I've read a lot of threads on stack exchange but haven't exactly found what I'm looking for. Everyone seems to have a slightly different problem/issue.
First, lets have a look at my data:
- 120 Users
- 80 Items per User
- Between factor with 4 levels
- Within factor with 4 levels
- Binary response variable
Now, usually one would perform a logistic regression. However, there are several issues with that:
- Categorical predictors have to be dummy coded?
- How do deal with the within-subject fator? -> lmm?
- How would you plot this data?
As I think (but I'm not sure? correct me if I'm wrong) that one assumption of binary logistic regression is the independence of errors which is - again not sure - violated with within subject factor I'm trying to perform a linear-mixed effects model for my data. Now here begins the actual problem:
First: I know, that I want to model the between-subjects and within-subject factors as fixed effects. However: which random effects should I implement?
- Random intercept of each subject as it can be assumed that they differ in they're apriori knowledge of the items (it's a performance test).
- Random intercept of the within-subject factor - as this is the reason for performing lmm in the first place?
- My data is actually not nested, so there is no sense in creating a random effect like all the examples "school", "county" and so on...
- other suggestions?
Okay my suggestion is to assume random intercepts of subjects (the first one):
lmm3 <- glmer(y ~ between * within + (1|user), data, family = binomial(link = "logit"))
But, first I would have to calculate the ICC 1 and ICC2 to support the use uf lmm.
for the ICC 1 I use the nullmodel:
lmm0 <- glmer(y ~ (1|user), data, family = binomial(link = "logit")) tau2<-lme4::VarCorr(lmm0)[] icc1 <- tau2/(tau2+pi^2/3)
No, again two questions arise:
- How do I calculate ICC2 for the logistic model? I know that there is a function for linear mixed models, but this is not the case here.
- However, my ICC1 is only 0.03760069 so it seems that this above model doesn't make a lot of sense. What kind of model should I try then?
I thank you a lot for your inputs. You need more specific information I would be willing to prepare some data for you. I know that this is a rather theoretical issue so I'm looking forward to a discussion.
Kind regards, David