Assert whether observations are similar across 3 variables

[Fahad Mirza]

Hello,

I have a small question regarding assert.

I want to check how many observations in a data are similar across a set of variables. Data example:

* Example generated by -dataex-. For more info, type help dataex
clear
input str3 name float(var1 var2 var3)
"Yes" 888 888 888
"Yes"   2   1   2
"Yes"   2   1   2
"Yes"   4   4   4
"Yes"   0   1   1
"Yes"   0   1   1
"Yes"   1   .   1
"Yes"   0   1   1
"Yes"   0   0   0
"Yes"   0   .   1
"Yes"   0   0   0
end

We can see that there are 4 observations that are similar across var1, var2, and var3 however when I use the assert command to check, I get the following message:

. assert var1 == var2 == var3
11 contradictions in 11 observations
assertion is false
r(9);

However, using the following code correctly identifies similar observations:

. assert (var1 == var2) & (var2 == var3)
7 contradictions in 11 observations
assertion is false
r(9);

What is the possible explanation behind why we can not directly assert 3 variables and instead have to use the "&" condition

[Nick Cox]

This is nothing to do with assert as such, as the same puzzlement can arise from Stata's processing of composite logical expressions in other contexts. The problem for your interpretation is that the expression

var1 == var2 == var3

is evaluated from left to right in steps, and so not simultaneously. Thus it is equivalent to

(var1 == var2) == var3

from which it can be seen that there are two possibilities

1 == var3

and

0 = var3

and only exceptionally will this give the same results as your other code.

For example, if var1 var2 var3 are all 1 then the intention behind writing var1 == var2 == var3 will be satisfied by accident. But any other constants won't give the desired result.

Otherwise put, this is why parentheses are not just redundant or decorative. They can be needed to insist on the interpretation you want.

More in the same vein at https://journals.sagepub.com/doi/pdf...6867X231162009

[Fahad Mirza]

Thank you Nick Cox ! that was super useful.

[Nick Cox]

You've posted some code at https://github.com/fahad-mirza/tag_o...tata/tree/main

It seems possible to approach the problem more concisely. If all the variables in a list are equal, then they are all equal to the first variable. It's safe to assume equality as our first guess but change our mind if we find an exception.

In your example you are checking whether var1 var3 var5 are equal.

* Loading example data
    * Example generated by -dataex-. For more info, type help dataex in Stata
    clear
    input str3 name float(var1 var2 var3 var4 var5)
    "Yes" 888 888 888 888 888
    "Yes"   2   1   2   1   2
    "Yes"   2   2   2   2   2
    "Yes"   4   4   4   4   4
    "Yes"   0   1   1   1   1
    "Yes"   0   1   1   1   1
    "Yes"   1   .   1   .   1
    "Yes"   0   1   1   1   1
    "Yes"   0   0   1   0   0
    "Yes"   0   .   1   .   1
    "Yes"   0   0   0   0   0
    end
    
gen same = 1

foreach v in var3 var5 {
    replace same = 0 if `v' != var1
}

Results

. l var1 var3 var5 if same

     +--------------------+
     | var1   var3   var5 |
     |--------------------|
  1. |  888    888    888 |
  2. |    2      2      2 |
  3. |    2      2      2 |
  4. |    4      4      4 |
  7. |    1      1      1 |
     |--------------------|
 11. |    0      0      0 |
     +--------------------+

.
. l var1 var3 var5 if !same

     +--------------------+
     | var1   var3   var5 |
     |--------------------|
  5. |    0      1      1 |
  6. |    0      1      1 |
  8. |    0      1      1 |
  9. |    0      1      0 |
 10. |    0      1      1 |
     +--------------------+

[Nick Cox]

Here is a quick egen function. Not much tested. If interested, store it appropriately, in directory _ of what adopath calls PLUS.

*! 1.0.0  NJC 16jul2023
program _gsame
    version 8
    gettoken type 0 : 0
    gettoken g 0 : 0
    gettoken eqs 0 : 0
    syntax varlist [if] [in]

    capture confirm numeric var `varlist'
    if _rc {
        capture confirm str var `varlist'
        if _rc {
            di as err "may not mix numeric and string variables"
            exit 109
        }
    }

    tempvar touse
    mark `touse' `if' `in'

    gettoken first others : varlist

    quietly {
        gen byte `g' = 1  if `touse' /* ignore user-supplied `type' */
        foreach v of local others {
            replace `g' = 0 if `v' != `first'  & `touse'
        }
    }

    if length("`varlist'") >= 72 {
         note `g' : same on `varlist'
         label var `g' "see notes"
    } 
    else label var `g' "same on `varlist'"
end

[Fahad Mirza]

Thank you for showing a more concise way of approaching this problem! I think I was just over complicating it in the github code. I guess my code on github takes inspiration from the graph codes that I write. Also, thank you for showing how it is done in a program format! Consider maybe releasing it as an extension in egen?