The reason for this question, is that I am trying to fit a variance components analysis with a single random effect and no fixed effects.The only way I know to test for the significance of the single level of random effects is by comparing the model with a glm without fixed effects and do a ChiSquare test.
This may or may not be known to you:
If one model is a special case of the other, i.e. its variance component equals zero, then the less complex model falls on the boundary of the parameter space relative to the more complex model. Hence the LR test needs to be adjusted, and in this simple case the adjusted p-value may be taken as half the p-value from the usual one degree of freedom chi-squared test, i.e. using a 50-50 mixture of chi-squared distributions with zero and one df as the reference.
In other cases, e.g. when simultaneously testing if two or more variance components equals zero, the asymptotic distribution isn't generally known. You may use a score test (Lin, Biometrika, 1997), but I don't think it's implemented in R or any of the add-on packages.
Pinheiro & Bates "Mixed-effects models in S and S-PLUS" p. 82-87 provide a good discussion in the context of linear mixed-effects models.
//Henric
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