Hi Matias,

there are different views on this.
In psychology, you often want to test main effects and interactions. This would come down to:
model 1: A + B + A:B
model 2: B + A:B (i.e., only thing missing is A)
However, if you implemented this with anova(), then R would actually not code the predictors as you think. Instead, you can use the afex package to implement this logic correctly. 
People from many other disciplines argue against this way of testing A, because if you found A to make a significant contribution, you could usually only interpret this as a main effect if A:B were not significant. This is because a significant interaction signifies that whatever A does is modified by the level of B. Therefore, they would argue that if you have found A:B to be significant, you should not look at A alone at all (i.e., not devise any test). You can search for a paper by Venables, titled “Exegeses on linear models” which is available on the net and discusses this view.
Best,
Tobias


From: Matías Muñoz <munozsandoval@ug.uchile.cl>
Reply: Matías Muñoz <munozsandoval@ug.uchile.cl>>
Date: July 1,2014 at 08:23:59
To: r-sig-mixed-models@r-project.org <r-sig-mixed-models@r-project.org>>
Subject:  [R-sig-ME] LRT on fixed-effects  

Dear list,  

I have a pretty basic question about how to specify the fixed-effects  
structure to perform likelihood ratio test, I can't figure it out on my own  
and couldn't find a proper answer/example elsewhere. For example, if i have  
the following model:  

m1 <- lmer(y ~ A * B + (1|C), REML=F)  

and I'm interested in the significance of the A:B interaction term, then  
the LRT should be:  

m2 <- lmer(y ~ A + B + (1|C), REML=F)  
anova(m1,m2)  

but if I'm also interested in testing the individual significance of A (or  
B), I'm not sure if the LRT should be performed as  

m3 <- lmer(y ~ B + (1|C), REML=F) #to test the significance of A  

anova(m1,m3)  
or  
anova(m2,m3)?  


Please excuse my poor English.  
Many thanks!  
Matías  

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