Discriminant validity in a CFA with c...
Message/Author
 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 five-points 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.
 Bengt O. Muthen posted on Saturday, April 06, 2002 - 8:40 am
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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