Yes, whenever you remover lower terms but keep higher level terms, you get
the simple effects at all levels of the lower level terms you 'removed'.
Quite convenient, I think ;)
On Tue, Sep 20, 2016, 16:52 João Veríssimo <jl.veriss...@gmail.com> wrote:
> Besides the case in which a 'main' effect is removed but the interaction
> is included, I've also noticed the same behavior when removing a 2-way
> interaction, but keeping the 3-way interaction included:
>
> > m1 <- lmer(RT ~ Type * Form * Group) + (1|Subject) + (1|Item), mydf)
> > m2 <- update(m1, . ~ . - Type:Form)
>
> > anova(m1, m2)
> m1: RT ~ Type * Form * Group + (1 | Subject) + (1 | Item)
>
> m2: RT ~ Type + Form + Group + (1 | Subject) + (1 | Item) +
> m2: Type:Group + Form:Group + Type:Form:Group
>
> Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
> m1 15 1657.2 1743.1 -813.59 1627.2
> m2 15 1657.2 1743.1 -813.59 1627.2 0 0 1
>
> Best,
> João
>
> On Tue, 2016-09-20 at 19:27 +0000, T. Florian Jaeger wrote:
> > Guys,
> >
> >
> > just a quick note, in case it's not apparent to everyone (I had
> > emailed this earlier to Rachel): what happens in Rachel's model is
> > simply that R defaults to simple effects coding when a 'main' effect
> > is removed while the interaction is still included (note that this, I
> > think, overrides whatever contrasts you have specified for the factor
> > you remove). That's actually a very useful default. To me, the thing
> > that was puzzling at first is the same thing that Roger commented on:
> > it should be just the same when you remove a two-way or a three-way
> > factor. indeed, when i tried to replicate Rachel's problem, I did/do
> > get the same (simple effects reparameterization) regardless of how
> > many levels the factor that I remove has.
> >
> >
> > Florian
> >
> > On Tue, Sep 20, 2016 at 2:41 PM Wednesday Bushong
> > <wednesday.bush...@gmail.com> wrote:
> >
> > Let me also say something w.r.t. coding because I think you
> > also expressed doubt about what kind of coding scheme to use.
> >
> >
> > The crucial thing to remember is that when interpreting
> > coefficients from R model summary outputs, a coefficient is
> > interpreted as moving from a value of 0 to 1 on that
> > particular variable, when the values of the other variables
> > are set to 0.
> >
> >
> > In the case of dummy coding, then, the "main effect" of
> > Listener is actually the difference in logodds going from the
> > first level of listener to the second level of listener when
> > the two SyntaxType dummy variables are at 0 -- that is, when
> > SyntaxType is at the first level. So this is really just a
> > pairwise comparison between two groups, and doesn't have
> > anything to say about the average effect of Listener across
> > the SyntaxType groups. In order to get the interpretation of
> > Listener to be across the average of all SyntaxType groups,
> > you would have to contrast code SyntaxType (b/c then 0 will be
> > the avg of all the levels). Similar interpretations in a fully
> > dummy-coded model go for the other main effect terms (i.e.,
> > each SyntaxType effect is interpreted w.r.t the reference
> > level of Listener) and the interaction terms
> > (Listener:SyntaxType will be the effect of listener at the
> > other SyntaxType levels; notice that this isn't even close to
> > what we would normally conceptualize as an "interaction"! So
> > be careful with coding!).
> >
> >
> > Of course, you can mix and match your coding schemes -- for
> > instance, if you want to get the main effect of Listener at
> > the avg. of SyntaxType but wanted pairwise comparisons of
> > SyntaxType within one particular Listener group, you could
> > contrast code SyntaxType and dummy code Listener appropriately
> > -- but in general, the most common thing to do will be
> > contrast coding all factors, which will give you the standard
> > ANOVA output interpretation.
> >
> >
> > -Wed
> >
> > On Tue, Sep 20, 2016 at 1:58 PM Wednesday Bushong
> > <wednesday.bush...@gmail.com> wrote:
> >
> > Hi Rachel,
> >
> >
> > I think at times like this it's useful to look at
> > exactly how R assigns factors. When you add
> > interactions, R does a lot of behind-the-scenes work
> > that isn't immediately apparent. One way to look into
> > this in more detail is this really nice function
> > "model.matrix", which given a data frame and a model
> > formula, will show you all of the coding variables
> > that are created in order to fit the model and what
> > their values are for each combination of factors in
> > the dataset. I've bolded this below.
> >
> >
> > # create data frame w/ each factor level combo
> > d <- data.frame(Listener.f = rep(c("Listener1",
> > "Listener2"), 3),
> > SyntaxType.f = c(rep("Syntax1", 2), rep("Syntax2", 2),
> > rep("Syntax3", 2)),
> > Target_E2_pref = rnorm(6))
> > # make factor
> > d$Listener.f <- factor(d$Listener.f)
> > d$SyntaxType.f <- factor(d$SyntaxType.f)
> >
> >
> > # create model formulas corresponding to full and
> > reduced model
> > mod.formula <- formula(~ 1 + Listener.f *
> > SyntaxType.f, d)
> > mod.formula.reduced <- formula(~ 1 +
> > SyntaxType.f + Listener.f:SyntaxType.f, d)
> >
> > # get var assignments for all factor level combos
> > mod.matrix <- model.matrix(mod.formula, d)
> > mod.matrix.reduced
> > <- model.matrix(mod.formula.reduced, d)
> >
> >
> > If you look at mod.matrix and mod.matrix.reduced,
> > you'll see that they each have the same
> > dimensionality. Digging in further, we can see why
> > this is. Let's look at the column names of each model
> > matrix:
> >
> >
> > colnames(mod.matrix)
> > [2] "Listener.fListener2"
> > [3] "SyntaxType.fSyntax2"
> > [4] "SyntaxType.fSyntax3"
> > [5] "Listener.fListener2:SyntaxType.fSyntax2"
> > [6] "Listener.fListener2:SyntaxType.fSyntax3"
> >
> >
> > colnames(mod.matrix.reduced)
> > [1] "(Intercept)"
> > [2] "SyntaxType.fSyntax2"
> > [3] "SyntaxType.fSyntax3"
> > [4] "SyntaxType.fSyntax1:Listener.fListener2"
> > [5] "SyntaxType.fSyntax2:Listener.fListener2"
> > [6] "SyntaxType.fSyntax3:Listener.fListener2"
> >
> >
> > I've bolded the differences. Now don't ask me why, but
> > the way that R appears to handle subtracting a main
> > effect from a model but keeping the interaction is to
> > add in another interaction dummy variable that makes
> > the model equivalent. (If you look at the values that
> > each factor combo takes on, you'll see that this
> > particular dummy variable is 1 when Listener =
> > Listener2 and SyntaxType = Syntax1, and 0 otherwise).
> >
> >
> > The way to solve this is presented in Roger's paper he
> > linked above (pg. 4 being the most relevant here). His
> > particular example is for contrast coding but you can
> > make it work in the exact same way with dummy
> > coding (but make sure that dummy coding is what you
> > really want to use given the specific hypothesis
> > you're testing!):
> >
> >
> > # make numeric versions of factors
> > d$Listener.numeric <- sapply(d$Listener.f,function(i)
> > contr.treatment(2)[i,]) # can easily replace w/
> > whatever coding scheme you want
> > d$Syntax1.numeric <- sapply(d$SyntaxType.f,function(i)
> > contr.treatment(3)[i,])[1, ]
> > d$Syntax2.numeric <- sapply(d$SyntaxType.f,function(i)
> > contr.treatment(3)[i,])[2, ]
> >
> >
> > # check model matrix
> > mod.formula.new <- formula(~ 1 + Syntax1.numeric +
> > Syntax2.numeric + Listener.numeric:Syntax1.numeric +
> > Listener.numeric:Syntax2.numeric, d)
> > mod.matrix.new <- model.matrix(mod.formula.new, d)
> > colnames(mod.matrix.new)
> >
> >
> > [1] "(Intercept)"
> > [2] "Syntax1.numeric"
> > [3] "Syntax2.numeric"
> > [4] "Syntax1.numeric:Listener.numeric"
> > [5] "Syntax2.numeric:Listener.numeric"
> >
> >
> > Now things are as they should be: no more mysterious
> > extra dummy variable containing information about the
> > main effect of Listener! This last model is what you
> > should compare your original to get the significance
> > of the main effect of Listener.
> >
> >
> > Hope this was helpful!
> >
> >
> > Best,
> > Wednesday
>
>
>
