[R] logistic regression for data with repeated measures

[Suzon Sepp]

Hi,

It seems that I'm quite lost in this wide and powerful R's universe, so I
permit myself to ask your help about issues with which I'm struggling.
Thank you,

I would like to know if the answer’s accuracy (correct = 1; incorrect = 0)
varies depending on 2 categorical variables which are the group (A and B)
and the condition (a, b and c) knowing that I’ve got n subjects and 12
trials by conditions for each subject (i.e. 12 repetitions).

To do that, I’m focusing on logistic regression analysis. I’ve got no
problem with this kind of analysis until now (logistic regression with
numeric predictor variables and/or categorical predictor with 2 levels
only) but, in this new context, I think I have to focus more specifically
on logistic regression including *nested (or random?) factors* in a*repeated
measures design* (because of the variables “Subject” and “Trial”) with a
categorical predictor variable with *more than 2 levels* (the variable
“Condition”) and I never did such a thing…yet.

mydata =
mydata$Subject: Factor w/38 levels: "i01", "i02", "i03", "i04"
mydata$Group: Factor w/2 levels: "A", "B"
mydata$Condition: Factor w/3 levels: "a", "b", "c"
mydata$Trial: Factor w/12 levels: "t01", "t02", ..."t12"
mydata$Accuracy: Factor w/2 levels: "0", "1"

Subject      Group      Trial      Condition      Accuracy
   i01              A           t01             a                   0
   i01              A           t02             a                   1
...
   i01              A           t12             a                   1
   i01              A           t01             b                   1
   i01              A           t02             b                   1
...
   i01              A           t12             b                   0
   i01              A           t01             c                   0
   i01              A           t02             c                   1
...
   i01              A           t12             c                   1
   i02              B           t01             a                   1
...

First, I’m wondering if I have to calculate a % of accuracy for each
subject and each condition and thus “remove” the variable “Trial” but
“lose” data (power?) in the same time… or to take into account this
variable in the analysis and in this case, how to do that?

Second, I don’t know which function I’ve to choose (lmer, glm, glmer…)?

Third, I’m not sure I proceed correctly to specify in this analysis that
the responses all come from the same subject: within-subject design =
…+(1|Subject) as I can do for a repeated measures ANOVA to analyze the
effect of my different variables on a numeric one such as the response
time: 
test=aov(Int~Group*Condition+*Error(Subject/(Group*Condition)*),data=mydata)
and here again how can I add the variable "Trial" if I don't work on an
average reaction time for each subject in the different conditions?

Below, examples of models I can write with glmer(),

fit.1=glmer(Accuracy~Group* Condition
+(1|Subject),data=mydata,family=binomial)

fit.2=glmer(Accuracy~Group* Condition
+(1|Subject)-1,data=mydata,family=binomial)   (“without intercept”)

fit.3=glmer(Accuracy~Group* Condition +(1|Subject)+(1|Trial)...??


I believed the analysis I've to conduct will be in the range of my
qualifications then I realize it could be more complicated than that of
course (ex GLMMs), I can hear "do it as we do usually" (=repeated measures
ANOVA on a percentage of correct answers for each subject ??) as if there's
only one way to follow but I think there's a lot, which one's revelant for
my data, that's I want to find.

Hope you can put me on the track,

Best

Suzon

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