I am using Stata and investigating the variable household net wealth NetWealth).
I want to construct the quintiles of this variable and use the following command--as you can see I use survey data and thus apply survey weights:
xtile Quintile = NetWealth [pw=surveyweight], nq(5)
Then I give the following command to check what I have obtained:
tab Quintile, sum(NetWealth)
This is the result:
Means, Standard Deviations and Frequencies of DN3001 Net wealth
5 |
quantiles |
of dn3001 |
-----------+-----------+
1 |1519.4221
|43114.959
| 154
-----------+-----------+
2 | 135506.67
| 74360.816
| 179
-----------+-----------+
3 | 396712.16
| 69715.49
| 161
-----------+-----------+
4 | 669065.69
| 111102.02
| 182
-----------+-----------+
5 | 2552620.5
| 3872350.9
| 274
-----------+-----------+
Total | 957419.29
| 2323329.8
| 950
Why do I get a different number of households in each quintile? In particular in the last quintile?
The only explanation that I can come up with is that when Stata constructs quintiles with xtile, it excludes from the computation those observations that present a replicate value of NetWealth. I have had this impression also while consulting the Stata material.
What do you think?
Your problem is not fully reproducible in so far as you don't give a self-contained example, but in general there is no puzzle here.
Often people seeking such binnings have a small problem in that their number of observations is not a multiple (meaning, exact multiple) of the number of quantile-based bins they want, but in your case that does not bite as calculation
. di 154 + 179 + 161 + 182 + 274
950
shows that you have 950 observations, which is 5 x 190.
The bigger deal -- here and almost always -- arises from Stata's rule that identical values in different observations must be assigned to the same bin. So, ties are likely to be the problem here.
You have perhaps three possible solutions. Only one involves direct coding.
Live with it.
Do something else. For example, why you are doing this any way? Why not use the original data?
Try a different boundary condition. To do that, just negate the variable and bin that version. Then values on the boundary will jump differently.
Adding random noise to separate ties is utterly indefensible in my view. It's not reproducible (except trivially using the same program and the same settings) and it will have different implications in terms of the same observations' values on other variables.
Here's an example where #3 doesn't help, but it sometimes does:
. sysuse auto, clear
(1978 Automobile Data)
. xtile bin5 = mpg, nq(5)
. gen negmpg = -mpg
. xtile bin5_2 = negmpg, nq(5)
. tab bin5
5 quantiles |
of mpg | Freq. Percent Cum.
------------+-----------------------------------
1 | 18 24.32 24.32
2 | 17 22.97 47.30
3 | 13 17.57 64.86
4 | 12 16.22 81.08
5 | 14 18.92 100.00
------------+-----------------------------------
Total | 74 100.00
. tab bin5_2
5 quantiles |
of negmpg | Freq. Percent Cum.
------------+-----------------------------------
1 | 19 25.68 25.68
2 | 12 16.22 41.89
3 | 16 21.62 63.51
4 | 13 17.57 81.08
5 | 14 18.92 100.00
------------+-----------------------------------
Total | 74 100.00
See also some discussion within Section 4 of this paper
I see no hint whatsoever in the documentation that xtile would omit observations in the way that you imply. You give no precise quotation supporting that. It would be perverse to exclude any non-missing values unless so instructed.
I don't comment directly here on use of pweights except that using pweights might be a complicating factor here.