The Effects of Different Correlation Types on Goodness-of-Fit Indices in First Order and Second Order Factor Analysis for Multiple Choice Test Data

Abstract

This study explores the effects of different correlation types (covariance and correlation matrix, obtained from Pearson, Goodman, and Tetrachoric) on goodness-of-fit indices in first order and second order factor analysis. The data included Math and Science subsets in
Student Selection and Placement Examination for Secondary Education test administered in 2001 with the participation of 553108 students. A first-order and second-order confirmatory factor analyses were performed on the matrix from item scores obtained from several correlation coefficients. The findings indicate that when second order factor loadings (first order correlations) were equal, solutions with Pearson correlation coefficients yielded the most satisfactory goodnessof-fit. When second order factor loadings (first order correlations) were not equal, solutions with tetrachoric correlations yielded the most satisfactory goodness-of-fit.