fscores + indeterminacy

[Michael Paul Grosz]

When computing factor scores based on an exploratory factor analysis, there is the problem of indeterminacy. That is, "an infinite number of sets of such scores can be created for the same analysis that will all be equally consistent with the factor loadings" (Grice, 2001; p. 432). Is this kind of indeterminacy also an issue when IRT based factor scores, say WLE scores, are computed? If not, why not?

[Phil Chalmers]

All latent variable models have indeterminate factor scores. The estimator does not matter. EFA models have two kinds of indeterminacy though: rotational (infinite number of rotations), and factor score (no perfect regression to the true scores). Confirmatory models only have the latter problem.

Phil

On Sun, Aug 14, 2016 at 5:47 AM, Michael Paul Grosz <michael.p...@gmail.com> wrote:

When computing factor scores based on an exploratory factor analysis, there is the problem of indeterminacy. That is, "an infinite number of sets of such scores can be created for the same analysis that will all be equally consistent with the factor loadings" (Grice, 2001; p. 432). Is this kind of indeterminacy also an issue when IRT based factor scores, say WLE scores, are computed? If not, why not?

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[Michael Paul Grosz]

Dear Phil,

Thanks.
Are there some functions / arguments implemented in mirt to assess the quality of the factor scores and the degree of indeterminacy?
cf. Grice (2001) Computing and Evaluating Factor Scores

Plus, are plausible values one way to handle the second kind of indeterminacy?

best,
Michael

Phil

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[Phil Chalmers]

On Mon, Aug 15, 2016 at 4:52 PM, Michael Paul Grosz <michael.p...@gmail.com> wrote:

Dear Phil,

Thanks.
Are there some functions / arguments implemented in mirt to assess the quality of the factor scores and the degree of indeterminacy?
cf. Grice (2001) Computing and Evaluating Factor Scores

No, and I doubt I'd ever add them. The factor score indeterminacy has IMO been blown out of proportion far too much in the literature. In IRT work specifically the topic rarely even comes up.

 

Plus, are plausible values one way to handle the second kind of indeterminacy?

They are two different things. Plausible values are not about inferences about individuals, but rather are Bayesian realisations of the posterior distributions. Hence, you use them for different kinds of inference that do not relate to the individual directly.

Phil

 

best,
Michael


On Sunday, August 14, 2016 at 5:17:33 PM UTC+2, Phil Chalmers wrote:

All latent variable models have indeterminate factor scores. The estimator does not matter. EFA models have two kinds of indeterminacy though: rotational (infinite number of rotations), and factor score (no perfect regression to the true scores). Confirmatory models only have the latter problem.

Phil

On Sun, Aug 14, 2016 at 5:47 AM, Michael Paul Grosz <michael.p...@gmail.com> wrote:

When computing factor scores based on an exploratory factor analysis, there is the problem of indeterminacy. That is, "an infinite number of sets of such scores can be created for the same analysis that will all be equally consistent with the factor loadings" (Grice, 2001; p. 432). Is this kind of indeterminacy also an issue when IRT based factor scores, say WLE scores, are computed? If not, why not?

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[Michael Paul Grosz]

On Tuesday, August 16, 2016 at 3:36:53 AM UTC+2, Phil Chalmers wrote:

On Mon, Aug 15, 2016 at 4:52 PM, Michael Paul Grosz <michael.p...@gmail.com> wrote:

Dear Phil,

Thanks.
Are there some functions / arguments implemented in mirt to assess the quality of the factor scores and the degree of indeterminacy?
cf. Grice (2001) Computing and Evaluating Factor Scores

No, and I doubt I'd ever add them. The factor score indeterminacy has IMO been blown out of proportion far too much in the literature. In IRT work specifically the topic rarely even comes up.

I also noticed that almost nobody in the IRT literature talks about the indeterminacy problem discussed extensively in the factor analysis literature. That was the reason why I was wondering whether it is still an issue in the IRT framework.

 

Plus, are plausible values one way to handle the second kind of indeterminacy?

They are two different things. Plausible values are not about inferences about individuals, but rather are Bayesian realisations of the posterior distributions. Hence, you use them for different kinds of inference that do not relate to the individual directly.

 I did not have in mind to use factor scores for individual diagnosis. I would like to use WLE scores in SEM models, as predictors, outcomes etc.