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From |
"Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: Drawing 3 normally distributed variable with a given correlation structure to an existing variable |

Date |
Wed, 26 Sep 2007 12:36:31 -0500 |

Rachel - Given the entire 4 x 4 covariance matrix and 4 x 1 mean vector, you can show that the joint distribution of X2, X3 and X4 given X1 is joint normal with mean vector mu2 + S21(S11^-1)(X1 - mu1) and covariance matrix S22 - S21(S11^-1)S12 where mu2 is the 3 x 1 mean vector for (X2,X3, X4)' and mu1 = E(X1) (scalar) and where the entire covariance matrix is (S11 S12 \ S21 S22) and where S11 is 1 x 1, S12 is 1 x 3, S21 is 3 x 1, and S22 is 3 x 3. [for example, see Ch 2 in T. W. Anderson - Introducton to Multivariate Statistics (Wiley) ] So given X1, you can then generate the other three using drawnorm and the above conditional mean and covariance matrix. Al Feiveson -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Rachel Sent: Wednesday, September 26, 2007 10:36 AM To: statalist@hsphsun2.harvard.edu Subject: Re: st: Drawing 3 normally distributed variable with a given correlation structure to an existing variable Hi Jeph, -drawnorm- will draw 4 new variables. In my case, X1~N(0,1) is already given, and I'm trying to draw X2,X3,X4~N(0,1) such that the four variables have a given correlation structure. * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Drawing 3 normally distributed variable with a given correlation structure to an existing variable***From:*Rachel <academicgirl@gmail.com>

**Re: st: Drawing 3 normally distributed variable with a given correlationstructure to an existing variable***From:*Jeph Herrin <junk@spandrel.net>

**Re: st: Drawing 3 normally distributed variable with a given correlation structure to an existing variable***From:*Rachel <academicgirl@gmail.com>

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