bfactor function: factor loadings and weights

[Benjamin Euen]

I have one general and one more specific question to the bfactor function of the mirt package:

My general question is concerning the factor loadings table: What is “h2” in the factor loadings table standing for? (I know that “G” is the general factor and “S1” to “Sn” are the specific factors.) Probably I missed a  brief statement and I would be thankful for a hint or reference.

My more specific question is, if it is possible to use student weights and how I can implement this in the statement.

I would be grateful for your information.

Cheers

Benjamin

[Phil Chalmers]

Hi Benjamin,

On Tue, Jun 3, 2014 at 10:22 AM, Benjamin Euen <benjam...@gmail.com> wrote:
> I have one general and one more specific question to the bfactor function of
> the mirt package:
>
> My general question is concerning the factor loadings table: What is “h2” in
> the factor loadings table standing for? (I know that “G” is the general
> factor and “S1” to “Sn” are the specific factors.) Probably I missed a
> brief statement and I would be thankful for a hint or reference.

h2 is the so-called 'communatily' found in linear exploratory factor
analysis. It's basically 1 - Σ λi2, and represents the amount of
residual variation in the item not predicted by the factors.

>
> My more specific question is, if it is possible to use student weights and
> how I can implement this in the statement.

What do you mean by student weights, could you describe this a bit more?

Phil

>
> I would be grateful for your information.
>
> Cheers
>
> Benjamin
>

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[Benjamin Euen]

I am working with TIMSS data. Each case in the dataset (respective each student) has a special weight depending on how representative the case is for the population.

[Phil Chalmers]

I see. No there currently is no way to incorporate survey weights into
the estimation algorithms, and I'm not really aware of any IRT
literature that has done this. Feel free to provide references, if you
know of any, and I'll see if it's possible to add this feature
sometime in the future. Cheers.

Phil

> --

[Benjamin Euen]

Thanks for your help and your very quick response!
Benjamin

[Phil Chalmers]

As it turns out, survey weights were quite easy to add to the package's EM engine thanks to some tips by a fellow IRT package writer, Alexander Robitzsch (maintainer of the sirt and CDM packages). The update is on the dev version 1.3.9 on Github, with an example added to the ?mirt Example section using the small Science dataset. Cheers.

Phil

[Aiden loe]

Hi Phil, 

Following the thread, could I clarify something with you real quick. I could be interpreting this wrongly, but I just wanted to be clear. The above you mentioned that the h2 in the mirt package is communality, which is the residual variations in the item not predicted by the factors. Is that not uniqueness instead? Is the term h2 differently applied for mirt? 

Kind regards,

Aiden

[Phil Chalmers]

Hi Aiden,

No, h2 is not the residual variation, it is the common variation. u2 = 1 - h2 is the residual variation not predicted by the latent traits, but I don't print that anywhere in the package. Just in case it's a definition thing: the factor commonality is the variance that is in common with respect predicting item variation, and it has the same meaning as in standard linear factor analysis texts. Cheers.

Phil