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 ;)

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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 > > >