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Mplus Discussion > Categorical Data Modeling >
 Jan Ivanouw posted on Thursday, August 19, 2010 - 10:46 am
I am working with a model for at psychological test with categorical indicators (items) trying to understand factor score calculation when there are no covariates (x)

Reading the Appendix 11, I find in expression 230 (for continuous y) both a representation of yi and of xi.
In expression 229, though, there are only an representation of xi, and no representation of yi. There are the thresholds to sort of represent the y-score, but they does not vary across individuals, so it seems impossible to calculate the factor scores for individuals. I apparently have misunderstood something, but what?
 Linda K. Muthen posted on Thursday, August 19, 2010 - 2:00 pm
Factor scores for categorical indicators cannot be calculated by hand. The procedure is iterative.
 Jan Ivanouw posted on Thursday, August 19, 2010 - 10:59 pm
Hi Linda,
Oh, I should have mentioned that I am building a simulation model (in Splus), så iteration is no problem.

It is important for me to be able to compare the factor scores I am producing in my program with the factor scores produced when using Mplus with the same data, and hence my problem:

I am using the expressions in the Technical appendix 11 to build into my program, but it seems that there might be an error in expression 229. To me there seems to be only parameters that vary over indicators, while the individual is only represented by eta, which is the variable the size of which for the individual is going to be determined using the iterative procedure.

But probably I am misunderstanding something?
 Linda K. Muthen posted on Friday, August 20, 2010 - 10:04 am
Formula 229 is correct. Subscript i should be only on Eta. Parameters do not vary over individuals.
 Jan Ivanouw posted on Thursday, September 09, 2010 - 2:46 am
I also thought I was wrong, but what I don't understand is:

The point is to find the value of eta (iteratively) that makes the observed score vector of the person most likely. To do this, the score vector must be included in the process somehow. Can you help me understand how the (categorical) score vector is used in the estimation of eta?
 Linda K. Muthen posted on Thursday, September 09, 2010 - 10:41 am
The observed score vector of each person is used. x_i is the observed score vector for individual i. Eta_i is the factor score. Lambda_j and Kappa_j are the slopes and intercepts for item j.
 Jan Ivanouw posted on Thursday, September 09, 2010 - 1:43 pm
I thought that x_i was observed scores for covariates (for instance gender or socio-economic category) while y_i would be the observed scores on the indicators (test items)?
 Linda K. Muthen posted on Thursday, September 09, 2010 - 3:19 pm
Yes, the observed score vector includes both x and y.
 Jan Ivanouw posted on Friday, September 10, 2010 - 3:43 am
But how is the y-part of the score vector included in the proces of estimating eta for a person?
 Linda K. Muthen posted on Friday, September 10, 2010 - 8:48 am
Please see formula 231. This function is minimized to obtain factor scores. Both x and y are part of this function.
 Jan Ivanouw posted on Friday, September 10, 2010 - 8:58 am
Sorry, this is where I probably am blind.

Where in formula 231 is y represented?

Sure, formula 229 is inserted into formula 231, and the left side of formula 229 is f_j(y_i_j|eta_i, x_i), but the right side of formula 229 does not seem to contain y?
 Linda K. Muthen posted on Friday, September 10, 2010 - 9:23 am
y is implicitly present on the right-hand side of formula 229 because the categories of y determine s in 229.
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