triple standardization

[gren spas]

I have a question about triple standardization and weighting. I came across a published article that standardizes 3 times the same data. My statistical knowledge is limited, by I am wondering if this makes any sense. Here is the situation: imagine you have a dataset with 40 variables measuring, let’s say, different forms of well-being. What the authors of this article do is first standardize ((var-(mean))/sd) each of the 40 variables. Then they grouped the 40 variables into 5 indexes and standardized the indexes. Finally, they combined the five indexes into a single measure and standardized it again. It goes approximately like this:

1. Standardize the raw data (which is on the same scale)
foreach var of varlist x1-x40 {
summ `var’ [aw=weight]
replace `var’ = (`var’-r(mean))/r(sd)
}

2. Combine the raw data into 5 indexes and then standardizing again
egen Index1=rowtotal(x1…x8)
…
egen Index5=rowtotal(x32-x40)

foreach var of varlist Index1-Index5 {
summ `var’ [aw=weight]
replace `var’ = (`var’-r(mean))/r(sd)
}

4. After presenting some descriptive evidence using the 5 indexes the authors combine them into a single measure, and then standardize it again.

gen Composite=Index1+Index2+Index3+index4-Index5
foreach var of varlist Composite {
summ `var’ [aw=weight]
replace `var’ = (`var’-r(mean))/r(sd)
}

My question is: Does this procedure makes sense? Does the triple standardization influence the results (in terms of significance)? And is it correctly, to use population weights 3 times?

I am asking these questions because I have a similar dataset as these authors and would like to follow their procedure, but I am not 100% convinced that it is correct.

[Carlo Lazzaro]

Gren:
welcome to the list.
What you ask is far away from my research field but I will give it a try anyway.
I woud take a look at -help factor- and see if it offers you some guidance.
As an aside (and as per FAQ), please provide the list with full reference whenever you quote somebody's published contribution, working paper or the like. Thanks.

[gren spas]

Dear Carlo, thank you very much for your reply and welcome.
I see now that I should have formulated my question much better. My post was not intended to be a reaction to a particular paper, but to describe a situation in which there is a triple standardization with weighting. So please consider my question as a hypothetical question. Does it make sense from a statistical point of view to standardize 3 times using population weights?
Using some artificial data I did some experiments and compared the results: (i) standardize 3 times, (ii) standardize only the raw data and the final composite index, i.e. 2 times, (iii) standardize only the raw index, i.e. 1 time, (iv) standardize only the final composite index, i.e. 1 time. Then I used the resulting composite index from (i)-(iv) as a RHS variable. In terms of the estimated coefficients it seems that it doesn't matter much how many times one standardizes. The p-value of the composite index changes only very slightly, and so do the size of the coefficient (once I account for different scales of the index). So my preliminary conclusion was that it doesn't matter how many times it is standardized, because the results from the experiment are practically unchanged... but of course, my experiment doesn't prove that standardizing 3 times is correct. So by posting my question here I tried to get an answer whether triple standardizing makes any sense in the situation at hand that I described.
Thanks and have a great rest of the day;-)

[Carlo Lazzaro]

Gren:
your question was clear in your first post (the FAQ recommendation of quoting the full reference of the article you mentioned still holds, though).
Whenever "odd" methodological approaches creep up as published contribution in a given reserch field, one can take them as a justification for her/his own approach (even though this road is not always toll-free: what was wrong once remains wrong, even if repeated thousand of times; hence reviewer and/or audience are legitimated to bark at you) or as a comparison to your own way of dealing with the same issue (i.e., comparing the results obtained with one vs three standardizations in yiur case).
That said, I've never heard about three standardizations, but it may well be because I haven't had the chance to.