When running a confirmatory factor analysis (CFA), users specify and interpret the pattern (loading) matrix. It has been recommended that the structure coefficients, indicating the factors’ correlation with the observed indicators, should also be reported when the factors are correlated (Graham, Guthrie, & Thompson, 2003; Thompson, 1997). The aims of this article are: (1) to note the structure coefficient should be interpreted with caution if the factors are specified to correlate. Because the structure coefficient is a zero-order correlation, it may be partially or entirely a reflection of factor correlations. This is elucidated by the matrix algebra of the structure coefficients based on the example in Graham et al. (2003). (2) The second aim is to introduce the method of Pratt’s (1987) importance measures to be used in a CFA. The method uses the information in the structure coefficients, along with the pattern coefficients, into unique measures that are not confounded by the factor correlations. These importance measures indicate the proportions of the variation in an observed indicator that are attributable to the factors – an interpretation analogous to the effect size measure of eta-squared. The importance measures can further be transformed to eta correlations, a measure of unique directional correlation of a factor with an observed indicator. This is illustrated with a real data example.



Recommended Citation

Wu, A. D., & Zumbo, B. D. (2017). Using Pratt's Importance Measures in Confirmatory Factor Analyses. Journal of Modern Applied Statistical Methods, 16(2), 81-98. doi: 10.22237/jmasm/1509494700