Perfect correlation
Message/Author
 MINHO KWAK posted on Thursday, October 25, 2018 - 10:08 am
Dear Dr. Muthen,

I'm writing to ask about the perfect correlation (r=1.00) in the variables. If a set of variables are identical, is it possible to fit CFA to the data?

I tried it, and I got the error message regarding a singular matrix problem.

I think it is impossible, but one of my colleagues consistently argue that it is possible in LISREL program.

Is there any way to fit CFA to the data with the perfect correlation in Mplus?

Thank you very much.
 MINHO KWAK posted on Thursday, October 25, 2018 - 10:26 am
Specifically, if there are 10 variables in the data set, two variables are identical. Is it possible to fit CFA to the data in Mplus?
 Bengt O. Muthen posted on Thursday, October 25, 2018 - 4:10 pm
Why would you want to include both of two variables that correlate 1? What do you gain?
 MINHO KWAK posted on Thursday, October 25, 2018 - 4:23 pm
Dr. Muthen,

The data set is regarding the test, and the observations are the time spent by the examinees for the items. For a specific item out of 9 items, it consists of two different sub-items. In this case, there is no way to know the exact time for both sub-items because the time is only measured by an item, not the sub-item. So, they just divided the time by 2, and use them as the time observed for two sub-items.

I suggested to use one of the variables, but my colleague still argues that we should we both items.
 MINHO KWAK posted on Thursday, October 25, 2018 - 5:32 pm
If it is impossible to fit CFA to the data set we have in Mplus technically, I think I can persuade my colleague to use one of the identical varialbes.
 MINHO KWAK posted on Friday, October 26, 2018 - 10:44 am
Is there any estimation option for the data set which has perfect correlation?
 Tihomir Asparouhov posted on Friday, October 26, 2018 - 12:52 pm
Using identical variables in a CFA model results in a model misspecifcation as the estimated model will not reflect the fact that the variables are equal and will jeopardize the rest of the model. We can't recommend this. In principle there are options to overrule Mplus to prevent you from doing this (variance=nocheck) etc. but this is not recommended.

The proper way to model your situation (if it is absolutely necessary) is to introduce a latent variable eta for the missing indicator - measured by the observed sum. However one indicator latent variable models are usually unidentified). So without any further information this might not be possible.
 MINHO KWAK posted on Friday, October 26, 2018 - 1:04 pm
Dr.Mother

It helps me a lot. Thank you for the answer.

Thanks again.