I am currently reviewing some work and have come across the following, which seems wrong to me. Two mixed models are fitted (in R) using lmer. The models are non-nested and are compared by likelihood-ratio tests. In short, here is a reproducible example of what I have:

`set.seed(105) Resp = rnorm(100) A = factor(rep(1:5,each=20)) B = factor(rep(1:2,times=50)) C = rep(1:4, times=25) m1 = lmer(Resp ~ A + (1|C), REML = TRUE) m2 = lmer(Resp ~ B + (1|C), REML = TRUE) anova(m1,m2)`

As far as I can see,

`lmer`

is used to compute the log-likelihood and the`anova`

statement tests the difference between the models using a chi-square with the usual degrees of freedom. This does not seem correct to me. If it is correct, does anyone know of any reference justifying this? I am aware of methods relying on simulations (Paper by Lewis et al., 2011) and the approach developed by Vuong (1989) but I do not think that this is what is produced here. I do not think that the use of the`anova`

statement is correct.

**Answer**

This is not correct ~~in two ways~~:

- (Ordinary) likelihood ratio test can only be used to compare nested models;
~~We cannot compare mean models under REML.~~(This is not the case here, see @KarlOveHufthammer’s comments below.)

In the case of using ML, I am aware of using AIC or BIC to compare the non-nested models.

**Attribution***Source : Link , Question Author : Community , Answer Author : Randel*