Solved – Repeated measures with lmer and logistic regression

lme4-nlmelogisticrrepeated measures

I have a question about the lmer() function and repeated measures design with R.

In my study, each participant sees 60 trials, presented at random. In each trial, the participants have to report whether they see something or not (so, it is a yes/no answer). I was recommended to use R and the lmer package. I built the following model, which seems to support my hypothesis. Yet, I want to be sure that I am building it correctly. Basically, the syntax is the following:

model.1 <- glmer(DV ~ X + Y + Z + Y:Z + (1|Trial/Subject), data=data, family="binomial")

X, Y, and Z are my predictors (all continuous variables).
I also tested a second model (see below):

model.2 <- glmer(DV ~ X + Y + Z + Y:Z + (1|Trial), data=data, family="binomial")

My questions are:

Is model.1 correct in terms of random effect?
What is the difference between the two models?

Best Answer

Given the information you provided, I would simply specify Subject as random:

model.3 <- glmer(DV ~ X + Y + Z + Y:Z + (1|Subject), data=data, family="binomial")

Having Subject specified in the model will account for the multiple measurements on the same subjects (the "repeated measurements" aspect of your study). Neither of your models (i.e. model.1 and model.2 does that; see further below).

Unless there is a reason that those 60 random trials might differ among subjects, which I don't know, I wouldn't take Trial into the model.

In the random statement, you want to include things that would fall under (a) "pseudo-replication" (temporal and spatial) and (b) factors for which you want a variance to be estimated. For example, if you were to repeat your experiment in different cities, or different hospitals, or other things that could affect the outcome, I would include this in the random statement as well. This will allow you to capture this additional potential variation, which may or may not be of interest to you.

To answer your second question, the difference between + (1|Trial/Subject) and + (1|Trial) is that the former has Subject nested in Trial, which expands to + (1|Trial) + (1|Trail:Subject) and means that you want to capture the variance (a) due to Trial and (b) the variance of the grouping of Trial with Subject; while in the latter you only want to account for the variation due to Trial. You should always check your model with summary(my.model) and find the line where it says Number of obs: and groups:. There you can double check whether your syntax captures the number of groups for which you wanted to the variances to be estimated.

Some useful links: http://glmm.wikidot.com/faq and in particular to understand the (g)lmer syntax for the random statement http://glmm.wikidot.com/faq#toc27

There are also a lot of other question regarding model specifications here on Cross Validated.

You may find this one helpful as well: http://rpsychologist.com/r-guide-longitudinal-lme-lmer

Related Solutions

Solved – Analyzing a 2×3 repeated measures design using a logit mixed model

I would definitely use all your data and add direction of intended bias induction as a variable. Since you already have variables in the model describing the difference between the tasks, I don't believe that adding task as a random effect is necessary. The model would be:

my_model = lmer(
    correct ~ (1|subject) + condition*distractor*direction
    , family = 'binomial'
    , data = my_data
)

Check out the ezMixed function from the ez package for an automated way of evaluating evidence for each effect in the model.

Solved – glmer vs lmer, what is best for a binomial outcome

1) In previous versions of the lme4 package, you could run lmer using the binomial family. However, all this did was to actually call glmer, and this functionality has now been removed. So at the time of writing Crawley was correct.

2) Yes, glmer is the correct function to use with a binary outcome.

3) glm can fit a model for binary data without random effects. However, it is incorrect to compare a model fitted with glm to one fitted with glmer using a likelihood-based test because the likelihoods are not comparable. From your description, you have repeated measures within chambers. So, assuming that you have sufficient chambers and these can be thought of as a random sample from a larger population of chambers, then a priori you should retain the random intercepts for Chamber to control for possible non-independence of observations within chambers. You can think of random intercepts as being part of the experimental design.

On the other hand, if the random effect variance is very small and/or the inference or predictions for both the glm and glmer model are the largely the same, then it really doesn't matter which you use anyway.

Best Answer

Related Solutions

Solved – Analyzing a 2×3 repeated measures design using a logit mixed model

Solved – glmer vs lmer, what is best for a binomial outcome

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