An Alternative Correlation Matrix Based Factor Analysis for Categorical Data:Goodman and Kruskal’s Gamma

Exploratory factor analysis (efa) is a frequently used method in social sciences while gathering evidence for the construct validity of data obtained from scales. when the data are categorical, efa is performed using the polychoric/tetrachoric correlation matrix, while analyses are performed using the pearson correlation matrix when the data are continuous. however, in some cases when the polychoric correlation matrix is used, non-convergence issues can emerge, and factor loadings can be underestimated when the pearson correlation matrix is used. therefore, this study aims to compare the efa results obtained from goodman and kruskal’s lambda and gamma coefficients as an alternative correlation matrix with the results obtained from the polychoric and pearson correlation matrix. in the monte carlo simulation study carried out for this purpose, variables such as number of categories, average factor loading, sample size, and distribution of variables were determined as the simulated conditions. as a result of the study, in some conditions unachievable using the polychoric correlation matrix, estimations are observed able to be made with the matrix formed by goodman and kruskal’s gamma coefficient. in certain conditions using the lambda coefficient, the model did not converge. lambda had underestimated factor loadings in the converged data sets. the results obtained from goodman and kruskal’s gamma are also observed to be less biased as the number of categories increases. researchers can be recommended to examine the results obtained from goodman and kruskal’s gamma while performing efa with categorical data.