Composite index of risk perceptions

[Julie Ann Basconcillo]

Good day!
I want to assess whether there are differences in risk perceptions of 2 subpopulations. Using 5-point Likert-scale responses (scale of 1-5 where 1=extremely serious and 5=not serious) to several Likert-type questions, I will build an index of risk perceptions for each subpopulation. I have 10 Likert-type questions and for each question (or risk perception category), I understand that I have to calculate the weighted mean of responses for each respondent, X
X = {5 x F(5) + 4 x F(4) + … 1 x F(1)} / N where F is the frequency of responses and N the total number of respondents/ observations. See:
5 = extremely serious...1= not serious
I have a total of 14 questions (or risk perception categories). To get the index (or mean score) for each subpopulation, I read that I just need to get the ratio of each weighed mean X and the total number of questions (i.e. 14). Is this correct?
If so, how do I do that in Stata? I cannot seem to find the correct command to recode the Likert scale responses. This index will then be used in an ordered logit regression as one of the dependent variables.
Thank you in advance.

[Svend Juul]

This is not as complicated as you think (unless you have a strange data structure). If the response variables are q1-q14, each coded 1-5, you get the mean response for each individual as:

egen qmean = rowmean(q1-q14)

[Phil Bromiley]

What is your original data like? Do you have individual responses or just the subpopulation numbers?

If you have the original (individual-level) data, you can just use the egen above to calculate the scale and then ologit.

There are several other ways to calculate scales - see the procedure called alpha for some ways.

With 14 questions each with 5 possible responses you have 70 possible values for your dv, although it is likely many will not actually appear in the data. While ologit makes sense in terms of not just assuming ordinal measures, I suspect your combination requires more than ordinal measures. That is, for the sum/scale to make sense, you must assume that the difference between 1 and 2 is the same as the difference between 2 and 3, etc. In other words, if you only had three items in the scale, you're assuming that 1 2 3 is the same as 2 2 2 and 3 2 1. This only works if the items are more than ordinal. Once you make this assumption in making the scale, there is no reason to treat the scale itself as just ordinal. This means you can probably use simple regression.

[Julie Ann Basconcillo]

Thanks, Svend! Yeah, it's not that complicated. The problem is I am not familiar with the code. And I'm afraid I might be spending too much time if I figure it out by myself.

Thanks as well, Phil! Yes, I have the individual responses. I will try alpha as you suggested. No, I don't think I could make the assumption of interval scales on the question of seriousness.