ENBIS-17 in Naples

9 – 14 September 2017; Naples (Italy) Abstract submission: 21 November 2016 – 10 May 2017

What is REML and Why Does It Work?

11 September 2017, 16:20 – 16:40


Submitted by
Chris Gotwalt
Chris Gotwalt (JMP Division of SAS Institute)
Estimating the parameters of the linear mixed model via Restricted Maximum Likelihood (REML) is one of the most widely used approaches to statistical estimation. The is because years of experience, gained over a broad array of applications from quality control to clinical trials, have shown that REML estimates of variance parameters often have lower bias than Maximum Likelihood (ML) estimates. However, outside of balanced cases, the reason for this superiority of REML remains a little mysterious. This presentation starts with a brief review of some of the classic motivations for, and derivations of, REML and then presents a new derivation that demonstrates that the REML estimator for a variance component model is an instance of a Firth adjusted estimator. This new derivation is advantageous for several reasons. It makes clear for which types of correlation structures we can expect less bias from REML compared with ML. It also shows that there are common correlation structures to which REML is often applied, but for which the hope for bias improvement is not on a solid theoretical footing. Fortunately, in such cases, the derivation also makes clear how the likelihood estimating equation can be adjusted so that the resulting estimates still enjoy reduced bias compared with ML.

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