# Showing shrinkage with a plot for the interaction coefficient in a mixed-model

I am trying to illustrate shrinkage in linear mixed models in a 2x2 factorial design. I would like to show the shrinkage effect for all coefficients including the interaction coefficient. However, I am unsure whether my approach is right. Here is what I did:

I fitted a linear-mixed model using lmer() from lme4. It is a complex model of the form:

 mod1 <- lmer(Val ~ Class * Complex
+ (Class * Complex | Subject)
+ (Class * Complex | Word),
data = Lex)


I used contrast coding in order to see main effects in the model output:

contrasts(Lex$Class) <- contr.sum(2) contrasts(Lex$Complex) <- contr.sum(2)


I then fit individual models per Subject and extract the coefficients:

df <- coef(lmList(Val ~  Class * Complex | Subject,
data = Lex))


Then I extract the coefficients per Subject from the mixed-model:

cc1 <- as.data.frame(coef(mod1)[["Subject"]])


And bind it all together in a data frame:

names(cc1) <- c("A", "B", "C", "D")
df <- cbind(df, cc1)


I then go on to plot the (Intercept) per subject on the y-axis and the corresponding (slope-) coefficient on the x-axis for both: the individual models (purple) and the mixed-model (blue). However, I am unsure if this is correct for the interaction coefficient:

• This looks reasonable at first glance, but (1) I don't quite understand your last sentence (" However, I am unsure if this is correct for the interaction coefficient:" -- please expand/clarify?) (2) Any chance of a reproducible example? – Ben Bolker Jun 19 '15 at 22:03
• Of course I can add a reproducible example. Here is a gist on github: gist.github.com/03ed993441f8574c5858.git or gist.github.com/brauner/03ed993441f8574c5858. The data frame is 2060x5 and it needs to be because otherwise this rather complex model would not converge! Regarding my last sentence: I am unsure whether it makes sense to plot per-item-intercept ~ per-item-interaction-coefficient to illustrate the shrinkage for the interaction coefficient. The reproducible example should help to clarify this. – lord.garbage Jun 20 '15 at 3:21