Comparison of crossed ranom effects: lmer vs. MCMCglmm
Hi, Yes, MCMCglmm fits two independent random effects. Bayesian approaches treat the variance components as random variables, and MCMC allows you to estimate their distribution. In general that distribution is not known, but if the response is Gaussian, the prior conjugate, and all fixed effects known, then the distribution is scaled inverse-Chi-squared. This distribution is skewed, particularly with low degrees of freedom. (RE)ML does not posit a distribution for the variance components, it simply finds the variance components that maximise the (restricted) likelihood. Sometimes an approximate distribution for the *estimates* of the variance components is posited: usually normal with mean equal to the (RE)ML estimates. This approximation is based on high-n, but in reality the sampling distribution will rarely be normal and will also have skew. The underestimation of the variance components via Maximum Likelihood is a separate issue. This arises because the deviation of observations from the estimated mean will always be smaller than the deviation of observations from the true mean. REML corrects for this by accounting for the uncertainty in estimated mean. Cheers, Jarrod Quoting Linus Holtermann <holtermann at hwwi.org> on Tue, 20 Jan 2015 10:50:41 +0100:
Thanks Jarrod. Just to be on the safe side, MCMCglmm indeed fits two independent random effects in the "mcmc"-specification? The different results emerge because the MCMC-Approach treat the variance components as random variables that capture more of the skewness? It is often claimed that mixed models fitted via Maximum Likelihood underestimate the random effect variance. Best regards, Linus Holtermann Hamburgisches WeltWirtschaftsInstitut gemeinn?tzige GmbH (HWWI) Heimhuder Stra?e 71 20148 Hamburg Tel +49-(0)40-340576-336 Fax+49-(0)40-340576-776 Internet: www.hwwi.org Email: holtermann at hwwi.org Amtsgericht Hamburg HRB 94303 Gesch?ftsf?hrer: PD Dr. Christian Growitsch | Prof. Dr. Henning V?pel Prokura: Dipl. Kauffrau Alexis Malchin Umsatzsteuer-ID: DE 241849425
________________________________________ Von: Jarrod Hadfield [j.hadfield at ed.ac.uk] Gesendet: Montag, 19. Januar 2015 19:25 An: Linus Holtermann Cc: r-sig-mixed-models at r-project.org Betreff: Re: [R-sig-ME] Comparison of crossed ranom effects: lmer vs. MCMCglmm Hi Linus, The point estimates are almost identical if the posterior mode is used: hist(mcmc$VCV[,"plate"], breaks=30) abline(v=VarCorr(ml)[["plate"]][1], col="red") The posterior mean (which is reported in the summary) is often not a good measure of central tendency for variance components because of the skew. Posterior modes have high Monte Carlo error though. Cheers, Jarrod Quoting Linus Holtermann <holtermann at hwwi.org> on Mon, 19 Jan 2015 18:39:52 +0100: Hello, I read that lmer can handle independent (often labelled as crossed) random effets in mixed models. It seems to be possible with MCMCglmm as long as groups for the random effects are uniquely labelled. I use the "Penicllin" data in the lme4-package to compare both approaches: library(lme4) library(MCMCglmm) str(Penicillin) attach(Penicillin) ml <- lmer(diameter~ 1 + (1|plate)+ (1|sample)) summary(ml) mcmc <- MCMCglmm(diameter~ 1, random=~ plate + sample,verbose=F, nitt=110000,burn=10000,thin=10,data=Penicillin) summary(mcmc) Why are the result for the plate-variance differ by a large amount? Is it because MCMCglmm applies Gibbs sampling? Or is MCMCglmm doing something else here, instead of fitting independent random effects? Best regards, Linus Holtermann Hamburgisches WeltWirtschaftsInstitut gemeinn?tzige GmbH (HWWI) Heimhuder Stra?e 71 20148 Hamburg Tel +49-(0)40-340576-336 Fax+49-(0)40-340576-776 Internet: www.hwwi.org Email: holtermann at hwwi.org Amtsgericht Hamburg HRB 94303 Gesch?ftsf?hrer: PD Dr. Christian Growitsch | Prof. Dr. Henning V?pel Prokura: Dipl. Kauffrau Alexis Malchin Umsatzsteuer-ID: DE 241849425 _______________________________________________ R-sig-mixed-models at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models -- The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336.
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