Let's say I have 3 factors f1
, f2
and f3
and fit these models
m1 <- lmer(y ~ f1 + (1|sub))
m2 <- lmer(y ~ f1*f2 + (1|sub))
m3 <- lmer(y ~ f1*f2*f3 + (1|sub))
Does it make sense to compare the models with anova(m1,m2,m3)
? Or would you first test every single step
m1 <- lmer(y ~ f1 + (1|sub))
m2 <- lmer(y ~ f1 + f2 + (1|sub))
m3 <- lmer(y ~ f1 + f2 + f3 + (1|sub))
m4 <- lmer(y ~ f1*f2 + f3 + (1|sub))
etc
I suppose the second example is correct. But what if m1
and m2
do not differ statistically? Does that mean I should not include f2
and f3
in my model? But what if for example f2
and f3
are significant in model m3
? This happens with my real data, for example m1
is not significantly different from m2
, but f1
interacts significantly with f2
when the interaction is added to the model. I just don't see the point in comparing models then.