SPSSX Discussion

Generating 2 variables with different correlations

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Jeff A

Generating 2 variables with different correlations

Is there a straightforward way to generate example data with several variables having different degrees of correlation? …having each normally distributed will work well.

E.g., if I want X1 and X2 to be correlated at .1, X1 and X3 to be correlated at .3, etc.

I can figure out how to do this by creating a few variables, sorting, adding random error, etc. but I’m hoping that there is a more straightforward way.

Best,

Jeff

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Jon Peck

Re: Generating 2 variables with different correlations

There is a custom dialog, File > New > Data with Cases that generates random data with any of a number of correlation patterns. For the arbitrary pattern, you enter the lower triangle of the correlation matrix you want. The correlations can be approximate or exact. See the help in the dialog for exactly how to enter this.

You can find this dialog on the old SPSS Community website, but I can send you the file directly if you want to go this way. If you do, send me an email, and I will reply with the dialog.

On Mon, Feb 11, 2019 at 3:36 PM Jeff <[hidden email]> wrote:

Is there a straightforward way to generate example data with several variables having different degrees of correlation? …having each normally distributed will work well.

E.g., if I want X1 and X2 to be correlated at .1, X1 and X3 to be correlated at .3, etc.

I can figure out how to do this by creating a few variables, sorting, adding random error, etc. but I’m hoping that there is a more straightforward way.

Best,

Jeff

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Jon K Peck
[hidden email]

Ware, William B

Re: Generating 2 variables with different correlations

In reply to this post by Jeff A

In R, check the mvnorm package...

William B. Ware, Professor Emeritus

Learning Sciences and Psychological Studies

Educational Psychology, Measurement, and Evaluation

School of Social Work, Adjunct Professor

University of North Carolina at Chapel Hill

From: SPSSX(r) Discussion <[hidden email]> on behalf of Jeff <[hidden email]>
Sent: Monday, February 11, 2019 5:35:28 PM
To: [hidden email]
Subject: Generating 2 variables with different correlations

Is there a straightforward way to generate example data with several variables having different degrees of correlation? …having each normally distributed will work well.

E.g., if I want X1 and X2 to be correlated at .1, X1 and X3 to be correlated at .3, etc.

I can figure out how to do this by creating a few variables, sorting, adding random error, etc. but I’m hoping that there is a more straightforward way.

Best,

Jeff

Kirill Orlov

Re: Generating 2 variables with different correlations

In reply to this post by Jeff A

Of my http://www.spsstools.net/en/KO-spssmacros
page MATRIX - END MATRIX collection, function !mvnorm generates normal data from a correlated population; !tocov transforms data to have exact correlations you want.

12.02.2019 1:35, Jeff пишет:

Is there a straightforward way to generate example data with several variables having different degrees of correlation? …having each normally distributed will work well.

E.g., if I want X1 and X2 to be correlated at .1, X1 and X3 to be correlated at .3, etc.

I can figure out how to do this by creating a few variables, sorting, adding random error, etc. but I’m hoping that there is a more straightforward way.

Best,

Jeff

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD

Bruce Weaver

Re: Generating 2 variables with different correlations

Administrator

In reply to this post by Jon Peck

Here is an old-fashioned "no Python required" (NPR) solution. (Jon, please
note that I did try Data with Cases first, but a website needed to install
part of it was down.)

Jeff, the main things you need to modify are the lines that set n and the
desired correlation matrix. HTH.

/* Source: https://www.uvm.edu/~dhowell/StatPages/More_Stuff/CorrGen2.html
*/

/* This program generates a multivariate random normal sample */
/* of size n from a population described by covariance matrix r */
/* Setting exact to 1 yields a sample that exactly reproduces */
/* the population matrix. Setting exact to any value other than 1 */
/* produces a sample from the population, which will be subject */
/* to random sample error, meaning that sample covariance */
/* matrix will not be exactly equal to the population matrix */
/* keep the seed constant to reproduce the data from run to run */

/* Written by Andrew F. Hayes */
/* School of Communication */
/* The Ohio State University */
/* [hidden email] */
/* Version 1.1, Sept 15, 2010 */

*set seed = 12343.
* UPDATE: Use MT and MTINDEX.
SET RNG=MT MTINDEX=120219.

matrix.
compute n = 500.
compute exact = 1.
* E.g., if I want X1 and X2 to be correlated at .1, X1 and X3 to be
correlated at .3, etc.
compute r =
{1, .1, .3;
.1, 1, .6;
.3, .6, 1}.
compute rn = nrow(r).
compute x1 =
sqrt(-2*ln(uniform(n,rn)))&*cos((2*3.14159265358979)*uniform(n,rn)).
compute x1=x1*chol(r).
compute ones = make(n,1,1).
compute sigma = (t(x1)*(ident(n)-(1/n)*ones*t(ones))*x1)*(1/(n-1)).
do if (exact = 1).
call eigen(r, vc, vl).
compute sqrtr = vc*sqrt(mdiag(vl))*t(vc).
call eigen(sigma, vc, vl).
compute sqrts = vc*sqrt(mdiag(vl))*t(vc).
compute x1 = x1*inv(sqrts)*sqrtr.
compute ones = make(n,1,1).
compute sigma = (t(x1)*(ident(n)-(1/n)*ones*t(ones))*x1)*(1/(n-1)).
end if.
print r/title = "Population Matrix"/format = F16.4.
print sigma/title = "Sample Matrix"/format = F16.4.
print n/title = "number of cases created"/format = F16.0.
save x1/outfile = *.
end matrix.

CORRELATIONS all.

I know there are some other old threads in this forum discussing the same
problem. You should be able to find them with appropriate search terms.

Jon Peck wrote
> There is a custom dialog, File > New > Data with Cases that generates
> random data with any of a number of correlation patterns. For the
> arbitrary pattern, you enter the lower triangle of the correlation matrix
> you want. The correlations can be approximate or exact. See the help in
> the dialog for exactly how to enter this.
>
> You can find this dialog on the old SPSS Community website, but I can send
> you the file directly if you want to go this way. If you do, send me an
> email, and I will reply with the dialog.

-----
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Bruce Weaver
[hidden email]
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"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

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Bruce Weaver
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"When all else fails, RTFM."

PLEASE NOTE THE FOLLOWING:
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Kirill Orlov

Re: Generating 2 variables with different correlations

Bruce, it looks like that the Hayes' code is almost the same thing as my two functions mentioned above. But my functions are (I think so) better implemented. And it is better to keep the "generate from population" and to "take to exact covariances" parts separate because in fact they are independent tasks.

13.02.2019 1:54, Bruce Weaver пишет:

Here is an old-fashioned "no Python required" (NPR) solution.  (Jon, please
note that I did try Data with Cases first, but a website needed to install
part of it was down.)