I'm not an IRT expert, but my best guess as to the answer to your question is that most IRT models in practice are unidimensional.

Factor score indeterminacy (as opposed to the introduction of error by making a manifest variable from a latent) is a feature of models with multiple factors -- it's introduced by the existence of equivalent models, which is not an issue with single-factor (or trait) models.

Thanks for a quick answer, but I don't think that the factor score indeterminacy has anything to do with the dimensionality. Factor scores are indeterminate because of the presence of the unique factor, which prevents the weighted sum of the manifest variables to equal the factor(s') values exactly (that's why the component scores are perfectly determinate - PCA is technically a factor analysis model with zero uniqueness). It's easy to check that the value of the factor score determinacy coefficient (a'*inv(R)*a) is less than 1 for one-factor solutions as well.

Ok, we're clearly using the terms differently. In my experience in psychology, FSI is most often invoked with respect to rotations (i.e., relevant to multi-factor solutions).

I understand and agree with your point about the residual components, but the difference in terminology threw me off of your intent.

Then you probably had the "rotational indeterminacy" in mind. This is an issue unrelated to the estimation of factor scores (for instance, you have rotational indeterminacy in PCA and in exploratory common factor analysis, but not in confirmatory FA; on the other hand, you have factor score indeterminacy in both exploratory and confirmatory FA, but not in PCA).

I think you are absolutely correct in that factor indeterminacy applies to IRT models as well. That is why it is better to use a latent IRT variable instead of the IRT score in for example a SEM model. If I am not wrong Thomas, Lu & Zumbo (2005) writes about this in "Embedding IRT In Structural Equation Models: A Comparison With Regression Based On IRT Scores".

@Jan: The most formal definition of FSI I can think of is that correlation between factor scores and their respective factors is less than unity, unless the unique factors have zero variance (which should never happen in real life). Therefore, values of factors cannot be exactly determined (even if we have an infinitely large sample and perfect model fit). Mulaik's Foundations of factor analysis provides an extensive discussion of various aspects of FSI.

In modelling like SEM, we usually work at the level of covariance structures rather than on the raw data level, so there is no need to mess with factor scores. In my view (I haven't read the paper mentioned by Kyrre yet – btw, thanks for the reference), using actual factor score estimates in modelling is not optimal because in this case we contaminate the data with the estimation error due to FSI.

SPSS program will do it.

What about IBM SPSS Amos 21 which goes together with IBM SPSS Statistics 21?

Are you sure?

Also each program has description in help which is very valuable for a researcher.

Http://statblogs.ru/tag/programma-amos/

@Jan:

Ad preliminary: your description is almost correct. “Almost” because it happens only with the common factor model, while the component scores are perfectly determinate.

Ad 1: In fact, correlation with a constant is undefined rather than zero. Anyway, in this case this is irrelevant, because we wish to estimate scores on common factors only, while the unique factors’ scores are not of interest.

Ad 3: In the classical context, the measured score (and consequently its variance) is divided into three uncorrelated parts: 1. the common part, due to the common factor(s), 2. the specific part (specific for a variable, systematic, ie. nonrandom, but uncorrelated with other measured variables) and 3. random measurement error. 2+3=value of the unique factor, 1+2=true score. But it may be true that in the latent trait theory context the specific parts are not very useful: both random and systematic error make a score a worse measure of the latent trait.

Ad4) FSI is a group level phenomenon because it is defined via correlation across persons.

There is no indeterminacy problem in unidmensional IRT (though there are still identification constraints required). In multidimensional IRT, there is indeterminacy in the origin, scale, and rotation of factors, similar to a factor analysis model. See for instance Mark Reckase's multidmensional IRT book (chapter 8 of http://goo.gl/nUrGCP).

One can express a unidimensional IRT model as a single-factor CFA model--and that factor is indeterminate. Guttman's measure of its indeterminacy is 2(LR-1L')2 -1, where L is a vector of loadings for the single, common factor and R is the correlation matrix for the observed variables; (LR-1L')2 is the squared multiple correlation between a factor estimate and the true factor. If the r-sqr is, say, .8 then Guttman's measure is .6 on a scale that goes from -1 (completely indeterminate) to 1 (completely  determinate). Indeterminacy is way overblown as a problem; there are an infinite no. of factor solutions that satisfy the equations, but there is only one that any sane person would ever choose--the least squares estimate, the one with the smallest L2 norm (in matrix parlance).