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From |
Robert Sutter <rdsutterjr@gmail.com> |

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

Subject |
Re: st: Poisson Two Level Random Intercept ICC |

Date |
Sun, 3 Mar 2013 15:41:01 -0600 |

Thanks! Sent from my iPad On Mar 1, 2013, at 5:55 PM, "JVerkuilen (Gmail)" <jvverkuilen@gmail.com> wrote: > On Fri, Mar 1, 2013 at 12:20 PM, Robert Sutter <rdsutterjr@gmail.com> wrote: >> How is the intraclass correlation coefficient calculated when using a >> two level random intercept model? >> >> Below is the output from a two level model for the count of excess >> deaths (oediff2) as the dependent variable and the clusters are >> attending physicians. sigma_u is the random intercept variance. >> >> In Rabe-Hesketh’s book the ICC for binary data is derived by the >> following formula:random intercept variance/( random intercept >> variance + π2/3). π2/3 represents the variance of the logistic >> distribution. >> > > Yes, this is one way to derive the ICC for binary data, working on the > scale of the linear predictor, which is the scale that the random > intercept variance exists on. There are others as the article I linked > to before by Harvey Goldstein and colleagues when this question was > posed. > > > >> Can the same formula be used for count data by replacing π2/3 with >> the variance of oediff2? > > I think the answer is no because the random effect variance isn't > directly comparable to the variance of the Poisson, because they are > on two different scales. > > > >> xtpoisson oediff2, i(attending_phy_id) normal >> >> Random-effects Poisson regression Number of obs = 75 >> Group variable: attending_ph~d Number of groups = 75 >> >> Random effects u_i ~ Gaussian Obs per group: min = 1 >> avg = 1.0 >> max = 1 >> >> Wald chi2(0) = . >> Log likelihood = -213.3618 Prob > chi2 = . >> >> ------------------------------------------------------------------------------ >> oediff2 | Coef. Std. Err. z P>|z| >> [95% Conf. Interval] >> -------------+---------------------------------------------------------------- >> _cons | 2.617512 .0323429 80.93 0.000 2.554121 2.680903 >> -------------+---------------------------------------------------------------- >> /lnsig2u | -5.924562 4.653182 -1.27 0.203 -15.04463 3.195508 >> -------------+---------------------------------------------------------------- >> sigma_u | .0517009 .1202868 .0005409 4.94192 >> ------------------------------------------------------------------------------ > > And with these data it's irrelevant because the random effect variance > is essentially 0 anyway. But that's not surprising because your group > size is 1 so you have no real ability to estimate this anyway. I > suspect the model is identified only due to the assumption of the > distribution and that it works only because the Poisson doesn't have a > separate variance term. > > > > -- > JVVerkuilen, PhD > jvverkuilen@gmail.com > > "It is like a finger pointing away to the moon. Do not concentrate on > the finger or you will miss all that heavenly glory." --Bruce Lee, > Enter the Dragon (1973) > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/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/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Poisson Two Level Random Intercept ICC***From:*Robert Sutter <rdsutterjr@gmail.com>

**Re: st: Poisson Two Level Random Intercept ICC***From:*"JVerkuilen (Gmail)" <jvverkuilen@gmail.com>

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