"t value" associated with nlme/lme4 I understand the problem of determining the degrees of freedom in multi-level models; hence, the decision by Doug Bates et al. not to report p values as part of the lme4 package in R. Not to mention the plethora of problems with, and undue focus on p values, in general.
However, I would like to clarify the nature of the "t value" reported in the summary output of a multi-level model in nlme or lme4.
Isn't it the case that the reported t value in nlme/lme4 from a data set comprising correlated data is actually not from the t-distribution? (regardless of whether we know the degrees of freedom or not).   
Isn't the "t value" in lme4 potentially misleading. 
 A: Correct, the Wald statistic (reported as a "t statistic" by lme4) is, in general, at best only approximately t-distributed for linear mixed models (LMMs). It is only exactly t-distributed in certain very special cases, for example, mixed-model ANOVA with nested random factors and balanced data.
For generalized linear mixed models (GLMMs) with a non-normal response, the distribution of the Wald statistic might not even be very t-like at all. For example, see this thread on logistic regression, where we show that the tails of the sampling distribution can tend be be thinner-than-normal rather than thicker-than-normal. (That thread does not focus on mixed models, but the same issue arises there.)
A: Basically $t$ is just $\beta/\mathrm{SE}(\beta)$, where $\beta$ is regression parameter. There is nothing misleading in this value if you consider it as this ratio, or as "standarized" parameter. If you look at Bates' original arguments against $p$-values in lme4 he writes mostly about the degrees of freedom that are problematic rather than the $t$ of $F$ values themselves (see also r-sig-mixed-models FAQ). Notice that different statistical software can have different naming convention, e.g. as SPSS calls parameters as $B$'s and standarized parameters as $\beta$'s -- lme4 follows the lm convention to call them Estimate and t value.
Pinheiro and Bates describe usage of $p$-values in "Mixed-Effects Models in S and S-PLUS", so it is hard to look for arguments against them in this book. The ratios are also discussed by Bates in "lme4: Mixed-effects modeling
with R" in comparison to $t$ and $F$ values for fixed effects models, for example (p. 70):

In a fixed-effects model the profile  traces  in  the  original  scale
  will  always  be  straight  lines.  For  mixed models these  traces 
  can fail to  be  linear,  as we  see here,  contradicting  the
  widely-held  belief  that  inferences  for  the  fixed-effects 
  parameters  in  linear mixed models, based on $T$ or $F$ distributions
  with suitably adjusted degrees of  freedom,  will  be  completely 
  accurate.  The  actual  patterns  of  deviance contours are more
  complex than that.

what makes them somehow similar while not exactly adequate as we would expect them to be for proper hypothesis testing.
Notice also that other authors not always consider the df issue to be problematic, e.g. Gałecki and Burzykowski in "Linear Mixed-Effects Models
Using R" just assume $n-p$ degrees of freedom and treat their distribution as approximately $t$, e.g. (p. 84):

The null distribution of the $t$-test statistic is the $t$-distribution
  with $n − p$ degrees of freedom.

and (p. 140):

Confidence intervals for individual components of the parameter vector
  $\beta$ can be constructed based on a $t$-distribution used as an approximate
  distribution for the test statistic

So it seems that the main rationale is that while $p$-values can be misleading because of unclear null distribution, $t$ values can still be useful, at least as standardized parameters. You can also use them for hypothesis testing but you need to make some assumption about their distribution and verify them by looking at profile plots.
What Bates seems to be saying is that you use them at your own risk.
