# 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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### 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 ...
41 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 ...
69 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 ...
14 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 (...
19 views

### How continuous predictors are dealt within (G)LMMs' inference procedures (such as ML and REML)?

When considering (G)LMs (with no mixed effects), handling both continuous and categorical predictors seems pretty straightforward, as ML gives us an estimation for the parameters, $\beta_i$. However, ...
98 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 ...
419 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 ...
227 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: ...
78 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 ...
325 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 (...
91 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 ...
850 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 ...
73 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; ...
43 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 ...
730 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 ...
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 ...
156 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 ...
677 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 ...
280 views

### meta-analysis in R REML estimator

Does the REML estimator (default) in the R metafor package provides inverse-variance weighting?
4k views

### 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 ...
72 views

### 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 $M^T M = I$.
673 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 ...
193 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 ...
555 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 (...
282 views

### 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, ...
402 views

### 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 ...
473 views

927 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 ...
1k views

### 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 ...
402 views

### Restricted Maximum Likelihood

Why don't we use restricted maximum likelihood to estimate parameters in non-mixed models?
65 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{...