Multiple Local Maxima in Restricted Likelihoods and Posterior Distributions for Mixed Linear Models

Lisa Henn and James S. Hodges

International Statistical Review, 2014, vol. 82, issue 1, 90-105

Abstract: type="main" xml:id="insr12046-abs-0001"> Scattered reports of multiple maxima in posterior distributions or likelihoods for mixed linear models appear throughout the literature. Less scrutinised is the restricted likelihood, which is the posterior distribution for a specific prior distribution. This paper surveys existing literature and proposes a unifying framework for understanding multiple maxima. For those problems with covariance structures that are diagonalisable in a specific sense, the restricted likelihood can be viewed as a generalised linear model with gamma errors, identity link and a prior distribution on the error variance. The generalised linear model portion of the restricted likelihood can be made to conflict with the portion of the restricted likelihood that functions like a prior distribution on the error variance, giving two local maxima in the restricted likelihood. Applying in addition an explicit conjugate prior distribution to variance parameters permits a second local maximum in the marginal posterior distribution even if the likelihood contribution has a single maximum. Moreover, reparameterisation from variance to precision can change the posterior modality; the converse also is true. Modellers should beware of these potential pitfalls when selecting prior distributions or using peak-finding algorithms to estimate parameters.

Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1111/insr.12046 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:istatr:v:82:y:2014:i:1:p:90-105

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0306-7734

Access Statistics for this article

International Statistical Review is currently edited by Eugene Seneta and Kees Zeelenberg

More articles in International Statistical Review from International Statistical Institute Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().