When to use a mL or REML model?
In practice, when we e.g. solve a Linear Regression model using ML, we rarely think about the bias in the variance estimator, since we are usually interested in the coefficients of the linear model, which is the mean, and often do not even realize that in parallel we estimate one more fitting parameter, which is the variance.
Why is the restricted maximum likelihood ( REML ) useful?
Today we will discuss the concept of Restricted Maximum Likelihood (REML), why it is useful and how to apply it to the Linear Mixed Models. The idea of Restricted Maximum Likelihood ( REML) comes from realization that the variance estimator given by the Maximum Likelihood (ML) is biased. What is an estimator and in which way it is biased?
How does a linear mixed model work in R?
Previously we talked about How Linear Mixed Model Works, how to derive and program Linear Mixed Model from Scratch in R from the Maximum Likelihood (ML) principle. Today we will discuss the concept of Restricted Maximum Likelihood (REML), why it is useful and how to apply it to the Linear Mixed Models.
How to fit LMM with fixed effects and random effects?
We fit the data using LMM with fixed effects for slopes and intercepts and random effects for intercepts using the lmer function from lme4 R package. Including random effects intercepts that account for grouping factor Ind (the individual ID), we will need too use a special syntax (1 | Ind) for the lmer function.
Is there a Wald test for linear mixed models?
For linear mixed models with little correlation among predictors, a Wald test using the approach of Kenward and Rogers (1997) will be quite similar to LRT test results. The SSCC does not recommend the use of Wald tests for generalized models.
Why is REML not used for AIC comparisons?
The reason is that REML estimates the random effects by considering linear combinations of the data that remove the fixed effects. If these fixed effects are changed, the likelihoods of the two models will not be directly comparable I’ll give an example to illustrate why the REML likelihood cannot be used for things like AIC comparisons.
What is the minimum number of random effects in a mixed model?
“: One point of particular relevance to ‘modern’ mixed model estimation (rather than ‘classical’ method-of-moments estimation) is that, for practical purposes, there must be a reasonable number of random-effects levels (e.g. blocks) — more than 5 or 6 at a minimum. So you are at the lower bound, but on the right side of it.
Why are longitudinal mixed effects models randomly sampled?
I know this is the usual course of action in longitudinal mixed effects models, to take account of the randomly sampled nature of the subjects and the fact that observations within subjects will be more closely correlated than those between subjects.
Can you use REML to compare two models?
Zuur et al., and Faraway (from @janhove’s comment above) are right; using likelihood-based methods (including AIC) to compare two models with different fixed effects that are fitted by REML will generally lead to nonsense.