Linear mixed models - significance of the "overall" fit

Hi all,

I' wondering if there's a test statistic that encompasses the overall fit of the linear mixed model. For example, if I fitted a model with 100 fixed effects I wouldn't jump straight into looking at the t tests for non-zero coefficients; I'd want a test statistic indicating that the overall model explains "something" before looking for the coefficients that do the explaining.

I guess another way to look at it is if I'm testing for differences between n treatments, I'd want a statistics telling me there is a treatment effect before looking at which treatments are different from each other.

Thanks, Andrew

Answer 1

[Star Strider]

I suggest Analysis-of-Variance ( anova ).

[Andrew]

Hi Star Strider, thanks for your response.

When I do anova(lme) I get an F test for each fixed effect, which have the same p values as the original coefficient t tests. Since my fixed effects are all dichotomous, anova's F tests are from F distributions where the first degree of freedom is one, whereas I expect the test I'm after to have the first F degree of freedom equal to the number of fixed effects.

I think(!?) I'm after a comparison of the residuals for the models:

lme_null = c + (1|random_effects)

vs

lme_alt = c + fixed_effects + (1|random_effects)

[Star Strider]

It’s been a while since I did anything with Linear Mixed Models (and then mostly with clinical trials). My recollection is that the ANOVA procedure gave overall information about the results, and then it was necessary to do t-tests (with corrections for multiple comparisons) to find out which were significant. You’ve probably already done the various versions of coefTest. It’s the only option I see that might give you the information you want.