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I'm building a model with a 3-level categorical response variable and both fixed and random effects to analyze data from a survey of volunteers. My response variable ('wellbeing', self-reported) has the levels 'no change', 'improved', and 'declined'. I have multiple predictor variables including, e.g., hours per month spent volunteering. I'm thinking I need something like this:

m <- glmer(wellbeing ~ hours.month + region + age + (1|participantID), data=vol.data)

However, I don't know what to use for family and link because it seems that the binomial family is just used for 2-level categorical responses. Would the following work, or does I need something else since I have a 3-level categorical response?

m <- glmer(wellbeing ~ hours.month + region + age + (1|participantID), 
           data=vol.data, family=binomial(link='logit'))
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Your dependent variable appears to be ordinal - that is, categorical with a natural ordering in the sense that declined is "less than" no change and no change is "less than" improved

lme4 does not handle ordinal responses. Instead you can use MCMCglmm or clmm from the ordinal package. Using the latter, you would fit a model like this:

m1 <- clmm(wellbeing ~ hours.month + region + age + (1|participantID), 
       data=vol.data, link = "probit", threshold = "equidistant")
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