Adding indicator residuals to a regre...
Message/Author
 Joe Crozier posted on Wednesday, July 18, 2007 - 11:21 am
Hi,

I am trying to respond to a reviewer's comment on a paper. I have been asked to estimate a two-group model in which an observed variable (Y) is regressed on a latent factor (F) which has six indicators (X1-X6). In addition, I have been asked to add the residuals of X1-X6 into the regression as well. I am not sure how to code this or if this is even identified. My initial attempt at a model statement is below:

Model:

F by X1-X6;

Y on F X1-X6;

Model Group2:

F by X2-X6;

Y on F X1-X6;

Is this correct?

Thanks!
Joe
 Bengt O. Muthen posted on Wednesday, July 18, 2007 - 2:02 pm
Saying "y on x1-x6" will regress y on the x variables themselves, not their residuals in the factor model. You have to define a factor corresponding to each residual and regress on those factors. And, delete the usual residual so you don't get two per indicator. So say,

f by x1-x6;
x1-x6@0; ! deleting the usual residual var

fx1 by; ! this will be a new residual
fx2 by;
---
fx6 by;

fx1 with fx2-fx6@0; !zero res covs
fx2 with fx3-fx6@0;
etc
fx1-fx6 with f@0;

x1 on fx1@1; ! this adds the new residual
! to x1
---
x6 on fx6@1;

y on f fx1-fx6;

I think that should work.
 Joe Crozier posted on Wednesday, July 18, 2007 - 3:49 pm
Hi,

Thanks for the help. I tried to implement this approach, but I received an error indicating that the model may not be identified. Here is the model statement that I used:

ASB by ly12ext abq12 a12agg sip2 sip4 sip5:

ly12ext@0;
abq12@0;
a12agg@0;
sip2@0;
sip4@0;
sip5@0;

fx1 by;
fx2 by;
fx3 by;
fx4 by;
fx5 by;
fx6 by;

fx1 with fx2-fx6@0;
fx2 with fx3-fx6@0;
fx3 with fx4-fx6@0;
fx4 with fx5-fx6@0;
fx5 with fx6@0;

fx1-fx6 with ASB@0;

ly12ext on fx1@1;
abq12 on fx2@1;
a12agg on fx3@1;
sip2 on fx4@1;
sip4 on fx5@1;
sip5 on fx6@1;

ev01hrNO on ASB fx1 fx2 fx3 fx4 fx5 fx6 ;

Does this look right?

Thanks,
Joe
 Bengt O. Muthen posted on Wednesday, July 18, 2007 - 4:13 pm
I don't see a problem off hand, so you'd better send the input, output, data, and license number to support@statmodel.com for further scrutiny.