aged 19‒46.ResultsThree factors could be interpreted: (i) a general risk factor for all psychopathology, (ii) a risk factor specific to internalizing disorders and traits, and (iii) a risk factor specific to externalizing disorders and traits. Heritability estimates for the three risk factor scores were 48% (95% CI 41‒54%), 35% (CI 28‒42%), and 37% (CI 31‒44%), respectively. All 11 disorders had uniform loadings on the general factor (congruence coefficient of 0.991 with uniformity). Ignoring sign and excluding the openness trait, this uniformity of factor loadings held for all the personality trait domains and all disorders (congruence 0.983).ConclusionsBased on our findings, future research should investigate joint etiologic and transdiagnostic models for normative and pathological personality and other psychopathology.