Single item indicator Multilevel SEM
Message/Author
 Andrea M Reina Tamayo posted on Friday, September 26, 2014 - 3:53 am
I have a two level data set, different time points (level 1) nested within individuals (level2).

I want to test my research model at level 1 because I am testing the momentary dynamics of my construct. However, because of the repeated measures, I used one item to represent a construct (latent variable).

If I want to use that item at level 1 as a latent variable, how can I specify that on Mplus.

If I use the ON command (see below), it would be a path a analysis, but I want a structural model with latent variables.

ANALYSIS:
TYPE = GENERAL TWOLEVEL;

MODEL:
%WITHIN%
F2 by X1 X2 X3;
Item1 ON F2

Is there another command that can be use for that? Thus, converting the observed variable (item 1) into a latent variable.
 Bengt O. Muthen posted on Friday, September 26, 2014 - 1:35 pm
Why would you want to convert the observed variable into a latent variable? Nothing is gained by that unless you fix the unreliability of the variable.
 Andrea M Reina Tamayo posted on Wednesday, October 08, 2014 - 10:31 am
Yes, you are right. I was reading the article Muthen (1991) -Multilevel factor analysis and achievement scores -in order to get the information for this syntax and apply to the within model.

F by y@1;
y@a;

a=(1-reliability)*sample variance.

I was able to obtain the variance from the ICC, however, I am still having trouble determining the reliability.
In the study Muthen (1991) pg. 345 , it is mentioned that within reliability = wf/(wf+we)
From the information I get on the ICC I can get the information below the equation, (wf+we), but I can't get the wf from anywhere.
I am still trying to decipher how to obtain wf in order to determine the within reliability.

Any tips or further information you have on this would be really appreciate it!
 Bengt O. Muthen posted on Wednesday, October 08, 2014 - 10:41 am
Your estimated 2-level factor analysis model gives wf as the estimated within-level factor variance and we as the estimated within-level residual variance.
 Andrea M Reina Tamayo posted on Monday, October 20, 2014 - 5:20 am
Hi Bengt, thank you for the reply. I think that would work out, if I already know the reliability of my item and can run the analysis. However, I do not have at the present moment. I am not sure from which sources can I obtain this reliability.

Do you have any suggestions or papers for estimating this reliability?
 Bengt O. Muthen posted on Monday, October 20, 2014 - 7:49 am
In my paper those reliabilities are not known but estimated from the data.