[R-sig-ME] anova() and the difference between (x | y) and (1 | y:x) in lme4

[Hans Ekbrand]

On Wed, Jun 11, 2014 at 02:21:40PM +0000, ONKELINX, Thierry wrote:
> Dear Hans,
> 
> I assume that var1 is a factor variable.

Yes.

> The difference is in the distribution of the random effects.
> 
> (1|var1:var2) : all random intercept come from the same univariate normal distribution rnorm(mean = 0, sd = sigma)
> (0 + var1|var2): the random intercepts come from a multivariate normal distribution: rmvnorm(mean = 0, sigma = Sigma). Sigma is a positive definite matrix
> 
> (0 + var1|var2) is a bit easier to understand because the BLUP's have the same interpretation of those of (1|var1:var2)
> 
> The bottom-line is that (var1|var2) and (1|var1:var2) allow the same model fit but (var1|var2) makes less assumptions at the cost of estimation more parameters. (var1|var2) requires n * (n + 1) / 2 parameters, with n = number of levels of var1. (1|var1:var2) requires just 1 parameter.

Thank you for the explanation, Thierry.

Do you know if it is sensible to compare the models with anova()?