Recently, I asked a question about what procedure to use to analyse mixed data with dichotomous outcomes, see [here]. Now I started running some first analyses (mainly with SPSS, but I'll post the model in R code) with GLMM.
That is how I defined a model in R:
model <- glmer(errorrate ~ item + warning + item*warning + (1|ID), data=data, family=binomial)
- AV -->
errorrate: dichotomous outcome variable 0 = correct, 1 = incorrect
- UV1 -->
item: item A and item B, manipulated within, 0 = item A, 1 = item B
- UV2 -->
warning: yes or no, manipulated between, 0 = no warning, 1 = warning
ID--> subject id
My question is the following: If the regression weight for
warning is significant, how can I interpret that?
This question arose because I noticed that the results depend on how categories (i.e. UV1 and UV2) are coded. As far as I understand, this is due to the fact that those categories coded with 0 are the reference categories. Hence, if item A = 0, a significant
warning effect refers only to item A. If item B = 0, a significant
warning effect refers only to item B. My impression is that these effects cannot be interpreted as main effects. Rather, they remind me of some kind of a partial test of an interaction. Hence, how can these fixed effects be interpreted meaningfully when they depend on the coding? Or asked otherwise: What are they good for?
I would be very interested in hearing other's opinion on my question and my assumptions formulated above.
I think the problem was the following: Because of the 0 and 1 coding, conditional main effects were calculated. These conditional main effects are indeed the same as what is tested in the interaction. To get the "main effect", the model has to be rerun without the interaction and with the two categories coded as -0.5 and 0.5 . As a consequence, 0 is the "average" effect and comes closest as an answer to my question.
As an alternative approach for getting more information on the average effect, I thought about building an index from 0-2 (how many of the two questions were answered incorrectly?; minimum = 0, maximum = 2) and running either a Mann-Whitney U-test (groups: warning yes/no) or a independent t-test.