# RE: st: Computation of Correlation Coefficients - COMPLEX

 From John Bunge To statalist@hsphsun2.harvard.edu Subject RE: st: Computation of Correlation Coefficients - COMPLEX Date Wed, 07 Nov 2007 18:36:20 +0100

```Dear Nick and Bill,

I think I was misunderstood by Bill and want to make my problem more explicit by stylizing the dataset I have:

. list

+-------------------------+
| cid   deid   year  dec |
|---------------------------|
| 1       1     1980  -1   |
| 1       2     1980   0   |
| 1       3     1980   1   |
| 1       4     1980   1   |
|  .       .         .        .   |
|  .       .         .        .   |
| 1    4000  1999  -1   |
| 2       1     1980   0   |
| 2       2     1980  -1   |
| 2       3     1980   0   |
| 2       4     1980   1   |
|  .       .         .        .   |
|  .       .         .        .   |
| 2    4000  1999  -1   |
|  .       .         .        .   |
|  .       .         .        .   |
|200    1     1980  -1   |
|200    2     1980   0   |
|200    3     1980   0   |
|200    4     1980  -1   |
|  .       .         .        .   |
|  .       .         .        .   |
|200  4000  1999  1   |
+-------------------------+

with cid - number of country (1-200), deid - number of decision (1-4000),
and dec - decision (1 for 'yes', 0 for 'abstain' and -1 for 'no').

(i do not know if this table will be displayed the way I see it here in my e-mail programme,
i only can hope that is going to be shown accurately)

The correlation coefficients (cc's) for the decisions I want to compute are:

between country 1 and 2, between country 1 and 3, ..., between country 1 and 200,...
between country 199 and 200, respectively. The total number of cc's
will be (200*199)/2 = 19,900.

Now note that I need these coefficients for every single year, not over all decisions
during the whole time period 1980 - 1999. So in the end, I will have the coefficients
for the country-pair 1-2 (and for all other country pairs, too) for 1980, for 1981, ...,
and for 1999. That is, in the end I will have 19,900*20 = 398,000 coefficients.

Any helpful suggestions are highly appreciated.

Sorry for having set up the problem in a precipitate manner.

Best,

John.

-----------------------------------------------------------------
Von: statalist@hsphsun2.harvard.edu
Gesendet: 07.11.07 17:03:04
An:
Betreff: RE: st: Computation of Correlation Coefficients - COMPLEX

Like perhaps some others, I wasn't clear on what John wanted, but now
that
Bill has offered a concrete interpretation, I am going to complicate
things
by saying what my guess would be:

for each decision in each year:

take all pairs of countries, and for each pair, create data
points based on the scores given: (-1, -1), (-1, 0), etc.

work out the correlation for that bivariate set.

I am not clear why that might be interesting or useful, but it's what
John's words seem to imply.

I agree with Bill's general advice.

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

William Gould

John Bunge <jota.be@web.de> wrote,

> I want to compute correlation coefficients within the following
setting:
>
> I have the variables CID (No. of country; 1-200), DEID (No. of
decision;
> 1-4000), YEAR and DEC (no, abstain, yes; expressed as: -1,0,1).
>
> There were several decisions per year in which more or less all the
> countries took part.
>
> I want to compute the correlation in these decisions between every
country
> pair for all single years.

I think John as a dataset that looks something like this,

. list

+-------------------------+
| cid deid year dec |
|-------------------------|
1. | 1 1 1990 1 |
2. | 1 2 1990 0 |
3. | 1 1 1991 0 |
4. | 1 2 1991 -1 |
5. | 1 1 1992 0 |
|-------------------------|
6. | 1 2 1992 1 |
7. | 2 1 1990 0 |
8. | 2 2 1990 -1 |
9. | 2 1 1991 1 |
10. | 2 2 1991 1 |
|-------------------------|
11. | 2 1 1992 -1 |
12. | 2 2 1992 0 |
+-------------------------+

As I understand it, John wants to correlate dec in 1990 with 1991, 1990
with
1992, etc., matching decisions on (cid, deid).

The answer is, of course, -correlate-, but -correlate- correlates
variables
in the same observation. So I need a dataset with dec in 1990, 1991,
and 1992
in the same observation. The first step is to convert the data to the
wide
form:

. reshape wide dec, i(cid deid) j(year)
(note: j = 1990 1991 1992)

Data long -> wide

---------------------------------------------------------------------
Number of obs. 12 -> 4
Number of variables 4 -> 5
j variable (3 values) year -> (dropped)
xij variables:
dec -> dec1990 dec1991
dec1992

---------------------------------------------------------------------

Now the data look like this,

. list

+------------------------------------------+
| cid deid dec1990 dec1991 dec1992 |
|------------------------------------------|
1. | 1 1 1 0 0 |
2. | 1 2 0 -1 1 |
3. | 2 1 0 1 -1 |
4. | 2 2 -1 1 0 |
+------------------------------------------+

and I can obtain the correlations by typing

. corr dec*
(obs=4)

| dec1990 dec1991 dec1992
-------------+---------------------------
dec1990 | 1.0000
dec1991 | -0.4264 1.0000
dec1992 | 0.0000 -0.8528 1.0000

-- Bill
wgould@stata.com

P.S. John also wrote,

> two days ago I posted a query, unfortunately there came no reply
> on it.

me

I would like to do just that, not only for John, but for others

In this case, John asked the question too concisely. John had an
excellent summary of his problem, but didn't go the extra step of
including an example to make it easy for me to answer his
question.
Instead, I HAD TO CONCOCT THE EXAMPLE and I spent more time doing
that

Questioners, understand: For those of us answering questions,
the satisfaction is in the answering. We are loath working on

John had a dynamite opening. I love it when questions are
concise,
because then I can quickly decide whether I have anything to
however,
John then needed to continue to set the problem up for me.
Give me a small example. Make everything explicit so that then,
all
I have to do is say, type this.

After John's concise intro, he could have added,

For instance, here's a small dataset with 2 countries, 3
years,
and 2 decisions:

<insert listing here>

What I want is the correlation of decisions in 1990 and 1991,
1990
and 1992, and 1991 and 1992, calculating the correlation
across
country. For instance, the correlation in 1990 and 1991 would
be
based on the correlation of

dec in 1990 dec in 1991
--------------------------
1 0 <- from obs 1 & 3; cid=1,
deid=1
0 -1 <- from obs 2 & 4; cid=1,
deid=2
0 1 <- etc...
-1 1

Remember, when asking a question, you are playing on our
sympathies
and our desire to show off. Those who answer cannot help but more

sympathetic when it appears you have invested time in formulating
the question.

*
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--
John Bunge
Debt and Finance Analysis Unit
Palais des Nations
1211 Genève 10
Switzerland
Office: +41 229175902
Mobile: +41 762901769

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