

Discriminant validity in a CFA with c... 

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Jean Frisou posted on Thursday, April 04, 2002  10:58 pm



I am using Mplus to conduct a confirmatory factor analysis. I have two latent factors S and F and six categorical indicators s1, s2, s3, f1, f2, f3. s1, s2, s3, are measured on a fivepoints scale, f1, f2, f3, are binary. The statements of model are F BY f1 f2 f3; S BY s1 s2 s3; F WITH S; In order to evaluate discriminant validity of the two constructs, I use the indice Rhovc suggested by Fornell and Larcker (Journal of Marketing Research, February 1981). Rhovc (X) measures the amount of average variance that is captured by a construct X. For example : Rhovc (S) = (Sum of the three squared loadings of S) / [(Sum of the three squared loadings of S)+(Sum of the three residual variances of indicators)] According to the autors, the requirements for discriminant validity are: Rhovc (S) > squared r and Rhovc (F)> squared r, where r is the correlation beetween S and F Squared r measures the shared variance the two constructs S and F. In a CFA with categorical data, the factor loadings given by Mplus are probit coefficients. The squared loadings are the R² displayed in the output file. These R² values are different of R² regression with continuous variables, because the error variances V(delta) is not a free parameter (Mplus User's guide page 341). My question: In these conditions, is it correct to compare Rhovc (S) and Rhovc (F) with squared r ? (The shared variance R² between indicators and constructs are different of the R² between F and S which are continuous variables) Thanks for your help. 


It seems like the reasoning would carry over if one considers the latent response variable y*. But I'm not familiar with the reasoning behind these indices. 

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