I have data from a sociology experiment with three groups. Each group is equivalent with a different treatment for a subject (n=700). The treatment were surveys, differing in the amount of information provided (info=0/1) and the response format (single vs multiple choice, choice=0/1). Group 1 (info = 0, choice = 0), Group 2 (info = 1, choice = 0), and Group 3 (info = 1, choice = 1) are coded as group (1-3) or alternatively the dummys info and choice. It should be noted that group 1 to 3 is also expressing ordinal degree of complexity of the treatment. From the responses of the treatment surveys I calculated the quality of the response (=y). This is the response variable I am interested in. Moreover, I have several information on the subjects, such as age (age), level of education (edu), level of trust (trust), and the time they spend "filling out" the treatment (time).
I am now mostly interested in the effect of the treatment:
y ~ group.
Yet, I want to include "random" factors as level of education, age etc in the model. As said, treatment in group 3 is more complicated than in 1, thus I expect to have "edu" a different effect among the groups. Similarly, i also expect "time" to have different implication for the different groups: e.g., the leverage of spending time in group 3 for increasing y is much greater due to the more information and more complex response options. At the same time, time is also correlated with the treatment - "info" and ”choice" provide incentives for subjects to engage longer. Additionally, I expect education to have an interaction effect with "time" (which again should differ between the treatment groups). Also, old subjects (going into the high eighties) can be expected to be slower in general, providing another contextual variable.
I am not sure how to construct a lmer model correctly. My idea is:
y ~ group + (time/edu/age | group)
I also tried a model without "group" as the grouping factor after reading other threads.
E.g., y ~ group + (group/edu | time)
However, I receive either a singular fit warning - even when only including the random effects. Sometimes I receive also "maxfun < 10 * length(par)^2 is not recommended." warnings. I assume, there is something wrong with my model, as n=700 should provide enough data. Does anyone have a suggestion?
UPATE BASED ON COMMENT:
group: 3 levels
edu: 8 levels
time: log transformed duration in seconds
age: number of years