[R-sig-ME] testing significance of fixed factors in a mixed model

[Julia Chacon Labella]

I am sorry if I am asking a naïve question or if that has been already
asked many times. I am not an expert in mixed models at all, but want to
understand and be confident about what I am doing.

Actually, I am analysing a data set of a experiment. I have several
treatments, a balance design, randomized by blocks, etc., and generally
following the recommendations of the FAQs by Bolker, what are really
usefull (Thanks!). http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html

But, I am pretty confused about how to test the significance of fixed
factors in a mixed model.
I find huge differences in the significance output when computing 1) Anova
from the car package or 2) anova from lmerTest with KR or satterthwaite
approaches (both, KR or Satterthwaite have similar results), or 3) a LRT
via anova. The biggest differences are found for car::Anova!

* First, I am not sure if I should employ a LRT or a conditional F-test
(lmerTest::anova, KR or satterthwaite approaches). Both results are pretty
similar in my case, but conditional F-test seem to slightly be more
conservative in my case. Can the F-test be somehow problematic in terms of
statistical power?

* Second, in case of using lmerTest::anova, I am not completely sure if I
should used a type I or type III anova.  There is any reason for using type
I anova in balanced designs?

Thanks in advance,
Julia

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