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From |
fjc <fjc120@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 09:41:34 -0300 |

Thanks, Tirthankar. This answers my question as originally posted. Now, something I didn't say in my earlier post (and I think I should have) is that after I generate the new variable (z) I would like to run a regression of y on x and z. But if I generate z in the way you propose, I will get perfect collinearity. ¿Is there any other way to generate z without getting this collinearity? Francisco. P.D. The reason I want to run the aforementioned regression is the following. Suppose I have an initial regression of y on x, and x turns out to be insignificantly different from zero at some chosen confidence level. Then I want to generate an example in which adding a new (artificial) variable z as a covariate I can get x to become significantly different from zero at the same confidence level. Based on the formula for the t-test, I think I can do this if I can control the correlations between the artificial variable and the original ones. The excercise is just for expositional purposes, I do not want to attach any deep meaning to it. On Wed, Aug 31, 2011 at 9:00 AM, Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com> wrote: > 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/ > * * 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:*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>

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

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