Can't find p-values in the output from lmer() in the lm4 package in R

I'm a new user of mixed models and through the material I've been reading there are always probability values (p>t) or (p>z) that estimate the importance of a level of a factor in the model. However, when using the lmer() function in R, which supposedly gives you those probabilities, I simply don't find them. Here is the output:

Linear mixed model fit by REML
Formula: Temp ~ depth + (1 | locality)
Data: qminmatrix
AIC   BIC logLik deviance REMLdev
561.3 581.3 -273.7    551.5   547.3
Random effects:
Groups   Name        Variance Std.Dev.
locality (Intercept) 4.7998   2.1909
Residual             4.0433   2.0108
Number of obs: 128, groups: locality, 4

Fixed effects:
Estimate Std. Error t value
(Intercept)  22.0103     1.1500  19.140
depth1        1.9564     0.6832   2.864
depth10       2.6624     0.5756   4.625
depth5        3.0209     0.4932   6.125
depthWS      -2.2585     0.5444  -4.149

Correlation of Fixed Effects:
(Intr) depth1 dpth10 depth5
depth1  -0.157
depth10 -0.175  0.189
depth5  -0.213  0.313  0.458
depthWS -0.191  0.334  0.373  0.441

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Since this question appears to be mostly about interpreting R's output, it may belong on Stack Overflow rather than here. OTOH, however, IIRC, the reason the package authors decided not to display the p-values has to do w/ the difficulty of determining the right number of degrees of freedom to use in assessing the t-values. This is a very subtle statistical issue, & requires some nuanced explanations, so it might be worth leaving this Q here to give CVers a chance to attempt to explain it first. – gung Sep 28 '12 at 14:20
@gung: Your comment actually answers the question. I've put a link to the author's explanation in my answer, below. – Wayne Sep 28 '12 at 14:47
I think this one should stay here, not go to Stack Overflow. This is about statistics, not about R. – Peter Flom Sep 28 '12 at 21:48
The function pvals.fnc does not work with model with random intercept and slope though. Do you have any other idea how I can get the p-values? PS: I do not understand why most journals want p-values despite many articles point out that the confidence intervals are more important than p-values. I cannot find papers with only confidence intervals, but no p-values. – user3288202 Feb 26 '14 at 9:19

use pvals.fnc() function the pMCMC here works like p-value which should be less than 0.05 to reject the null hypothesis.

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The lmer package's author made a conscious choice not to create p-values for the fixed effects. Some packages do, but he feels that they are doing simplistic calculations that are misleading. (Many statisticians feel that there's a p-value obsession that causes confusion in and of itself, but that's a separate matter.)

He addresses the question in: this post. I believe the summary paragraph is:

"Most of the research on tests for the fixed-effects specification in a mixed model begin with the assumption that these statistics will have an F distribution with a known numerator degrees of freedom and the only purpose of the research is to decide how to obtain an approximate denominator degrees of freedom. I don't agree."

I don't understand the issue well enough to paraphrase it.

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Install the coda and languageR package and run the pvals.fnc as follows for p-value:

Model.pval<-pvals.fnc(Model, nsim = n, withMCMC = TRUE)

Note that this will not work for level 3 or above in nested random effects models.

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