A Monte Carlo Study of the Sampling Distribution of the Congruence Coefficient

Abstract

The effects of sample size, number of variables, and population value of the congruence coefficient on the sampling distribution of the congruence coefficient were examined. Sample data were generated on the basis of the common factor model, and principal axes factor analyses were performed. The results indicated that when the population congruence coefficient is zero, the sampling distribution of the congruence coefficient is relatively stable and is similar to the sampling distribution of the correlation coefficient. The congruence coefficient was found to be positively biased for values of psi from .10 to .40 and negatively biased for the following values of psi: .50, .60, .90, and .99. The amount of bias (a) depends on the sample size and the number of variables used and (b) tends to decrease as sample size increases.

Relationships Between Objective and Perceived Housing in Very Old Age

“…The problem is that words denoting core concepts are frequently being used in everyday communication between actors in planning processes, in legislation and other official documents, in disability movement material, in research reports, and so on, without explicit definitions. Consequently, the new knowledge contributed (Broadbooks & Elmore, 1987). Congruence scores of the first canonical correlation loadings between each research site are listed boldfaced in the lower diagonal part of the table; congruences of the second canonical loadings are shown in the upper right part.…”

“…Canonical coefficients yield information on patterns of associations, and their relation to the correlation of the variables gives information on redundancy, meaning that high correlation and low standardized canonical coefficients indicate redundancy. For comparison of the patterns of canonical correlations (i.e., loadings) across the countries, we used Tucker's coefficient of congruence (Broadbooks & Elmore, 1987). This coefficient ranges from À1 to 1; the closer to 1, the higher the similarity between the samples.…”

The factor structure of the Fear Survey Schedule for Children—II in Trinidadian children and adolescents

“…In addition, to determine whether the factor structure was invariant across sex and age in the present sample, the coefficient of congruence between the factor structure derived for males and the structure derived for females was calculated, as was the coefficient of congruence between the factor structure derived for 11-to 14-year-olds and the structure derived for 15-to 18-year olds (these factor structures were derived through the procedures specified previously for the common factor analysis of the overall sample). These coefficients can be interpreted like a correlation coefficient (Broadbooks & Elmore, 1987). Congruence coefficients equal to or greater than .90 were considered to be indicative of a high degree of factor similarity.…”

A new set of 299 pictures for psycholinguistic studies: French norms for name agreement, image agreement, conceptual familiarity, visual complexity, image variability, age of acquisition, and naming latencies

“…Linear congruence coefficients (e.g., Broadbooks & Elmore, 1987) between the factors in the two analyses (Alario and Ferrand's, 1999, and ours) were computed. 6 As can be seen from Table 5, the coefficients between all pairs of factors of the same order were very close to 1, indicating that the three dimensions are similar in the two samples.…”