Linear mixed model: question about t-values

Kostenko, Olga <O.Kostenko <at> nioo.knaw.nl> writes:

I have a question about the output of linear mixed model fitted in R
using nlme package. In particular, what are the t-values that are given
in an output, how are they calculated and based on what test? I guess it
cannot be a simple Student t-test, otherwise how can the simple Student
t-test test for significance of interactions, right? I cannot find this
information in any of R help resources on linear-mixed models and I also
checked few books.

The t-statistics are the ratio of the previously quoted
Value (parameter estimate) and Std.Error columns;
the p value is a 2-sided test against
the null hypothesis that this t-statistic is drawn from
a standard t distribution with "DF" degrees of freedom, i.e.

2*pt(abs(tstat),df=DF,lower.tail=FALSE)

  You will find this referred to in the literature as a "Wald test".
For more information the best reference is Pinheiro and Bates 2000
(Springer)