Ofer Harel has published on the distribution of the FMI (e.g., Harel 2007 Statistical Methodology), there may be something of use there, though I believe he focuses on the between component. -Rebecca -- Rebecca R. Andridge, Ph.D. Assistant Professor, Division of Biostatistics College of Public Health The Ohio State University 242 Cunz Hall 1841 Neil Avenue Columbus, OH 43210 Phone: (614) 247-7912 [email protected]
From: David Judkins <[email protected]<mailto:[email protected]>> Reply-To: Impute -- Imputations in Data Analysis <[email protected]<mailto:[email protected]>> Date: Tuesday, October 2, 2012 10:08 AM To: "[email protected]<mailto:[email protected]>" <[email protected]<mailto:[email protected]>> Subject: Re: Distribution of variance components Paul, I assume you mean the joint distribution of the estimated between-imputation and within-imputation variance components as opposed to variances on Bayesian posterior distributions or between-PSU and within-PSU variance components. Seems to me that the distribution of the estimated within-imputation variance component depends on the variance estimation method. Kirk Wolter’s book (An Introduction to Variance Estimation) is a good source for information on various variance estimation methods. Also see chapter 4 of Wayne Fuller’s newer text (Sampling Statistics). One way to discover more on this topic is to search for “variance of the variance.” Here are a few relevant links. http://www.amstat.org/sections/srms/proceedings/papers/1989_030.pdf http://www.amstat.org/sections/srms/Proceedings/y2004/files/Jsm2004-000354.pdf http://www2.math.su.se/~rolfs/Publikationer/Biometrika94.pdf --Dave Judkins Abt Associates From: Impute -- Imputations in Data Analysis [mailto:[email protected]] On Behalf Of Paul von Hippel Sent: Tuesday, October 02, 2012 8:23 AM To: [email protected]<mailto:[email protected]> Subject: Distribution of variance components Is there any work on the joint distribution of the Between and Within variance components that are used in calculating the usual multiple imputation standard error? The Between component is Wishart, that's pretty clear, but the marginal distribution of the Within component is trickier, and then there's the joint distribution. -- Best wishes, Paul von Hippel Assistant Professor LBJ School of Public Affairs Sid Richardson Hall 3.251 University of Texas, Austin 2315 Red River, Box Y Austin, TX 78712 (512) 537-8112 ________________________________ This message may contain privileged and confidential information intended solely for the addressee. Please do not read, disseminate or copy it unless you are the intended recipient. If this message has been received in error, we kindly ask that you notify the sender immediately by return email and delete all copies of the message from your system.
