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From |
rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp) |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: -predict , reffects- after -xtmelogit- |

Date |
Mon, 20 Dec 2010 12:09:09 -0600 |

Jeph Herrin <stata@spandrel.net> asks: > I am using -xtmelogit- to estimate a random effects model, and am wondering > about what is being predicted by -predict, reffects-. > Example: > clear > use http://www.stata-press.com/data/r11/bangladesh > xtmelogit c_use || district: > predict re_cons, reffects When you use -predict, reffects- after -xtmelogit-, you obtain estimates of the modes of the posterior distribution of the random effects given the data and estimated parameters; see pg. 277 of [XT] xtmelogit postestimation for a complete discussion. > Now, I would expect the standard deviation of the random effect reported by > the model: > -------------------------------------------------------- > Random-effects Parameters | Estimate Std. Err. > -----------------------------+-------------------------- > district: Identity | > sd(_cons) | .4995265 .0798953 > -------------------------------------------------------- > To be approximately the standard error of the predicted randome effects, at > the district level: > bys district : gen tolist = _n==1 > sum re_cons if tolist > Variable | Obs Mean Std. Dev. Min Max > -------------+-------------------------------------------------------- > re_cons | 60 .0069783 .3787135 -.9584643 .9257698 > But it seems very different, 0.4995 vs .37871. I must be missing something > obvious, but what? The phenomenon you are seeing is known as "shrinkage". Predictions based on the random-effects posterior distribution tend to be closer in magnitude to zero because they are incorporating the prior information that the random effects have mean zero. That is, if you have a relatively small cluster size the prior information that the random effect should be zero tends to dominate. The estimate of sd(_cons) is, in contrast, based on maximum likelihood where all the clusters are considered jointly. Thus, prior information tends to not dominate as much because all clusters are pooling what they have to say about the random-effects standard deviation. Shrinkage dimishes as cluster size gets larger. To see this, try . clear . set seed 1234 . set obs 100 // 100 clusters . gen u = sqrt(2)*invnorm(uniform()) // random effects . gen id = _n . expand 1000 // cluster size is 1000 . gen e = log(1/runiform() - 1) // logistic errors . gen y = (e + u) > 0 // binary response . xtmelogit y || id: . predict r, reffects . bysort id: gen tolist = _n==1 . sum r if tolist The standard deviations match much more closely -- having a cluster size of 1,000 helps! --Bobby rgutierrez@stata.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: -predict , reffects- after -xtmelogit-***From:*Jeph Herrin <stata@spandrel.net>

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