Questions tagged [reml]

Restricted maximum likelihood (reml) is a variant of maximum likelihood when estimation is based on some transformations of the data, typically to residuals.

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Statistical formula of likelihood in nlme

I understand that nlme package in r uses REML method for estimation. Where can I find the statistical expression of this likelihood (for a single level of grouping) ...
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Using restricted maximum likelihood on marginal residuals

In a mixed-model setting, I want to estimate the variance components and the pertaining random effects of a random-intercept/random-slope model. The coefficients of the fixed effects have already been ...
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REML for multilevel modeling comparison

With the very same data, I want to compare the two multilevel models. (these two models differs in both fixed and random effects) so, I am planning simulation study. I will generate the data set, and ...
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emmeans, should I use ML or REML fitted models [duplicate]

I see a lot of examples out there which use ML or REML fitted models as an input for emmeans. If I understand correctly for model comparison of fixed effects for "fixed effects nested models"...
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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. ...
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Mixed effect regression with gamma family using REML?

I am trying to fit a generalized mixed effect model for gamma family. I am using the following R ...
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What is the relationship between GLS and REML?

I know, that there are several parameter estimation methods for models: OLS, GLS, TLS and maybe others. There is also the MLE - maximum likelihood estimation and the REML for models with non-constant ...
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How to check p-value in REML (or mixed model) in R? [duplicate]

This is my data and I'd like to do REML analysis to see variance components of random factor. ...
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78 views

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 ...
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Model smoothness selection for GAMs: GCV vs. REML vs. ML?

I am studying patterns of bird abundances with certain habitat variables and how they vary over time. I am interested in using GAMs with smooth terms for some of the variables. I am, however, confused ...
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What does it mean to have a model fit via GLS with REML? Aren't GLS and REML two different methods of estimation?

As in the title. I am confused. We often read that a regression model was fit using the OLS, GLS, TLS or ML. But recently I found a text about the analysis of repeated data, where it was modelled ...
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Score test using restricted mle

I am doing a study on Rao score test and still confused about the score vector. How am I supposed to calculate the score vector? Can I just use (ˆθn - θn) for the score vector? As I understood that ...
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Show why the estimate of variance component using REML is unbiased

I'm trying to use a very simple example to illustrate how REML makes the estimate of variance component unbiased: Consider $X_1,\dots,X_n\overset{i.i.d.}{\sim}\mathcal{N}(\mu,\sigma^2)$, we denote one ...
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Why do I not get confidence intervals for interactions using confint with glmmTMB (nbinom2) and REML=TRUE

I run a model where I test the effects of different parameters on the number of individuals (no_ind) in a field experiment. I would like to report the confidence intervals and use confint() which ...
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440 views

mixed model variance-covariance matrix| parameter estimation

I am fairly new to LMM's and I am trying to undestand how the parameter estimation happens; According to this: Beta is obtained with equation 13.28. Beta is supposed to be the parameters for the ...
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REML in non-mixed models

I want to know if the concept of Restricted Maximum Likelihood (REML) applies to non-mixed models. For example, suppose we want to perform a test equivalent of the one-sample t-test, it may be ...
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Hartung-Knapp-Sidik-Jonkman variance correction in meta-analysis

I am doing a meta-analysis of continuous data (SMD), number of studies (k) around 75, heterogeneity high (Tau-squared around 0.15, I-sqr over 75%). Our interest is in fact in a key subgroup analysis (...
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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 ...
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14 votes
1 answer
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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 ...
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2 votes
1 answer
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Why does the glmmTMB gives different fixed effects when random slopes are requested vs just intercepts?

I am trying to fit a beta regression to my data using mixed models, as there are 4 repeated observations per subject. Legend: p = (time) point: t1...t4 ID = subject ID When I try: ...
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2 votes
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121 views

Model selection with different fixed effects and different corARMA structures

I analyzed the effect of temperature (4 different areas) on laying date: LDT ~ Aa3+Bb+Cc+Dd. Because of autocorrelation in residuals I used ...
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15 votes
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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 (...
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1 answer
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Does "random effect" really exist in real data when we use random/mixed effect model? [closed]

If I understand correctly, here is a standard case when we need the mixed effect model: We are interested in studying the how drugs influence human health conditions, so we collected information ...
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3 votes
1 answer
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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 ...
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tau2 estimation using reml in SAS

I would like to obtain tau2 estimation using REML by making use of PROC MIXED procedure in SAS to compare the estimation result obtained from rma function in R. I have used the following SAS code; ...
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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 ...
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2 votes
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Deriving the maximum likelihood of REML for linear mixed model

Consider the linear model $Y = X \beta + e$, $e \sim N(0, V(\theta))$, where $Y$ is a $n \times 1$ vector, $X$ is the $n \times p$ full rank design matrix, $V(\theta)$ is the covariance matrix. I drop ...
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Mixed-model in R - Am I doing this right? Why is it always significant?

Here is my experiment: I evaluated the same individuals before applying treatment1, treatment2, a combination of both or none of ...
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Using ML or REML when comparing factor levels with Wald test?

I have finished my model reduction of a linear mixed model (and have used ML for this) and have found which factors that are significant in my final model. I am aware of that using ML is necessary ...
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972 views

"Time" as continuous, ordinal, or nominal in this REML design?

I've assayed two treatment groups at three time points. The time points are "days post inoculation" (specifically, 0, 20 and 40 days), so the interval between the measure is meaningful. I've ...
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1 vote
1 answer
405 views

meta-analysis in R REML estimator

Does the REML estimator (default) in the R metafor package provides inverse-variance weighting?
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2 votes
1 answer
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How to obtain REML estimates in a glmer? Optimizing random effects structure in glmer function (lme4 R package)

I'm trying to fit a model with the function glmer (lmer4 1.1-7 package) in R using REML. I tried to use the argument method=REML to do it, but this argument is deprecated. It seems that the way to ...
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1 vote
1 answer
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Why does $y \text{~} N(X \beta, \sigma^2 V)$ $\implies$ $M^T y \text{~} N(0, \sigma^2 M^T V M)$

Why does $$y \text{~} N(X \beta, \sigma^2 V)$$ $\implies$ $$M^T y \text{~} N(0, \sigma^2 M^T V M)$$? When $M^T X=0$ and $M^T M = I$.
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1 vote
2 answers
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Kenward-Roger and REML

I am doing some mixed model analyses using the lmer function in R's lme4 package. I am using the ...
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2 votes
1 answer
261 views

How does case-resampling bootstrap work for positive-value estimators?

I've looked at some other questions on bootstrap significance testing: Non-parametric bootstrap p-values vs confidence intervals Computing p-value using bootstrap with R p-value vs. confidence ...
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1 vote
1 answer
930 views

Big Misconception in the use of REML to estimate Variance Components?

I often hear from my classmates, and even in resources on the internet such as in the abstract to this paper, what I now believe to be a misconception regarding the motivation of using REML (...
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What is the difference between Restricted Maximum Likelihood (REML) and Maximum Likelihood (ML)? [duplicate]

I am a first year graduate student in biostatistics, and I have somewhat of an idea of the difference between REML and ML. However, I want a more in-depth understanding of each estimation method, ...
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7 votes
1 answer
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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 ...
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14 votes
1 answer
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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)),...
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4 votes
1 answer
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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 ...
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Restricted Maximum Likelihood Estimation for Linear Mixed Model

The maximum likelihood estimation procedure for linear mixed model is described in this link. It seems to me that something is wrong there. In their Restricted Maximum Likelihood section the first ...
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5 votes
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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. ...
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Restricted Maximum Likelihood Estimates of Multilevel Regression Model

A two-level regression model : $$Y_{ij} = \gamma_{00} + \gamma_{10}X_{ij} + \gamma_{01}Z_j + \gamma_{11}X_{ij}Z_j + u_{0j} + u_{1j}X_{ij} + e_{ij}$$ where $e_{ij}\sim N(0,\sigma^2_e)$ and , $$ \...
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7 votes
1 answer
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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 ...
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1 vote
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211 views

Mixed Linear Model - REML approach AI or FS algorithm

I am trying to see if there is a situation where Fisher scoring algorithm would be better than Average Information algorithm. I know that Average information algorithm is more efficient for large data ...
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11 votes
2 answers
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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 ...
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3 votes
1 answer
491 views

Restricted Maximum Likelihood

Why don't we use restricted maximum likelihood to estimate parameters in non-mixed models?
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2 votes
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69 views

REML estimation - matrix algebra internals

In the context of REML estimation there is the result (ignoring some constants) that (my interest is in the matrix algebra so some notation is suppressed): $l(\mathbf V_0)=\log |\mathbf V_0| + \text{...
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17 votes
3 answers
6k views

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 ...
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2 votes
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assumptions of REML

In Patterson and Thompson 1971, $L$ is the log-likelihood of $y$ $$ L = const - \frac{1}{2}log |H| - \frac{1}{2}n log (\sigma^2) - \frac{1}{2\sigma^2} (y - X\alpha)'H^{-1}(y-Xa) $$ They consider the ...
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