EFA With Two Cross Random Factors?
Message/Author
 David Sidhu posted on Thursday, April 05, 2018 - 3:55 pm
I have a set of 20 items that have each been rated by thirty participants, on 25 dimensions. I am interested in performing factor analysis on those 25 dimensions.

I gather that it would be no problem to conduct a multilevel factor analysis, and account for the fact that observations are nested within participants. But, could I also model the fact that observations are nested within items? Note that subjects and items would be fully crossed random effects, not nested within each other.

I can't quite figure out if MPlus can do this?
 Tihomir Asparouhov posted on Thursday, April 05, 2018 - 5:22 pm
Something like that should work

VARIABLE: NAMES = y1-y25 subject item;
CLUSTER = subject item;
ANALYSIS: TYPE = CROSSCLASSIFIED;
ESTIMATOR = BAYES;
MODEL: %WITHIN%
f BY y1-y25;
%BETWEEN item%
y1-y25; [y1-y25@0];
%BETWEEN subject%
y1-y25; [y1-y25];

Search the user's guide for CROSSCLASSIFIED to see more examples or take a look at
 David Sidhu posted on Thursday, April 05, 2018 - 6:34 pm
Thanks for getting back to me! I will try that. I realize that I may not have been specifying the random terms correctly. In my attempt to run a model with observations nested within subjects, I did this:

TITLE: exploratory factor analysis
DATA: FILE IS wordtriallevelmplus.dat;
VARIABLE: NAMES ARE...(removed to save space);
USEVARIABLES ARE ...(removed to save space);
CLUSTER = PPT;
MISSING ARE ALL (999);
ANALYSIS: TYPE = TWOLEVEL EFA 1 5 UW 1 5 UB;
OUTPUT: MODINDICES;

Did I also need to add the extra bits you did for the MODEL? I.e., also add:

MODEL: %WITHIN%
f BY y1-y25;
%BETWEEN subject%
y1-y25; [y1-y25];
 Tihomir Asparouhov posted on Friday, April 06, 2018 - 8:44 am
No. EFA models don't need a model statement.
 David Sidhu posted on Monday, April 09, 2018 - 11:22 am
Okay thanks!

Am I correct that the syntax you wrote out originally isn't for an EFA? Rather, I would have to adopt that for an EFA?
 Bengt O. Muthen posted on Monday, April 09, 2018 - 4:03 pm
Yes, Tihomir's syntax was not for an EFA. EFA is not available for cross-classified analysis.
 David Sidhu posted on Monday, April 09, 2018 - 4:07 pm
Okay, thanks very much for the response!