Additive index

[Serena Gallo]

Hi dears,
I have an issue in creating of an additive index.
I have 11 variables that are normalized using the min-max method. Therefore, their interval varies from 0 to 1.
However, by typing the command:
g index= x1+....+x11
The index does not take values between 1 and 11.
How Can I solve it?

[Felix Bittmann]

What values do you get? Theoretically, they should be between 0 and 11. Maybe check on the input first:

summarize x1 - x11

[Serena Gallo]

I have values from 2 (min) and 6.8 (max).
Each variable has a min value equal to 1 and a max value equal to 10. The variables are 11 and I have expected that the index takes value from 1 to 11.

[Felix Bittmann]

Now I am confused. In your first post you say that the input vars are normalized between 0 and 1, now you say they have values from 1 to 10. This will clearly affect your resulting scale. Maybe you want to standardize or normalize it after adding them up?

[Serena Gallo]

I'm sorry I have made confusion, the vars range between 0 and 1. I have tried to normalize it after adding them, but now the index range between 0 and 1.
I want that the index to range between 1 (the minimum value) to 11 (the maximum value).

[Nick Cox]

I agree with Felix Bittmann

If each variable of 11 is scaled from 0 to 1, then

1. The maximum possible for their sum will be 11, but that will occur if and only every value is 1 in an observation.

2. The minimum value for their sum will be 0, but that will occur if and only every value is 0 in an observation.

If the logic doesn't convince, an example with 3 variables may help.

* Example generated by -dataex-. For more info, type help dataex
clear
input float(var1 var2 var3)
1 1 0
0 0 1
0 1 0
1 1 1
0 0 0
end

Here the sum will be 3 and 0 in the last two observations, so the maximum and minimum possible are -- indeed -- possible -- but their existence in data isn't guaranteed by the rules.

[Serena Gallo]

I have understand it. But the variables take value from 0 to 1 not only 0 and 1. And, when I create the index I have an issue.
How can I solve it? I want to create an index by adding up them and it should take value from 1 to 11.

[Nick Cox]

The fact that values may lie between 0 and 1 doesn't disturb the principle behind my post.

[Serena Gallo]

Ok, but I would like that my index has discrete values from 1 to 11. However, when I add the variable by summing them the index takes continuous values.

[Nick Cox]

Again, do you want your limits to be attained in the data or just possible? You can enforce a range of 1 to 11 by a linear transformation and integer values can be insisted by using a rounding function such as round() floor() ceil().

A small but realistic data example would allow us to suggest code, but if you want integers only you need to state your rounding rule.

[Serena Gallo]

These are the variables in my dataset.

Variable	Obs	Mean	Std. Dev.	Min	Max
X1	110	0.192	0.218	0	1
X2	103	0.206	0.28	0	1
X3	110	0.019	0.095	0	1
X4	110	0.549	0.254	0	1
X5	110	0.457	0.285	0	1
X6	110	0.238	0.281	0	1
X7	110	0.537	0.165	0	1
X8	100	0.062	0.13	0	1
X9	107	0.491	0.228	0	1
X10	105	0.501	0.236	0	1
X11	110	0.652	0.261	0	1

[Nick Cox]

Sorry, but that's not a data example. It's the results of summarize.

[Maarten Buis]

In theory your index can take the values from 0 (not 1) to 11, but that does not mean that it will take that range in your data. What is required for your index to take the minimum value for an observation? All variables X1 to X11 would have to have the value 0 for that observation. This is possible, but there is nothing that guarantees that such an observation exists in your data. Similarly, in order for an observation to have the maximum value of 1, all variables X1 to X11 have to have the value 1 for that observation. Again, this is possible, but nothing guarantees that such an observation exists in your data. The fact that your variable does not exhaust its theoretical range is not a problem, it is just an empirical result, and a fairly common one at that.