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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Generalized additive model: Variable & model selection

I know this type of question has been asked many times before, so I apologize for re-posting about it. I bring it up again because it's been taught in one of my courses of study and I want to make ...
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Residual likelihood ratio test for fixed effects in a linear mixed model

I know (but now I have doubts) that "Comparing models that are fitted with REML and differ in their fixed effects never makes sense," just as @BenBolker explains in this answer. I've been ...
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Significance testing between two set of SNPs

After performing GWAS, I calculated the percentage of phenotypic variance (SNP-based heritability) for top SNPs and random SNPs using GREML (GCTA). The variance of random SNPs was calculated for 3 ...
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How is REML used in gls?

I am trying to understand gls and I have two questions: (1) How are the standard errors of the coefficients calculated? (2) what role REML plays in gls?
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I am trying to understand if my data are MAR and if using REML is a sufficient solution to dealing with this

I am analyzing longitudinal data from high school students measured across 4 waves (2010, 2011, 2012, 2013). Of course not all high school students were Freshmen in 2010 so I have missing data for ...
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What interpretation do REML/fREML values provide in generalized additive models (GAMs)?

I'm continuing my slow trudge through Simon Wood's book on generalized additive models (GAMs), and it has given me some new useful insights. However, I am still confused after reading through Chapter ...
Shawn Hemelstrand's user avatar
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Why does using "REML" in mgcv give error for generalized additive models?

I have fitted gam for a generated data with binomial responses. The problem is, many times while running this gam with different bootstrap samples, error occurred.
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Discrepancy between model selection based on REML score vs explained deviance in GAMs

Will be grateful for insights into the issue below! I have two explanatory GAMs below (in this example implemented with mgcv), where the effects of x1 and x2 are of interest. x1 is air temperature, x2 ...
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Comparing different GAMs using AIC when the models were fitted using "method=REML" in mgcv

I am new to GAM and comparing several subsets of these model from the same data(multiple covariates). Now if I set the "method" to "REML" and then compare their AIC values, would ...
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386 views

Comparing GAM models with/without fixed effect interactions using REML versus ML

I have several GAM models fit with package mgcv that share the same smooths and random effects groups. I would like to compare support for whether interactions ...
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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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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. ...
max's user avatar
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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 ...
user321797's user avatar
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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 ...
zira's user avatar
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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 ...
Chris Cloud's user avatar
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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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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 (...
Ioana Cristea's user avatar
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1 answer
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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 ...
Stéphane Laurent's user avatar
19 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 ...
humbleasker's user avatar
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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: ...
humbleasker's user avatar
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161 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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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 (...
David C. Norris's user avatar
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1 answer
162 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 ...
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3 votes
1 answer
2k 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 ...
Student's user avatar
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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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1 answer
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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 ...
GZ1995's user avatar
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1 answer
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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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353 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 ...
Ditlev Reventlow's user avatar
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1k 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 ...
gladys_c_hugh's user avatar
1 vote
1 answer
461 views

meta-analysis in R REML estimator

Does the REML estimator (default) in the R metafor package provides inverse-variance weighting?
Nadine's user avatar
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3 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 ...
daniel felipe zuleta zapata's user avatar
1 vote
1 answer
117 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 $M^T M = I$.
mavavilj's user avatar
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4 votes
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 ...
Peat's user avatar
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2 votes
1 answer
348 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 ...
Count Zero's user avatar
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1 vote
1 answer
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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 (...
RMurphy's user avatar
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0 answers
380 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, ...
Shyamali Mukerjee's user avatar
8 votes
1 answer
1k 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 ...
Clarinetist's user avatar
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15 votes
1 answer
776 views

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)),...
KOE's user avatar
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5 votes
1 answer
2k views

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 ...
ken's user avatar
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1 vote
0 answers
246 views

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 ...
user81411's user avatar
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6 votes
1 answer
896 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. ...
user81411's user avatar
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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 , $$ \...
user81411's user avatar
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9 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 ...
Tom Carpenter's user avatar
1 vote
0 answers
216 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 ...
DaveRowan's user avatar
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11 votes
2 answers
2k 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 ...
Paul's user avatar
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