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From |
Stas Kolenikov <skolenik@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: clustering and log likelihood. |

Date |
Thu, 7 Mar 2013 08:30:28 -0600 |

Since your data are not i.i.d., you don't have likelihood anymore. A long technical story inappropriately short, 1. What you write down is pseudo-likelihood, and it looks exactly the same as how the likelihood would look for the i.i.d. case. Think about OLS: you can still minimize the sum of squared errors to get some sort of idea about the line of best fit. That's what pseudo-likelihood is for, to generate some sort of point estimates. 2. Now, having obtained the point estimates, you need to recognize that the model as fitted to the data is not the true likelihood. Hence, the nice theorems about the asymptotic variance being the inverse Hessian do not work. Instead, you need to use the more general theorems from M-estimation theory, which give you a sandwich variance estimator (inverse Hessian times the variance of scores times inverse Hessian). In the variance of scores computation, you need to account for clustering: this is the sum over the clusters, rather than individual observations. If you were to try to incorporate the cluster effects explicitly into your likelihood, (i) the likelihood is the sum over clusters; (ii) each cluster contribution is an integral of products of the observation-level likelihoods, conditioned on the random effect. You can assume normal random effects, and integrate over them. What you will get in the end is -xtprobit, re-, which is a very different model. -- -- Stas Kolenikov, PhD, PStat (SSC) -- Senior Survey Statistician, Abt SRBI -- Opinions stated in this email are mine only, and do not reflect the position of my employer On Thu, Mar 7, 2013 at 1:54 AM, Elin Vimefall <Elin.Vimefall@oru.se> wrote: > Hi > > I'm running a probit model like: > probit enrol x1 x2 [pweight=weight], cluster(prov) > > I understand why I should use the cluster option but I'm really struggling with understanding what's happening more formally. > I would like to write the log likelihood function. However; I do not understand how to incorporate the clusters. > Will the clusters influence the likelihood function? > > I guess my question is stupid but I'm really struggling with this and would really appreciate any help I could get. > > Best regards > /Elin Vimefall > > * > * 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: clustering and log likelihood.***From:*Elin Vimefall <Elin.Vimefall@oru.se>

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