Restricted maximum likelihood (reml) is a variant of maximum likelihood when estimation is based on some transformations of the data, typically to residuals.
Wikipedia has an article with further references.
Questions tagged [reml]
48 questions
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What is "restricted maximum likelihood" and when should it be used?
I have read in the abstract of this paper that:
"The maximum likelihood (ML) procedure of Hartley aud Rao is modified by adapting a transformation from Patterson and Thompson which partitions the likelihood render normality into two parts, one…
Joe King
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Why does one have to use REML (instead of ML) for choosing among nested var-covar models?
Various descriptions on model selection on random effects of Linear Mixed Models instruct to use REML. I know difference between REML and ML at some level, but I don't understand why REML should be used because ML is biased. For example, is it wrong…
quibble
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Does a Bayesian interpretation exist for REML?
Is a Bayesian interpretation of REML available? To my intuition, REML bears a strong likeness to so-called empirical Bayes estimation procedures, and I wonder if some kind of asymptotic equivalence (under some suitable class of priors, say) has been…
David C. Norris
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Restricted maximum likelihood with less than full column rank of $X$
This question deals with restricted maximum likelihood (REML) estimation in a particular version of the linear model, namely:
$$
Y = X(\alpha)\beta + \epsilon, \\
\epsilon\sim N_n(0, \Sigma(\alpha)),
$$
where $X(\alpha)$ is a ($n \times p$) matrix…
ekvall
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How are PQL, REML, ML, Laplace, Gauss-Hermite related to each other?
While learning about the Generalized Linear Mixed Models, I often see the above terms. Sometimes it seems to me these are separate methods of estimation of (fixed? random? both?) effects, but when I read the literature, I see the terms mixed. For…
humbleasker
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Why does Restricted maximum likelihood yield a better (unbiased) estimate of the variance?
I'm reading Doug Bates' theory paper on R's lme4 package to better understand the nitty-gritty of mixed models, and came across an intriguing result that I'd like to understand better, about using restricted maximum likelihood (REML) to estimate…
Paul
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How are calculations done for REML?
I've read a few questions on this site (e.g., https://stats.stackexchange.com/a/48676/46427), but they rarely go beyond intuitive explanations. I am particularly interested with how to calculate an estimate via REML, not the intuition behind REML.
I…
Clarinetist
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Citation for ML vs. REML
Quick question: can anyone give me a citation that I can use to justify using ML when doing model comparisons?
Background: I am fitting some multilevel models in R using lme4, and I do a series of model comparisons. One reviewer told me I should…
Tom Carpenter
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Which iterative algorithm lmer uses for REML estimation?
For mixed model, when we estimate variance component by restricted maximum likelihood estimation procedure, an iterative algorithm is required to solve the estimating equations for variance component. Two main iterative algorithms are :
(1)…
user81411
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Estimate of $\text{Var}(\hat\beta)$ in a linear mixed model
Let $Y = X\beta + Zu + \sigma\epsilon$ be a Gaussian linear mixed model.
Let $V = Var(Y)$ be the marginal variance matrix of $Y$. Define the matrix
$$
\Phi = {(X'V^{-1}X)}^{-1}.
$$
According to this SAS documentation, $\Phi$ underestimates…
Stéphane Laurent
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How to use REML to estimate correlation with missing data in R?
In JMP Multivariate Methods, REML is used to estimate correlation when there are missing data values (pg. 28). However, there is no documentation describing how this is done.
I'm trying to compare my results in R with my results in JMP. However,…
ken
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Derivation of integrating over many parameters in Neyman-Scott Problem?
I am trying to follow the derivation for the variance estimator in the Neyman-Scott problem given in this article. However, I'm not sure how they go from the 2nd to the 3rd line of this derivation. Any help is appreciated, thanks!
max
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Why is REML default if it inflates MSE?
Within the mixed effects model world, REML has become the method of choice in order to correct for the downward bias in variance components. For years, I accepted this rationale without thinking about the potential effects this bias-correction might…
user321797
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Why are the coefficients of REML and ML estimation the same? What does that mean?
I have estimated a linear mixed model with REML and ML estimation. However, the estimated coefficients do not differ. The standard errors of the coefficients are slightly higher for the REML estimation.
The regression output is the following:
My…
Student
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Are REML estimators of variance-covariance parameters consistent?
I am trying to locate some reference papers about consistency of REML estimators in linear mixed effects models. My understanding is that in linear model scenario, REML will produce the exact same estimator for residual variance as OLS, thus it is…
Vincent
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