Message/Author 


I heard at your short course (day 1) of using the CFA framework to conduct an EFA. I was hoping that you could help me w/ the correct restrictions to place on the model to be able to work it, if it is even possible w/ dichotomous variables. Thanks. 


EFA within CFA works the same for categorical outcomes as for the continuous case we discussed in our Mplus short course. 

Yuan H Li posted on Thursday, August 02, 2001  8:13 am



ear Dr. Muthen: I am working on the multidimensional IRT (MIRT) data modeling. Conceptually, MIRT is the same as the Factor analysis with categories variables. Item discriminations in MIRT is similar to factor loadings and item difficulty in MIRT is similar to the item mean in FA analysis. I am wondering how many categories variables MPLUS can handle under the confirmatory FA with mean estimates? Thanks. Yuan H LI 


Yes, MIRT can be seen as factor analysis with categorical observed variables in Mplus. Item difficulty is related to the threshold parameter. Mplus allows for a maximum of 10 categories for ordered polytomous variables, that is 9 thresholds. 

Anonymous posted on Sunday, May 01, 2005  10:33 pm



Can you explain " what do u mean by EFA within CFA frame work?" and how to do it? Actually I read this help to get the factor scores. 


EFA within a CFA framework is a CFA model where an EFA model is specified. Restrictions equal to the number of factors squared must be specified to identify the model. For example, in a 3 factor model, nine restrictions must be placed. Three of them can be achieved by fixing the factor variances to one. The other 6 are achieved by fixing factor loadings to zero. How to do this is described in the Day 1 course handout. 

Anonymous posted on Monday, June 13, 2005  10:35 am



Hi Linda, Can you give an intuitive explnation for EFA within CFA framework? I have hard time understanding the why we are doing this and what we can gain from it intuitively. Thank you. 


It is setting up an EFA model in the CFA framework. This gives you the advantage of seeing standard errors for the factor loadings and also seeing modification indices including those for correlated residuals. 

Anonymous posted on Wednesday, June 22, 2005  9:12 pm



Hello, is my understanding from Bengt's UCLA web lecture correct? Thank you. For an efa in a cfa framework, the appropriate K^2 restrictions (for oblique and orthogonal solutions) are for identification purposes, achieve the least restrictve Kfactor CFA models possible, and the models are therefore considered unrestricted by Bengt, and Karl Joreskog (1969). These models will have the same chisq and df as ML EFA solutions. If the K^2 restrictions are distributed appropriately, the solutions are also unique. When models have > K^2 restrictions they are considered restricted. 

BMuthen posted on Thursday, June 23, 2005  3:44 am



All of what you say is correct. 

Cintia posted on Friday, March 30, 2007  6:05 pm



Hello, I am analyzing the structure of an established questionnaire. It has 31 dichotomous items. I first did an EFA (ULS estimator) that yielded a fivefactor solution. Then I wanted to study the correlation between these factors and other variables such as gender, age, etc. So I did an EFA in CFA framework to find the factor scores but I got the message: FATAL ERROR THERE IS NOT ENOUGH MEMORY SPACE TO RUN THE PROGRAM ON THE CURRENT INPUT FILE. THE ANALYSIS REQUIRES 5 DIMENSIONS OF INTEGRATION RESULTING IN A TOTAL OF 0.75938E+06 INTEGRATION POINTS. Would you have any suggestions as to how I should proceed? Thank you. 


It sounds like you are using the maximum likelihood estimator. You can try INTEGRATION = MONTECARLO; or you can switch to the WLSMV estimator. 

Cintia posted on Sunday, April 01, 2007  8:59 am



Thank you for the suggestions. I used WLSMV as the estimator and received the message: FACTOR SCORES COULD NOT BE COMPUTED. AT LEAST ONE OF THE RESIDUAL VARIANCES FOR THE CATEGORICAL VARIABLES IS NOT POSITIVE. With INTEGRATION = MONTECARLO, the output stated: THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NONZERO DERIVATIVE OF THE OBSERVEDDATA LOGLIKELIHOOD. THE MCONVERGENCE CRITERION OF THE EM ALGORITHM IS NOT FULFILLED. Could you please explain what might be going on? Would there be other alternatives to obtain the factor scores? Thanks. 


You have a negative residual variance which makes the model inadmissible. You need to change your model. If this does not help, you need to send your input, data, output, and license number to support@statmodel.com. 

Xuan Huang posted on Friday, July 06, 2007  1:34 pm



Dear Professors, Could you help me with the syntax of an EFA within CFA model?I am running factor analyses on 9 acculturation items. The EFA reveals one factor. I followed the Mplus handout 1 that was ordered from Mplus website to set up an EFA within CFA model. Because I am new to Mplus, I am not so sure whether my syntax is right. TITLE: acculturation data: file is 'acculturationw1.dat'; format is (F4.0, 09F10.2); variable: names are id facclt01 facclt03 facclt05 facclt09 facclt11 facclt13 facclt15 facclt17 facclt19; MISSING = blank; USEVARIABLES ARE facclt01facclt19; analysis: estimator = ml; model: acc BY facclt01facclt19*0 FACCLT13*1; acc@1; output: standardized modindices(3.84) sampstat fsdeterminacy; Could you take a look to see whether the syntax is OK? Thank you so much for your time and help! 


EFA in a CFA framework is not needed for only one factor. 

Ken Cor posted on Thursday, May 07, 2009  4:22 pm



Hello, I've successfully run an EFA in CFA using your workshop framework but am unsure if I can trust the results. The following is a portion of my input code: VARIABLE: NAMES ARE q1q14; CATEGORICAL ARE q1q14; ANALYSIS: ESTIMATOR = ML; MODEL: f1 by q1q14*0 q2*1; f2 by q1q14*0 q12*1 q2@0 q4@0 q6@0; f1f2@1; I get the following message in my output: ONE OR MORE PARAMETERS WERE FIXED TO AVOID SINGULARITY OF THE INFORMATION MATRIX. THE SINGULARITY IS MOST LIKELY BECAUSE THE MODEL IS NOT IDENTIFIED, ... THE FOLLOWING PARAMETERS WERE FIXED: 25 Pameter 25 is the factor loading of factor 2 on item 14 (Lambda 2,14) I also get some hard to believe model fit results: Pearson ChiSquare Value 9742.828 Degrees of Freedom 16322 PValue 1.0000 One final note, I've tried running this with the WLSMV estimator and I get the message that standard errors could not be calculated because my model is not identified. Any insights on how I've gone wrong and ways I can correct the problem would be much appreciated. Thank you, Ken Cor 


With the introduction of "ESEM", the new Exploratory Structural Equation Modeling approach in Mplus, you no longer need to do "EFA in a CFA framework". See the Mplus home page about ESEM and its User's Guide example addendum. One possible reason for your problem is that you might need more than one item per factor to have a good starting value of 1. The Pearson chi2 is not trustworthy with 14 categorical items because of too many empty cells. Around 8 is probably the limit. 


Hello, I am having difficulty in making the better fit decision between one and twofactor models (on binary data) thru chisquare tests. Here is what I did: I conducted CFA models (on both models in line with Mplus directions) with DIFFTEST and received a significant chisquare difference indicating that constraining the parameters (two factor model) worsens the fit of the model. Here is where I have the problem: Brown (2006) on CFA suggests a different conclusion for the comparison of chisquare values for the nested models. He interprets a significant chisquare difference as an indicator that the twofactor model fits the data better. So, which one is correct? Thanks, Cengiz 


Two factors should not worsen fit, please send the two relevant outputs and your license number to registration@statodel.com. 


Hello Dr. Muthen, I am examining the factor structure of a measure with 63 items in 23 countries and subsequently, do a test of invariance for countries that meet model fit. The items have 2 options and hence, I used Mplus CFA with WLSMV as estimator. As an initial step, run a CFA with variance of the latent factors fixed @ 1. In 4 countries, I got this message in the output: WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE F3. Kindly help me to fix this problem. Also, In all the 23 countries the CFI and TLI were below .90 but the RMSEA was above .o6. Is there any problem that you can see on this? I would appreciate if you can check one of my CFA output. Thanks, Melo 


Please send the outputs with this message and your license number to support@statmodel.com. It sounds like the model does not fit based on those fit statistics. 

Back to top 