Scale Transformation

[Nastia Nadroni]

Dear Community,

I am currently sitting on the preparation of my variables. I have already searched the whole forum and can't find a suitable post, although the problem I have is probably a common one?

I am trying to convert a 5 point Likert scale to a 4 point scale and the same with an 11 point scale, this should also be converted to a 4 point scale.

One example for the 11 point scale would be:
mueclt
Country's cultural life undermined or enriched by immigrants
Value Category
0 Cultural life undermined
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 Cultural life enriched
77 Refusal*
88 Don't know*
99 No answer*

One example for the 5 point scale would be:
mnrgtjb
Men should have more right to job than women when jobs are scarce
Value Category
1 Agree strongly
2 Agree
3 Neither agree nor disagree
4 Disagree
5 Disagree strongly
7 Refusal*
8 Don't know*
9 No answer*

In one paper I found the following hint:
"Here we follow the approach of Proto and Rustichini (2012). Specifically, we transform the 11-response scales using the formula (X-5)*4/10, and we transform the 5-response scales using the formula X-3."
The paper referred to: https://warwick.ac.uk/fac/soc/econom...2012_proto.pdf

Unfortunately I don't know how to implement this one and wanted to try my luck and ask in this forum, thanks in advance!

[Clyde Schechter]

gen mueclt_4 = (mueclt-5)*4/10
gen mnrgtjb_4 = mnrgtjb-3

will implement the transformations you show. On the other hand, those transformations do not work in the way you describe. The X-3 transformation involves no rescaling at all: it is just a shift transformation that centers the scale at zero, so it now runs -2 to 2. The (X-5)*4/10, again, centers the scale at zero, and also rescales it to run from -2 to +2. But in neither case does it change the number of points in the response scale. The scales still have 5 and 11 distinct response values, respectively. But now both of them range from -2 to 2.

By the way, make sure you recode the magic number responses (7 through 9, and 77 through 99 in the two scales, respectively) to Stata missing values. Leaving these non-response values coded as actual numbers will get you in trouble in Stata when you start analyzing your data.