Totally confused! re-scaling using rank ties command?

#1
Hi, Thank you all for all those kind helps all the time. I'm always getting useful advices here.


This time, I have a question on making a composite variable and rescaling...

let's say I have these three variables
- V_club : number of clubs a respondent join (range 0 ~ 10)
- V_talk : frequency of talk a respondent have with club members (7 point likert scale, where 1:never, 7:always)
- V_Ch : number of friends a respondent have in clubs attending (range 0 ~ 8)


I want to combine these three variables into one composite variable using this formula new variable = sqrt(V_club*V_talk) + sqrt(V_club*V_Ch) + sqrt(V_talk*V_Ch)

# sqrt = squre root


First of all, I tried to z-transform all the three variables(V_club, V_talk, V_ch) since they are measured on different scales.
However, by the formula above, I cannot just z-transform all since by doing that, I will have negative and zero values which should be avoided when calculating square root.


So, I asked my adviser, and she said to me to
"rank the variables, and make 5 ties (using spss 'rank cases' command and use 'Ntiles=5' subcommand), and use them as 5 point likert scaled variables"

(In other words, lowest 20% values is grouped and recoded to '1', values from lowest 20% to 40% is recoded to '2', values from lowest 40% to 60% is '3', values from 60% to 80% is '4', highest 20% values to '5')


Now I am really confused since, to me, the newly calculated variables by 'rank command' looks like 'ordered categorical variables', not interval (or assumed interval variables),
so I don't think the variables can be calculated like the formula above (sqrt... etc)



Sorry for the babbling, but
1) is it right way to rank the variables and make 5 ties and use them like '5 point likert scale'?

2) if 1) is wrong, then what should I do to calculate the formula?



Thank you very much!!!