Combining different scales to one factor

[Tilman Woerz]

Hey everyone,

I'm kind of new to stata and currently working on my bachelors thesis. I'm trying to create a "migration hostility index" from different variables using the european social survey, unfortunately they do not have the same scales (some have 5 point likert, some have 10 point semantic differential). As the index will be my dependent variable in an OLS Regression, it would be great to find a way combining the different variables into one index. The easiest way, of course, would be to standardize every variable. However, I believe this would not be statistically correct, as 5-point likert and 10-point semantic differentials can not be treated alike. So what I did is run factor analysis using "factor" in stata with all 10 variables. Fortunately I found only one factor with eigenvalue beyond 1 (i.e. eigenvalue of 4.25), and therefore I used "predict" to create a new variable containing each observation's score on said factor. So far this kind of works out, however, I'm not completely sure if this way of dealing with the above issue of combining different scales is statistically proper. It would be great to hear some experts' comments on my procedure.

Thanks,
Tilman

[Konrad Zdeb]

Tilman, there is an abundance of literature concerned with the development of indexes. For instance, in the UK, New Zealand, Canada different deprivation indecies are used in resource allocation formulas. Before combining the data I would explore literature for guidelines. The actual way of combining variables would depend on weighting weighting, selected measures and how do you want to use the index (whether you are looking for a rank or a relative figure corresponding to prevalence of certain attitudes, is index spatially aggregated, etc.). You may also want to have a look at this Stata programme used to generate Human Opportunity Index here.

[Tilman Woerz]

Hey Konrad,

thanks a lot for your quick answer. There might have been some kind of misunderstanding, though. I mainly want to combine 10 variables that had questions like "If immigrants are long term unemployed they should be made to leave" (5-Point Likert) or "Immigrants make country worse or better place to live" (10-Point semantic differential) into one variable. If all 10 Variables used a 5-point likert scale I would simply calculate each observations mean on those 10 variables (which is not possible, as different scales were used). So the main question is whether it is valid to use "predict" after "factor" (using all 10 Variables) to create a new variable that gives the values of this factor for each observation. I hope this clarifies my issue a bit.

Thanks,
Tilman

[Nick Cox]

Tilman: I don't think your question can be easily answered. Across the sciences this approach is variously regarded as a practical way to proceed by some and as highly objectionable, dubious or dangerous by others. There isn't a sense in which the question of valid or invalid would get unanimous agreement from statistically-minded researchers.

What we don't have is the context of what you have been taught. It seems to me that there should be someone at your own institution who should be much better placed to give you advice. The internet is not an oracle that can give you the best advice for your circumstances.

[Jonathan Muringani]

Hi Tilman

If I understand you, you want to do the following

1. Standardise your scales
2. You want to aggregate the individual measure (meaning the actual survey question\answers into a composite measure, which can be aggragated again if necessary.

I am a novice but had a similar challenge, it think I overcame it. Is that what you mean.

Regards

Jon