# Specifying random effects for individual differences data

I am using the lmer function in R to examine the effect of skill (continuous) and context on eye movement data. I am new to lmer and not by nature statistically inclined. It is my understanding that it is best to include random intercepts and random slopes for subject and item like below.

lmer(GD~condition+skill+condition:skill*(1+condition*skill|subject)*(1+condition*skill|item)


However, I am particularly interested in the effect of skill on the eye movement record. It seems to me that the subject random effect may be diminishing the ability of the model to find significant skill interactions with context (condition). Am I correct in thinking the subject random effect is parceling out the variability for my skill measure?

Also, I am really only interested in those who scored either high or low on the skill measure. The dataset I am using contains those in the middle where there is a lot of variability. Would it be appropriate to remove these subjects from analysis?

Finally, I am unsure whether or not subject should be nested within skill as each subject was given only one value for skill.

Any guidance would be greatly appreciated.

## 1 Answer

If each subject was given only one value for skill, your design doesn't allow you to assess among-subject variation in response to skill. Also, (1) condition*skill stands for "main effects + interaction" (i.e. expands to condition+skill+condition:skill), (2) all terms in R formulas include the intercept 1 term unless explicitly suppressed (although you may choose to include them for readability), (3) you need to separate terms with +, not *. I think this results in the following formula:

GD~condition*skill+(condition|subject)+(condition*skill|item)


which includes main effects plus interaction of condition and skill; among-subject variation in response to condition; and among-item variation in effects of condition, skill, and their interaction.

You do in general need to keep random-effect terms in your model if they are estimable; removing that variability is pretending it doesn't exist (pseudoreplication; see Schielzeth and Forstmeier 2008). However, there is quite a bit of controversy at the moment as to whether including all terms in the model is really a good idea; Barr et al. 2013 say yes ("keep it maximal"); Matuschek et al. say no (wasting power), and Vasishth (a co-author of Matuschek) has other concerns.

The answer to "should I drop data ..."? is almost always "no".