Categorical factor indicators
Message/Author
 student07 posted on Thursday, July 26, 2007 - 5:50 am
Hi there

I am new to SEM with categorical data and wonder how (if at all) one could quantify the reliability for a latent variable measured with categorical indicators?

Thanks
 Linda K. Muthen posted on Thursday, July 26, 2007 - 8:24 am
Do you want the reliability of the factor or the factor indicators?
 student07 posted on Thursday, July 26, 2007 - 8:37 am
Of the factor, the underlying latent variable (I do not use latent class modeling).
 Bengt O. Muthen posted on Thursday, July 26, 2007 - 9:01 am
Then you are probably thinking of the precision with which the factor scores can be estimated for each individual. This topic is studied in Item Response Theory under the heading information curves which describe the inverse of standard error for each estimated factor score (called theta-hat in IRT). The curves vary over true theta values. Mplus provides these information curves in its plot command; see the UG and also this web site's description of IRT capabilities in Mplus.
 RuoShui posted on Monday, September 23, 2013 - 2:11 pm
I am new to use SEM with categorical indicators. I have two independent latent variables: f1 has 5 binary indicators (yes/no), f2 has 5 ordinal indicators (ordered as 0,1,2,3). f3 and f4 have continuous indicators. v1 and v2 are observed test scores. I wonder if the following syntax is correct? Thank you very much!

use variables X1-X20 v1 v2
CATEGORICAL ARE X1-X10

f1 BY X1-X5;
f2 BY X6-X10;
f3 By X11-X15;
f4 BY X16-X20;
f3 f4 v1 v2 on f1 f2;
v1 v2 on f3 f4;
TYPE=Basic;
 Linda K. Muthen posted on Monday, September 23, 2013 - 2:14 pm
You should remove TYPE=BASIC and add MODEL:

use variables X1-X20 v1 v2
CATEGORICAL ARE X1-X10
MODEL:
f1 BY X1-X5;
f2 BY X6-X10;
f3 By X11-X15;
f4 BY X16-X20;
f3 f4 v1 v2 on f1 f2;
v1 v2 on f3 f4;

See the examples in Chapter 5 of the user's guide.
 RuoShui posted on Tuesday, September 24, 2013 - 10:49 pm
Thank you very much for the information. My model cannot converge. I know that my observed test scores are on a different scale and result in large variance. I tried to rescale the variance. The model had a poor fit. The modification indices suggest me correlating f3 and f4. Can I do this?

Thank you.
 RuoShui posted on Tuesday, September 24, 2013 - 11:07 pm
I am sorry. It was actually after I rescaled the test scores , the model won't converge unless I correlate f3 and f4. What does this suggest? Can I do it?

Thank you.
 Linda K. Muthen posted on Wednesday, September 25, 2013 - 6:42 am
Please send the output and your license number to support@statmodel.com.