From the MODEL command, f1 WITH f2 is a residual covariance. From your MODEL command, f13 WITH f7 is also a residual covariance. Note that you have two factor loadings fixed to one in your BY statements.
Alex Zammit posted on Tuesday, August 05, 2008 - 5:22 am
When I run a MIMIC model with the following statement:
FACTR1 ON AGE GENDER SEVERITY ACCDAYS LITIGATE EDUCN; the model results for GENDER are:
Estimate S.E Est/S.E. -0.452 0.184 -2.453
I believe the Est/s.e. of -2.453 means the regression of FACTR1 on GENDER is significant.
However, if I change the above statement to FACTR1 ON Gender; the model results for GENDER are:
Estimate S.E Est/S.E. 0.092 0.146 0.631
Now it seems the regression is no longer significant. Why does the significance change when the additional covariates are removed?
In the first case, the coefficient for gender is a partial regression coefficient controlling for age, severity, accdays, litigate, and educn. In the second case, it is not a partial regression coefficient. Another issue is sample size. It may have changed between the two analyses.
Alex Z posted on Tuesday, August 05, 2008 - 4:08 pm
Thanks for your response.
It would then seem that using GENDER as a partial regression coefficient, controlling for age, severity, etc., would be the correct way to demonstrate the significance of the effect of GENDER on FACTR1? is this because all other effects have been eliminated and GENDER is being considered in isolation?
1) I'm having difficulty understand "why" a significant effect of "u1 ON covariate" indicates differential item functioning. It is my understanding that would simply indicate that one group endorses that item at a higher rate. It's possible that higher rates of endorsement do not indicate DIF.
2) Also, my second concern is how to interpret the DIF result. For example, if I had a 1-factor model (f1) where u1 ON covariate (male = 0, female =1) was significant (estimate = .433). How would that be interpreted as affecting the difficulty parameter by sex?
1) The "u1 on covariate" effect is only half of it. It is not a matter of a marginal difference in u1 ("higher rates of endorsement") at certain covariate values, but instead the conditional difference in u1 at certain covariate values given a certain factor value. In other words, for two people with the same factor value, the u1 probability differ depending on their covariate value.
2) See our handout for the Topic 2 course on our web site where we go through the ASB example and gender differences in shoplifting. This course is also available for free viewing as a video on the web - see our home page.
I have a very basic question about CFA with covariates (MIMIC) to assess DIF. I am trying to use a MIMIC model in a paper for the first time using Mplus. In my case, I have a single factor, a single covariate, and binary items. I am using the default WLSMV estimator. In the short course handout, the first step involves establishing the model without covariates. In the ASB example, all indicator errors are uncorrelated. Would anything change in the following steps (i.e., add covariates, add direct effects suggested by modification indices, and interpret the model) if a model includes factor indicators with one or more correlated errors?
I am attempting to run a MIMIC model in a MC simulation. I would like to have the mean/variance of the latent variable differ between groups, while simultaneously being able to regress the latent variable/indicators onto the grouping variable (hence MIMIC model). Is it possible to do this in MPlus? I would appreciate any help on this matter. Thanks!