# [R] Mixed Effects Model on Within-Subjects Design

David Atkins datkins at u.washington.edu
Thu May 20 07:08:03 CEST 2010

```Dave--

Given that you want all comparisons among all means in your design, you
won't get that directly in a call to lme (or lmer in lme4 package).
Take a look at multcomp package and its vignettes, where I think you'll
find what you're looking for.

cheers, Dave

--
Dave Atkins, PhD
Research Associate Professor
Department of Psychiatry and Behavioral Science
University of Washington
datkins at u.washington.edu

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Dear R Experts,

I am attempting to run a mixed effects model on a within-subjects repeated
measures design, but I am unsure if I am doing it properly. I was hoping
that someone would be able to offer some guidance.

There are 5 independent variables (subject, condition, difficulty,
repetition) and 1 dependent measure (value). Condition and difficulty are
fixed effects and have 3 levels each (1,2,3 and 25,50,75 respectively),
while subject and repetition are random effects. Three repeated measurements
(repetitions) were taken for each condition x difficulty pair for each
subject, making this an entirely within-subject design.

I would like an output that compares the significance of the 3 levels of
difficulty for each condition, as well as the overall interaction of
condition*difficulty. The ideal output would look like this:

condition1:diff25 vs. condition1:diff50  p_value = ....
condition1:diff25 vs. condition1:diff75  p_value = ....
condition1:diff50 vs. condition1:diff75  p_value = ....

condition2:diff25 vs. condition1:diff50  p_value = ....
condition2:diff25 vs. condition1:diff75  p_value = ....
condition2:diff50 vs. condition1:diff75  p_value = ....

condition3:diff25 vs. condition1:diff50  p_value = ....
condition3:diff25 vs. condition1:diff75  p_value = ....
condition3:diff50 vs. condition1:diff75  p_value = ....

condition*diff  p_value = ....

Here is my code:

#get the data
attach(study.data)
subject = factor(subject)
condition = factor(condition)
diff = factor(diff)
rep = factor(rep)

#visualize whats happening
interaction.plot(diff, condition, value, ylim=c(240000,
450000),ylab="value", xlab="difficulty", trace.label="condition")

#compute the significance
library(nlme)
study.lme = lme(value~condition*diff,random=~1|subject/rep)
summary(study.lme)

Thank you so much for your generous help!!!

Best,
Dave Deriso
UCSD Psychology

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