# 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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43 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 ...
12 views

### Regression model selection and specification for unbalanced repeated measures data

My hypothesis is that person's blood oxygen level is affected by their age, gender, and drugs they have taken in the previous 24 hours. I would like to confirm and quantify effects associated with ...
18 views

### Random-intercept model with three levels: heteroschedasticity of level-1 and non-normality of level-2 residuals?

I am working on a random-intercept model with three levels and I have questions regarding the distribution of the residuals and its effect on coefficients and confidence intervals. But first let me ...
696 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 (...
249 views

### 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 ...
112 views

### 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 ...
30 views

### Are the Generalized Least Square (GLS) and Maximum Likelihood (ML) two different ways of estimation?

I was taught, that OLS and ML are two different ways of estimation. ML gives OLS estimates under met assuptions, but it doesn't change the fact the two approaches differ. If so, how is that possible ...
30 views

### 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 ...
9 views

### 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 ...
44 views

### 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 ...
54 views

### 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 ...
139 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 ...
77 views

### 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 ...
22 views

### 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 (...
803 views

### 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 ...
404 views

### 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 (...
164 views

### 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 ...
482 views

### 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: ...
97 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 ...
801 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 ...
573 views

### 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. ...
872 views

### Kenward-Roger and REML

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

### 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 ...
204 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 ...
105 views

### 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 ...
1k views

### 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 ...
81k views

### 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 ...
90 views

### 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; ...
345 views

### meta-analysis in R REML estimator

Does the REML estimator (default) in the R metafor package provides inverse-variance weighting?
71 views

### 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 ...
49 views

### 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 ...
821 views

### 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 ...
186 views

### 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 ...