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From |
Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: RES: generating a variable with pre-specified correlations with other two (given) variables |

Date |
Wed, 31 Aug 2011 05:00:29 -0700 |

This question has appeared a few times before - in that you want to create a variable with a pattern of correlation with _existing_ variables, which -corr2data- does not do. In an example where means are normalised to zero, this can be had by solving a system of linear equations in appropriate expectations. Suppose you generate a variable as Z = a*X+ b*Y ---(0) where a, and b are constants to be determined. Then you can derive the following identities under the zero mean assumption: Cov(Z, X) = a*Var(X) + b*Cov(X, Y) ---(1) Cov(Z, Y) = b*Var(Y) + a*Cov(X, Y) ---(2) Here you know everything (you set Cov(Z, X) and Cov(Z, Y)), and this is a system of two equations in two unknowns, a and b. Solve them and generate your variables as in equation (0). So for example, if I have Cov(X, Y) = .6, and Var(X)=Var(Y)=1, then a =0.15625 , b=0.40625. /************************************/ mat mCov = (1, .6\ .6, 1) // generate x and y corr2data x y, cstorage(full) cov(mCov) n(100000) clear // generate z based on current sample of x and y g z = .15625*x+.40625*y corr, covariance /************************************/ All these calculations are assuming zero means - more tedious algebra will allow you to generalise. T On Wed, Aug 31, 2011 at 3:53 AM, Henrique Neder <hdneder@ufu.br> wrote: > Try corr2data: > > matrix C = (1,0,.80,-.80\0,1,0,0\.80,0,1,-.80\-.80,0,-.80,1) > corr2data hsperc corzer1 corpos1 corneg1, n(4137) corr(C) > > Henrique Neder > > > -----Mensagem original----- > De: owner-statalist@hsphsun2.harvard.edu > [mailto:owner-statalist@hsphsun2.harvard.edu] Em nome de fjc > Enviada em: terça-feira, 30 de agosto de 2011 23:00 > Para: statalist@hsphsun2.harvard.edu > Assunto: st: generating a variable with pre-specified correlations with > other two (given) variables > > Dear Statalisters: > > I have a dataset with two variables, x and y. > > I would like to generate a new artificial variable, z, with > pre-specified correlations with x and y (no particular distribution > required). > > Any help would be greatly appreciated. > > Best, > > Francisco. > > P.D. I'm using Stata 11 (on Windows XP) > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > > ----- > Nenhum vírus encontrado nessa mensagem. > Verificado por AVG - www.avgbrasil.com.br > Versão: 10.0.1392 / Banco de dados de vírus: 1520/3868 - Data de Lançamento: > 08/30/11 > > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > -- Tirthankar Chakravarty tchakravarty@ucsd.edu tirthankar.chakravarty@gmail.com * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: RES: generating a variable with pre-specified correlations with other two (given) variables***From:*fjc <fjc120@gmail.com>

**Re: st: RES: generating a variable with pre-specified correlations with other two (given) variables***From:*Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>

**References**:**st: generating a variable with pre-specified correlations with other two (given) variables***From:*fjc <fjc120@gmail.com>

**st: RES: generating a variable with pre-specified correlations with other two (given) variables***From:*"Henrique Neder" <hdneder@ufu.br>

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