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# RE: st: ranking with weights

 From "Nick Cox" To Subject RE: st: ranking with weights Date Tue, 2 Dec 2008 19:45:41 -0000

```The following example code with a toy dataset may help:

. list expenditure frequency

+---------------------+
| expend~e   freque~y |
|---------------------|
1. |     1000       8000 |
2. |     1000      10000 |
3. |     2000       6000 |
4. |     2000       9000 |
5. |     3000       8000 |
|---------------------|
6. |     3000       4000 |
7. |     4000       7000 |
8. |     4000       6000 |
9. |     5000       6000 |
10. |     6000       5000 |
|---------------------|
11. |     7000       4000 |
12. |     8000       3000 |
13. |     9000       2000 |
14. |    10000       1000 |
+---------------------+

. bysort expend : gen totalfreq = sum(frequency)

. by expend : replace totalfreq = totalfreq[_N]
(4 real changes made)

. by expend : gen first = _n == 1

. gen rank = sum(totalfreq * first)

. replace rank = rank - 0.5 * totalfreq
(14 real changes made)

. list

+------------------------------------------------+
| expend~e   freque~y   totalf~q   first    rank |
|------------------------------------------------|
1. |     1000       8000      18000       1    9000 |
2. |     1000      10000      18000       0    9000 |
3. |     2000       6000      15000       1   25500 |
4. |     2000       9000      15000       0   25500 |
5. |     3000       8000      12000       1   39000 |
|------------------------------------------------|
6. |     3000       4000      12000       0   39000 |
7. |     4000       7000      13000       1   51500 |
8. |     4000       6000      13000       0   51500 |
9. |     5000       6000       6000       1   61000 |
10. |     6000       5000       5000       1   66500 |
|------------------------------------------------|
11. |     7000       4000       4000       1   71000 |
12. |     8000       3000       3000       1   74500 |
13. |     9000       2000       2000       1   77000 |
14. |    10000       1000       1000       1   78500 |
+------------------------------------------------+

There is a little inaccuracy there: the average of ranks 1...18000 is strictly 9000.5 not 9000, so you may want to make the appropriate corrections.

Nick
n.j.cox@durham.ac.uk

Cindy Gao

The observations (analytic units) are households. Expenditure is the monthly expenditure of household. This is household survey data. The weights are frequency weights, to weight the sample to the whole country. The weights are likely to vary across for example regions, to compensate for oversampling or undersampling.

Basically I need to rank all households according to their expenditure, from lowest to highest. But, I must take account of the weightings. If for example there are 2 households with the same expenditure, they must be ranked the same and this rank must take account of weightings. If there were no ties (households with same expenditure), I could achieve mission by generating a variable "rank", like  -g rank=sum(weight)-. The problem comes because of ties. If i could -expand- my dataset using weights, then i could simply say -egen rank =rank(expenditure)- ; the problem is that dataset is too large for this.

Steven Samuels

Cindy, What are the analytic units (people? regions?).  What are the "weights"? What is "expenditure"?  How is it measured.  What do you mean that some regions are "less sampled" than others.  It's not clear, for example, if this is a sample, and if so, of what? So, please describe the  study design in detail.  Last question: what is the purpose of the ranking?

On Dec 2, 2008, at 12:54 PM, Cindy Gao wrote:

> I am trying to find a way to rank weighted data (since the egen function -rank- does not work with weights). A simple way would be order the data in terms of variable that I have interest in (monthly expenditure) and then create a new variable like -g rank1=sum(weight)-. But, there is problem. Some of my observations are "tied" as they have the same level of expenditure. Using the simple method I mention means that some observations are ranked above others even though they have same level of expenditure. This is a problem as the weights are large so you find that 2 observations are ranked with bug gap in between even though same level of expenditure. It is even bigger problem because the weights might be correlated with some other variables I am interested in (like region, since some regions are less sampled than other). I also try multiplying the expenditure ranking by the weight, but this gives wrong results (for example they do not add up to weighted
>  total). Can anyone help? In other words, I would like for all observations with same expenditure to have same rank, which I assume would be some average of all the weighted observations having that same expenditure..  I include a sample dataset below:
>
> expenditure       weighting        rank       rank1      weighted_rank
> 10                          341            1           341          341
> 12                          1065          2.5        1406         ???
> 12                          98             2.5        1504
> 15                          254            4          1758
> .......

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