How to get an "overall" p-value and effect size for a categorical factor in a mixed model (lme4)? I would like to get a p-value and an effect size of an independent categorical variable (with several levels) -- that is "overall" and not for each level separately, as is the normal output from lme4 in R. It is just like the thing people report when running an ANOVA.
How can I get this?
 A: In regard to calculating significance (p) values, Luke (2016) Evaluating significance in linear mixed-effects models in R reports that the optimal method is either the Kenward-Roger or Satterthwaite approximation for degrees of freedom (available in R with packages such as lmerTest or afex).

Abstract
Mixed-effects models are being used ever more frequently in the analysis of experimental data. However, in the lme4 package in R the standards for evaluating significance of fixed effects in these models (i.e., obtaining p-values) are somewhat vague. There are good reasons for this, but as researchers who are using these models are required in many cases to report p-values, some method for evaluating the significance of the model output is needed. This paper reports the results of simulations showing that the two most common methods for evaluating significance, using likelihood ratio tests and applying the z distribution to the Wald t values from the model output (t-as-z), are somewhat anti-conservative, especially for smaller sample sizes. Other methods for evaluating significance, including parametric bootstrapping and the Kenward-Roger and Satterthwaite approximations for degrees of freedom, were also evaluated. The results of these simulations suggest that Type 1 error rates are closest to .05 when models are fitted using REML and p-values are derived using the Kenward-Roger or Satterthwaite approximations, as these approximations both produced acceptable Type 1 error rates even for smaller samples.

(emphasis added)
A: I use the lmerTest package. This conveniently includes an estimation of the p-value in the anova() output for my MLM analyses, but does not give an effect size for the reasons given in other posts here. 
