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In Technical appendix 11 factor score estimation is described for continuous and for binary y variables. Is there any technical appendix or other notes describing factor score estimation for categorical y variables with more than two categories and with y count variables? 


No. But with ML estimation and categorical and count outcomes factor scores are obtained by the standard EAP approach discussed in IRT, where EAP stands for expected a posteriori. 


Concerning count indicators: Could you give a little more hints on how the factor scores are calculated? 


It is done in line with factor scores for the IRT model as discussed in for instance http://apm.sagepub.com/content/9/4/417.abstract or any IRT book. It requires progamming an iterative algorithm  cannot be done by hand. 


Thank you for your help. I have a problem whith understanding the litterature, though. As far as I understand the Muraki/Engelhard paper and other IRT textbooks (Embertson & Reise, 2000; Ayala, 2009), they assume categorical indicators with a preestablished number of possible response categories (like dichotome data or Likerttype data). My problem is how to apply the EAP to obtain factor scores with count data (Poissontype). 


The principle is the same for counts. I don't know off hand of a reference for EAP with counts  we haven't written it down explicitly in a paper. 

Jan Ivanouw posted on Wednesday, September 28, 2011  8:57 am



I am sort of stuck with this problem. I don't know if you could help me a little further. I have not found any useful reference for calculating factor scores using EAP with counts. Can I use for instance an adaptation of eq 229 and 230 from appendix 11? In the output from either Poisson or Negative Binomial models, I don't get any residual variances, but they seem to be necessary for calculating factor scores? 


Mplus computes factor scores for count factor indicators. The general formula of (222) of Appendix 11 is used. With counts the f(y) part of the formula is a Poisson or Negative binomial distribution. The expected value of this expression is used as the estimated factor score. This is obtained via numerical integration. In other words, there is not an explicit formula that can be used. The formulas for computing the posterior on page 151, bottom two formulas, in http://statmodel.com/download/ChapmanHall06V24.pdf may also be helpful. Poisson and negbin don't estimate residual variances, although negbin gives a scale factor which is used in the above computation. 

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