Creating an Index in Stata

[Marie Lohrum]

Dear Statalisters,
I have searched the Internet now for over 2 hours, but it seems like no one had ever online asked something about the problem I am facing at the moment. Maybe it is also a stupid question.

So, I want to build an Index on the respondents attitude towards a latent construct. The variables I want to combine differ in their scales. One of them has 3 answer categories (good thing, bad thing, neither nor), two have an answer scale of 0-10 and one only has 2 answer categories (Approve, disapprove). I have recoded my nominal variable into a dummy, where 0=disapprove and 1= approve.
Now, I can't just add these variables up to build an index as they are scaled differently. My supervisor told me to rescale the variables, meaning to scale the 10-scaled ones down to a 3 scale and "puff" the 2-scaled ones up, so I can build an index. Does someone know a code on how to do this?
I would also have no problem with kicking the nominal variable out, as I know that puffing it up may be impossible.

Thanks in advance. I'm looking forward to your answers,
Marie

[ericmelse]

The big assumption here is that each of the three groups of respondents tap the same latent construct for their response. My "exploratory" approach would be to run for each group separately an IRT-model and (assuming these models are acceptable) predict the theta score for the respondents for each group. Next, I would standardize these three scales and then analyse all respondents using there scores as if it is one scale. I suppose you have some other measurement (characteristic or outcome?) that is identical for the respondents of the three groups. Possibly, you can regress your theta scale on that measurement using linear or logistic regression etc.

[Marie Lohrum]

Thank you for your answer.
I think I was a bit unclear in my question (maybe also because I don't know all of the technical terms). I am working with the European Election Survey, so with a dataset of 30.000+ respondents. I don't have three different groups of respondents. My question refers to how I can combine items that were asked differently into one index. They were still asked to the same respondents.
Further, I am well aware that rescaling items is not particularly academic, as this means that I either loose information or assume information that was not even given. In my particular case however, it is a necessary evil.
I want to include the different indices I create into a linear regression model as independent variables.

[ericmelse]

Actually, this is not that difficult to do with Stata. You could use a so-called hybrid IRT model. Consult the Stata help file - help irt hybrid - as well as the PDF of the documentation. It is then a matter of deciding which type of IRT meets best your assumptions regarding the sets of questions. It might be useful to first run separate IRT models for each set of questions and inspect the various test graphs (I always do). Next, you run the hybrid model and use that model, after checking if the model meets your assumptions, to predict your latent theta. Again, to be able to analyse group differences it is best to standardize the theta (which would not make that much difference with the original theta given that your cohort is large). This approach should produce what you are looking for without rescaling any items.

[wbuchanan]

A first step before fitting any IRT models would be to confirm the dimensionality of the items. Stata’s IRT models are very specifically unidimensional IRT models and will have some suboptimal properties if applied to a multidimensional construct.