Dear Dr. Zeileis, Thank you for pointing out on the maximum likelihood estimator property as well as the delta method to obtain the standard error of estimated Theta.
I agree with you in that whether getting the standard error of estimated Theta is useful or not. I will think about this further. Best regards, Tzeng Yih Lam ------------------------------------------------------------------------------ PhD Candidate Department of Forest Engineering, Resources and Management College of Forestry Oregon State University 321 Richardson Hall Corvallis OR 97330 USA Phone: +1.541.713.7504 Fax: +1.541.713.7504 ------------------------------------------------------------------------------ ________________________________________ From: Achim Zeileis [achim.zeil...@uibk.ac.at] Sent: Monday, February 15, 2010 2:03 AM To: Lam, Tzeng Yih Cc: r-help@r-project.org Subject: Re: [R] Estimated Standard Error for Theta in zeroinfl() On Sun, 14 Feb 2010, Lam, Tzeng Yih wrote: > Dear R Users, > > When using zeroinfl() function to fit a Zero-Inflated Negative Binomial > (ZINB) model to a dataset, the summary() gives an estimate of log(theta) > and its standard error, z-value and Pr(>|z|) for the count component. > Additionally, it also provided an estimate of Theta, which I believe is > the exp(estimate of log(theta)). As maximum likelihood estimation is employed, this does not matter for point estimation. theta is the ML estimator for theta and log(theta) is the ML estimator for log(theta). I don't think that there is an unibiasedness result for either one, but both are consistent (if the model is correctly specified). What is done internally in zeroinfl() is that log(theta) is employed which is a standard approach for numeric optimization of positive parameters. > However, if I would like to have an standard error of Theta itself (not > the SE.logtheta), how would I obtain or calculate that standard error? You can do so by means of the delta method which is rather simple in this case: The standard error of theta is: theta * SE(logtheta). Thus, if obj is a fitted "zeroinfl" object: ## theta obj$theta ## associated standard error obj$theta * obj$SE.logtheta Whether this is very useful is another story, of course...see also Rolf's remarks. Z > Thank you very much for your time. > > Best regards, > Tzeng Yih Lam > > ------------------------------------------------------------------------------ > PhD Candidate > Department of Forest Engineering, Resources and Management > College of Forestry > Oregon State University > 321 Richardson Hall > Corvallis OR 97330 USA > Phone: +1.541.713.7504 > Fax: +1.541.713.7504 > ------------------------------------------------------------------------------ > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
