Message/Author 

Anonymous posted on Monday, March 29, 2004  12:53 pm



I am running a CFA with 36 items and 9 factors. I have no problem generating the CFA, all of the factor variances are positive and all of the residual variances for the items are positive. However, when I try to save the factor scores I get the error message: THE MODEL COVARIANCE MATRIX IS NOT POSITIVE DEFINITE. FACTOR SCORES WILL NOT BE COMPUTED. CHECK YOUR MODEL. I have done all the model checks that seem reasonable and I'm not sure what to do at this point. Please advise. 


Look at TECH4. You probably have latent variable correlations greater than one. 


Hello Linda or Bengt Could you kindly tell me the command for generating factor scores for categorical dependent variables please? I used FSCOEFFICIENT, but the output stated that this command was not available for analysis with at least one categorical dependent variable. Thanks... 


See the FSCORES option of the SAVEDATA command. 

Kihan Kim posted on Monday, April 06, 2009  5:16 pm



Dear Dr. Muthen: Hello, using Mplus 5.1, I was able to run ESEM with a series of binary data (coded 0 or 1) to obtain factor scores. If, for example, the input data measured the presence or absences of various medical symptoms, then what do the factor scores represent? I'm having a little trouble understanding the conceptual meaning of the factor scores based on binary data. In other words, what do the continuous factor scores (i.e., the degree of the latent factor) mean when the items are measured on the basis of presence or absence of certain elements? Could you please let me know your thoughts? (and/or refer me to relevant readings) Many thanks, Sincerely, Kihan 


In your medical application, the factor might correspond to the degree of the medical problem studied that an individual has. With an item having a positive loading, say, a higher factor value of the problem gives a higher probability of a positive symptom. For literature, see e.g., Muthén, B. (1996). Psychometric evaluation of diagnostic criteria: Application to a twodimensional model of alcohol abuse and dependence. Drug and Alcohol Dependence, 41, 101112. (#66) 


Hi Drs. Muthen, I am wondering if the formula for calculating factor scores differs when dealing with categorical manifest variables, compared to continuous manifest variables? It seems that when you have categorical manifest variables, a raw score of "1" isn't really a "1" anymore because it is transformed into a probability. I am trying to calculate factor scores on my own based on the factor structure and polychoric correlation matrix as output by an EFA in Mplus. Is it statistically safe to apply the factor score operation on the raw categorical data? Sincerely, Erik 


Yes, they differ. See Technical Appendix 11 on the website. You cannot calculate factor scores for categorical outcomes by hand. The procedure used is iterative. 

Sam Smith posted on Friday, May 21, 2010  11:24 am



I am having some trouble understanding the metric of a factor score when the indicators are ordered categorical variables and the estimation method is WLSMV versus ML in Mplus. I estimated the factor model first using WLSMV and then the same factor model using ML (the model is a CFA with one factor and indicators defined as categorical variables). The factor score saved by Mplus has a larger variance when using ML compared to its variance when using WLSMV estimation. Is this related to the fact that logistic regressions are used in the ML estimation and probit regressions are used in the WLSMV estimation and logit coefficients usually run higher than probit coefficients or is this due to something else? And what is the metric of the factor score constructed using WLSMV and ML respectively? Thank you very much. 


To compare the factor scores, fix the metric of the factors by having all factor loadings free and the factor variance fixed to one. Note also that ML uses EAP and WLSMV uses MAP so that will also account for differences. 


I ran two identical ESEM models that differ only in that one requested to save factor scores and the other didn’t. Both models terminated normally and show good model fit. But, the model where the factor scores were requested returned the message: “The model covariance matrix is not positive definite. Factor scores will not be computed.” There are no negative residual variances or correlations greater than 1. What needs to be adjusted in the model so factor scores can be computed? 


Perhaps your ESEM model allows correlated residuals in which case the estimated covariance matrix for the residuals (Theta matrix) may not be pos def. Look at the standardized solution. 


Thank you very much for your response. I have another related question. There are 86 categorical indicators with 10 factors: 1 formative factor and 9 reflective factors in the above mentioned ESEM model. The residuals of the formative factor are correlated, by definition. After reading your response, I found factor scores were generated when I ran a model with the 9 reflective factors only. Does this mean that factor scores can't be generated when a formative factor is included in the model? 


Formative factors do not have residuals. I'm not sure what you mean by them being correlated. I think they are not generated for formative factors because of the residuals being fixed at zero. 

Ben Tabak posted on Saturday, February 09, 2013  10:24 am



We’d like to generate factor scores from two different TSO models. In the first model, “state” factors are measured by three continuous observed variables and factor scores are generated with no problem. In the second model, “state” factors are measured by two continuous and one categorical observed variable. In this case, when attempting to generate factor scores, we get the following error: THE MODEL ESTIMATION TERMINATED NORMALLY THE MODEL CONTAINS A NONZERO CORRELATION BETWEEN DEPENDENT VARIABLES. SUCH CORRELATIONS ARE IGNORED IN THE COMPUTATION OF THE FACTOR SCORES. THE MODEL COVARIANCE MATRIX IS NOT POSITIVE DEFINITE. FACTOR SCORES WILL NOT BE COMPUTED. CHECK YOUR MODEL. In a previous post, you suggested looking at TECH4 to identify latent variable correlations greater than one when receiving an error such as this. We do not have any latent variable correlations greater than one, so I wanted to ask if you have any further suggestions that will assist us in generating factor scores for our second model? 


Please send the output and your license number to support@statmodel.com. 


I am using EFA on a set of categorical and count observed variables and want to output the factor scores. I understand EFA factor scores can only be saved using ESEM. However, as of version 7.11, ESEM cannot handle count variables. Is it possible to compute the EFA factor scores using any of the Mplus technical outputs? I have controlled for complex survey design in my EFA analysis and want to do the same in my factor score computation. Thank you. 


Factors scores for count variables are not available. 


That is, they are not available for EFA. 


Thank you, Linda, for your prompt reply. I know that Mplus EFA cannot output factor scores, and EFA factor scores can only be saved using ESEM approach for all variable types except 'count' variables. My question is: Is it possible for users to compute the factor scores from their EFA (on count variables) using any of the Mplus technical outputs provided by the EFA module? Thank you. 


It would be quite difficult for a user to compute factor scores with counts. The best you can do is probably to redo your EFA as an EFAwithinCFA and then request factor scores in the CFA setting. EFAwithinCFA is described in Topic 1 of our short courses shown on our website. 

Ian Koh posted on Sunday, February 23, 2014  6:54 pm



Hi Linda and Bengt, My lab are analysing a dataset using a behavioural adjustment scale using CFA. We want to see if we could further develop this scale into a predictive tool for local practitioners (i.e., practitioners in the same country as our study). We would like to know if we could use factor scores for this purpose. To elaborate, each latent factor has several observed variables, so that there are several equations for one latent factor. Is it possible to combine the equations representing these observed variables, and then make the factor score the subject? All this might seem excessive; however, our idea is to use the factor loadings obtained in our study as a standard that local practitioners could apply to their item scores. Combined with item scores, factor scores would then be obtained which could be compared with each other on the national level. This would yield greater utility to a behavioural adjustment scale that was originally conceptualised in a completely different cultural setting. We look forward to hearing your opinions on this matter. Thanks! 


It sounds like you want to use a CFA model as a prediction model. You can do this by fixing all parameters at their model estimated values and then predicting factor scores for new observations. You make the assumption the the new observations are from the same population as the sample used to create the prediction model. You can use the SVALUES option of the OUTPUT command to obtain input with starting values of the final values of the estimated model. Change the * to @ for fixed values. 

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