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Re: st: Generating indices over nominal data?


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Generating indices over nominal data?
Date   Thu, 21 Jun 2012 12:42:07 +0200

On Thu, Jun 21, 2012 at 12:21 PM, Andrea Bennett wrote:
> I have data on individual background knowledge
> on 10 different topics. 3 of the topics are theoretically
> similar (e.g. knowledge on public goods or
> common pool resources or market externalities
> could be considered as linked). For each item I have
> a 3-point scale that says "no knowledge",
> "some minor knowledge", and "deepened knowledge".
>
> I use all of the 3 linked items as unique controls in a regression,
>  that is a dummy of each item and level. However,
> this becomes tedious when interacting my treatment
> variable with each of these items separately. Still
> I do not feel very confident aggregating all three variables
> since one item might be more relevant that the other.

The easiest solution would be to add those indicator variables. This
is equivalent to constraining the effects of the three items to be the
same, which in some cases makes sense and in others less so. Anyhow,
it is a testable constraint. See:
<http://www.maartenbuis.nl/publications/sum_constr.html>

If you think of these items as adding up to a total pool of knowledge
on this issue and that total pool in turn influences whatever outcome
variable you have, than you can look at:
<http://www.maartenbuis.nl/wp/prop.html>

If you think that these items are influenced by some latent variable
(probably knowledge) than you could look at (Hardouin et al. 2011).
Notice that the distinction between this way of thinking and the
previous one is that now the latent knowledge is influencing the
observed items, while in the preceding way the observed items are
influencing the latent pool of knowledge. Choosing between these two
is just a matter of theory and substantive knowledge of the phenomenon
being studied.

Hope this helps,
Maarten

Jean-Benoit Hardouin, Angélique Bonnaud-Anti, Véronique Sébille (2011)
"Nonparametric item response theory using Stata". The Stata Journal,
11(1):30-51.
<http://www.stata-journal.com/article.html?article=st0216>


--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany


http://www.maartenbuis.nl
--------------------------

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