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From |
"Joseph Coveney" <jcoveney@bigplanet.com> |

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

Subject |
Re: st: Multivariate Poisson - Correlation of Error Terms |

Date |
Sun, 13 Jul 2008 15:52:22 +0900 |

Austin Nichols wrote: U.G. Narloch --- -nlsur- estimates the equations jointly but -suest- just reestimates standard errors (not point estimates). I gather from your question that you want some postestimation tools for -nlsur- that don't currently exist... webuse nhanes2, clear egen c=group(strat psu) poisson iron black [iw=fin] est sto p1 poisson lead black [iw=fin] est sto p2 suest p1 p2, cl(c) nlsur (iron=exp({b1}+{b2}*bl)) (lead=exp({b3}+{b4}*bl)) [pw=fin], vce(cl c) -------------------------------------------------------------------------------- It seemed as if Ulf wanted to do Poissson regression. It's my understanding that you don't normally consider correlation of residuals from Poisson regression, and that's why I suggested examining the presence of correlation via a random effects (a.k.a., latent variable, factor) approach, such as what would be the -gllamm- equivalent of something like the following Mplus code: VARIABLE: NAMES = y1 y2 y3 y4 x z1 z2 z3 z4; COUNT = y1 y2 y3 y4; MODEL: y1 ON x z1; y2 ON x z2; y3 ON x z3; y4 ON x z4; f1 BY y1 y2 y3 y4; where y's are the response variables ("COUNT =" stipulates Poissson regression), x is a predictor common to all four equations (there could be several x's in Ulf's case), and the z's are predictors peculiar to respective equations (again, there could be several for each equation). I say "something like", because I suspect that the model is naive and could probably be better specified after some reflection--constraining to zero correlations between the z's across equations, for example--whether it's identified is an exercise still outstanding. (There might even be a short cut through all of this via MPlus's ANALYSIS: TYPE = RANDOM statement; I'm still getting up to speed.) The thinking goes that, if correlation exists, then the random effect, f1, will demonstrate a variance greater than zero (either by the Wald test that's normally a part of the Mplus printout, or by a likelihood ratio test against the reduced model). If true multivariate distribution was of interest, then you could try for four random effects and the correlations between them, if you can get an identified model from that proposal. Even so, that's a lot of integration points just to see whether the four equations may be considered independently. Joseph Coveney clear * set more off set seed `=date("2008-07-13", "YMD")' set obs 200 generate double x1 = invnorm(uniform()) generate double x2 = invnorm(uniform()) generate double xb = -1 + 0.5 * x1 + 1.5 * x2 genpoisson y, xbeta(xb) poisson y x1 x2, nolog predict y_po, n nl (y = exp({b0} + {b1} * x1 + {b2} * x2)), initial(b0 -1 b1 0.5 b2 1.5) /// nolog predict y_nl, yhat pause on graph7 y_nl y_po y_po, xlabel ylabel connect(.L) symbol(oi) pause graph7 y_nl y_po y_po, xlabel ylabel connect(.L) symbol(oi) xlog ylog signrank y_po = y_nl exit * * 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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