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I am trying to find out the effects of the condition (3 levels) on the 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:

enter image description here

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: Checking assumptions lmer/lme mixed models in R mixed models can account for.

enter image description here

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:

enter image description here

The questions that I have are the following:

  1. Is the model outlined above appropriate for the data and the question that I have?
  2. If not, what would be the alternative, given the data that I have?
  3. How do I interpret the significant intercept? Since I'm not really interested in that, but in the contrasts, I'm not sure how to deal with it/report it. The contrasts are as follows (using modelbased::estimate_contrasts()):

enter image description here

  1. 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.
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Not a full answer, I just wanted to point out that your response variable, intention, is ordinal in that it is bound between 1 and 7 with discrete levels. If you use ordinary regression, with or without random effects, then you allow the fitted model to "overshoot" and predict below 1 or above 7. You could use ordinal regression but with random effects may be tricky, see How to use ordinal logistic regression with random effects? for inspiration.

As a side note:

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.

That applies also to ordinary linear models without random effects.

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  • $\begingroup$ Thanks for the answer! 1. I didn't know that ordinary linear models don't need normally distributed dependent variable, thanks for clarifying that. 2. I've looked through the stuff you linked and I might be able to apply some of that from the worked example shown there. I'll report again soon whether it worked. $\endgroup$ Apr 26 at 9:59

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