I am trying to find out the effects of the condition (3 levels) on a dependent variable (intention to use a certain mode of transportation; assumed to be continuous, 1-7 scale), whilst controlling for the influence of demographic variables (education, income, mode_use; all categorical, 8 levels) as random effects.
Basically, I want to know whether one group (Level 3 of the condition) better predicts the outcome than the alternatives (Level 1 - control, and another experimental condition - Level 2), whilst controlling for the demographics.
The model that I currently have is the following:
model <- lmer(intention ~ condition + (1|education) +(1|income) + (1|mode_use), REML = TRUE, data = data)
These are the results:
I think this could be done with a simple
lm model, especially because the ICC of the random effects is miniscule ($0.075$). The problem is that the dependent variable is not normally distributed (see below) which, according to the answers here, mixed models can account for.
As per the link above, what to watch out for with mixed models isn't the normality of the dependent variable, but whether the residuals of the model are normally distributed. This is how they look:
The questions that I have are the following:
- Is the model outlined above appropriate for the data and the question that I have?
- If not, what would be the alternative, given the data that I have?
- How do I interpret the significant intercept? Since I'm not really interested with that, but in the contrasts, I'm not sure how to deal with it/report it. The contrasts are as follows (using
- How do I interpret the residual plot in terms of whether the assumptions are met? How can I diagnose whether the model meets the assumptions? Most of the tools I tried are visual with no clear criteria, which leaves my (inexperienced) judgment to decide and I'm not comfortable with that.