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 Gabriella Fu posted on Wednesday, December 05, 2018 - 3:59 am
Dear Professor,

I was trying to build a bifactor ESEM model and I came across a problem, that is, I would like the general factor uncorrelated with sepcific factors, and sepcific factors correlate with each other. the UG said for oblique rotation all factors are expected to be correlated and for orthonogal rotation all factors are uncorrelated. Since ESEM is both exploratory and confirmatory, I wonder if I could set the factor correlations as I wish. If I can set correlation, how should I do so? Thank you.
 Tihomir Asparouhov posted on Wednesday, December 05, 2018 - 3:31 pm
It is not possible to fix these correlations to 0, however they usually do come out 0 as a part of the estimation procedure. In fact I don't really recall an example where they don't. Check that the general factor is not the second or third factor - sometimes that happens.
 Gabriella Fu posted on Thursday, December 06, 2018 - 4:13 am
Thank you for your reply.

FYI, if I use both general factor and specific factors as exploratory factors, and use the default rotation, the G factor and S factors would come out correlated with each other. But, if I set the general factor as a confirmatory factor, it would turn out uncorrelated with the other factors. That means, if I want the G factor and S factors uncorrelated, I would have to set G factor as confirmatory, and S factors could be exploratory. Is this correct?
 Tihomir Asparouhov posted on Thursday, December 06, 2018 - 1:50 pm
I don't think so. You have to use rotation=bi-geomin

See user's guide example 5.29.

F1 WITH FG 0.000 0.000 -7.217 0.000

F2 WITH FG 0.000 0.000 -7.931 0.000

As you can see there is no correlation between the general and the specific.
 Gabriella Fu posted on Thursday, December 06, 2018 - 6:08 pm
Thank you for your reply.

The Bi-geomin rotation would produce loading matrix with g factor uncorrelated with s factors, but what if I use target rotation? Say, I have prior information regarding the model, and would like to use target rotation, but the g factor is uncorrelated with the s factor. Is it possible to set g factor and s factor uncorrelated, and s factors correlated with each other under target rotation?

Thank you so much.
 Tihomir Asparouhov posted on Friday, December 07, 2018 - 9:23 am
It is not possible under target rotation at this time. You can use BI-GEOMIN or BI-CF-QUARTIMAX.
 Stefano Cacciamani posted on Tuesday, December 11, 2018 - 11:42 pm
Dear Colleagues,
I 'm writing for a question.

We run an Exploratory Structural Equation Modelling (ESEM), 20 items, 380 participants, 2 factors, estimator= MLR, number of classes =15. The fit indexes are quite good but we had this output "THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE

TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE

FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING

VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE

CONDITION NUMBER IS -0.196D-15. PROBLEM INVOLVING THE FOLLOWING PARAMETER:

Parameter 15, [ R15 ]

THIS IS MOST LIKELY DUE TO HAVING MORE PARAMETERS THAN THE NUMBER

OF CLUSTERS MINUS THE NUMBER OF STRATA WITH MORE THAN ONE CLUSTER.".

Have you got any suggestions regarding what should better to do to go ahead?

Many thanks for your help
Stefano Cacciamani
 Tihomir Asparouhov posted on Wednesday, December 12, 2018 - 11:31 am
You can ignore the error message if the model looks OK. Because you are using type=complex the MLF model identifiability check needs more clusters than number of parameters, which you don't have, so the actual check fails.
 Stefano Cacciamani posted on Thursday, December 13, 2018 - 12:30 am
Dear Colleague,
many thanks for your kind reply.
Stefano Cacciamani
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