Fixing correlations in a CFA PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
 Jonathan Bruce Santo posted on Monday, March 03, 2008 - 11:09 am

This might be a silly question but I haven't been able to find the answer elsewhere.

I have a CFA with a number of variables and factors and I want to constrain the correlation between two factors.

When free, the correlation is .271. If I try to set it to .28 (f1 WITH f2@.271;) the model fails to converge (NO CONVERGENCE. SERIOUS PROBLEMS IN ITERATIONS. ESTIMATED COVARIANCE MATRIX NON-INVERTIBLE. CHECK YOUR STARTING VALUES).

Again, I'm sorry if this is a silly question but am I missing something here?

Jonathan Bruce Santo
Interpersonal Relationships and Development Lab
Centre for Research in Human Development
Concordia University
PY 205-2
Tel: (514) 848-2424 Ext. 2849
 Linda K. Muthen posted on Monday, March 03, 2008 - 4:44 pm
Please send your input, data, output, and license number to
 Elina Dale posted on Thursday, April 25, 2013 - 8:05 am
Dear Dr. Muthen,

Could you please, point out where in the Output I should look for correlations between my factors and an observed variable? Also, my indicators are categorical but so is my X. However, when I try to put in the same line as CATEGORICAL, MPlus gives me warning that only dependent variables are inserted there.

Here is the input:
CATEGORICAL = i1 i2 i3 i4 i5 i6;
Analysis: TYPE = COMPLEX ;
f1 BY i1* i2 i3;
f2 BY i4* i5 i6 ;
f1-f2 WITH q1cat ;

Do I look under STDYX or unstandardized model results for correlations between by f1 and q1cat, f2 and q1cat? They are slightly different, and unstd are > than those under STDYX. Also, since q1cat is categorical, does MPlus I suppose polychor corr should be used. But I don't know what MPlus uses when it gets WITH command for correlation of an observed var with a factor. Thank you!
 Bengt O. Muthen posted on Thursday, April 25, 2013 - 8:53 pm
Categorical variables not declared as such are treated as continuous. A correlation with a categorical variable treated as continuous isn't very informative. If q1cat is categorical, are you sure you don't want to instead either do multiple-group analysis with respect to q1cat or say

f1-f2 ON q1cat;

Correlations are obtained using STDYX.
 Elina Dale posted on Thursday, April 25, 2013 - 10:04 pm
Thank you, Dr. Muthen!
But ON statement is for regressing Y ON X, not for correlation. Isn't it? So, I'd get beta, not correlation coefficient, is it correct?
What I need is to show criterion validity and my criterion observed variable is categorical.
It is usually advised to do correlation between a scale score and the criterion. Since I am not using a scale score (given the measurement error of the latent variable), I want to correlate the criterion with my factors. What would you advice then for me to do, if my criterion variable is observed categorical? Thank you!
 Bengt O. Muthen posted on Friday, April 26, 2013 - 1:50 pm

Is your categorical criterion an ordinal or a nominal variable, or is it binary?
 Elina Dale posted on Saturday, April 27, 2013 - 10:52 am
Thank you again Dr. Muthen! I have actually three criterion variables:
(1) ordinal variable (overall motivation), (2) binary variable (gender), and
(3) nominal variable (health worker position).

What would you advice?

Thank you!
 Bengt O. Muthen posted on Monday, April 29, 2013 - 4:29 pm
I would not show criterion validity as a correlation when the criterion is gender or worker position. It seems much more natural to ask if there is a significant mean difference in the factor between the different criterion categories.

For the ordinal variable I could imagine a correlation, and use a polychoric if you have strong floor or ceiling effects. But you should ask these types of general analysis questions on SEMNET instead.
 Elina Dale posted on Thursday, June 20, 2013 - 7:22 am
Dear Dr. Muthen,

I would like to examine whether motivation factors are good predictors of intention to quit the job. Motivation is measured through factors made up of 15 items in total. Intention to quit is an observed categorical variable.

So, my X is a latent var, whereas my Y is an observed cat var.

Could you please, let me know if the coding below is correct for what I want to do? Many thanks!

CATEGORICAL = Ycat i1 i2 i3 i4 i5 i6 i7 i8 i9 i10 i11 i12 i14 i15;
Analysis: TYPE = COMPLEX ;
f1 BY i1 i2 i3 i4 ;
f2 BY i5 i6 i7 i8 ;
f3 BY i9 i10 i11 i12 ;
f4 BY i13 i14 i15 ;
Ycat ON f1;
Ycat ON f2;
Ycat ON f3;
Ycat ON f4;
 Linda K. Muthen posted on Thursday, June 20, 2013 - 7:53 am
That looks correct. I will fit the measurement model alone as a first step.
 Elina Dale posted on Thursday, June 20, 2013 - 10:27 pm
Thank you, Dr. Muthen! I did fit the measurement model first and it seemed to fit well. But then when I try to fit the model above, things don't look as good, so that's why I was wondering if the coding was correct. But perhaps it just means that motivation in this case is not a good predictor of intention to stay?
 Bengt O. Muthen posted on Friday, June 21, 2013 - 6:30 pm
Your coding is correct. If you have poor fit for this model, it implies that Ycat is not related to i1-i15 only through f1-f4 as you have specified the model, but that there are some direct relationships.
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