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From |
"FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" <alan.h.feiveson@nasa.gov> |

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

Subject |
st: RE: `binorm' in Multivariate Maximum Likelihood |

Date |
Tue, 8 Feb 2005 14:38:47 -0600 |

Jason - Have you tried reparameterizing to force a positive definite covariaance matrix for your bivariate normal? e.g. log(v_11)=th1; log(v_22)=th2; logit((1+rho)/2)=th3 in terms of th1, th2 and th3, the 2 x 2 covariance matrix (v_ij) is then v_11=exp(th1); v_22=exp(th2); v12=v21=rho*sqrt(v_11*v_12) where rho=-1 + 2*exp(th3)/(1+exp(th3)) Al Feiveson -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Jason Hwang Sent: Friday, February 04, 2005 5:28 PM To: statalist@hsphsun2.harvard.edu Subject: st: `binorm' in Multivariate Maximum Likelihood Dear Statalist Users, I would very much appreciate your help with the following problem. I'm trying to write a maximum likelihood procedure for a system with: - a binary dependent variable - a binary endogenous explanatory variable - two continuous endogenous explanatory variables In matrix form, it's easy to derive the likelihood function: express the joint density of all four variables as the product of the joint density of the two binary variables conditional on the continuous variables and the joint density of the continuous variables. The first part, the density of binary variables requires calculating probabilities for the four relevant cases. (Greene pg. 855 as well as Wooldridge) I am using the function `binorm' to calcluate the density of the two binary variables. `binorm' takes three inputs, (conditional) means for the two variables and a correlation coefficient (variances are normalized to one). Now there three arguments are, in my model, complicated functions of elements from the 4 x 4 covariance matrix of the full system. The problem is Stata can't find any starting values for this procedure. I've looked at the correlation coefficient that is being generated and often it exceeds 1 or is smaller than -1, in which case binorm produces on output. I have tried imposing restrictions on various parameters when running `ml search' to see if I can get a correlation coefficient in the unit interval, but that didn't work either. Any suggestions for how to proceed? Thanks very much for your help, Jason * * 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/

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