[R] Interpreting the result of a model with random effects

[Frank S.]

Dear R users,

 I'm analyzing a particular score "y" among several individuals, each of which belongs to a center, a factor with three
different levels (3 possible centers). I have treated the "center" as a fixed effect, and as a random term (package lme4):

1) model.fix <- glm(y ~ var.1 + var.2 + var.3 + var.4 + var.5 + center, family = "binomial", data = dat)
2) model.rand <- glmer(y ~ var.1 + var.2 + var.3 + var.4 + var.5 + (1 | center), family = "binomial", data = dat)

The issue is that both models provide exactly the same coefficients and p-values for the 5 baseline variables, so I assumed
that it was due to the small number of levels (in fact,  too few ). However, when computing anova(model.rand, model.fix),
the output indicates a p-value < 0.001 in favour of the "model.rand". What's happening? Should I take the random terms?

Thanks for any help!

Frank S.

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