[R-sig-ME] Is it ok to use lmer() for an ordered categorical (5 levels) response variable?

[Nicolas Deguines]

Hello everyone,

I am investigating how engagement into a citizen science program can change
participants' behavior in terms of implementing gardening techniques
benefitting biodiversity.
There are 2362 participants, distributed into 7 cohorts (= year in which
they joined the program), and I have repeated gardening technique
information for multiple years for each participant.
So I need to use mixed modeling.

One of the response variable is a score that can takes 5 values: 0, 1, 2,
3, or 4. It's ordered, it's not continuous (there are 5 levels).
I would analyze this into a cumulative link mixed models (using clmm() from
ordinal package) but the Hessian condition I obtained with such model is >
5.0e+06. I.e. assumption is violated (simplifying my initial full model did
not help at all).

As an alternative, I am wondering if I could treat this response variable
has a continuous one into a lmer() model.
When I do:
- Normality of model residuals is nicely met
- Homoscedasticity of model residuals is met as well.
=> does meeting these two assumptions is enough to validate the use of a
lmer() model for an ordered categorical response variable?

In one of Douglas Bates' presentation (slide 3 of Jan. 2011, Madison:
http://lme4.r-forge.r-project.org/slides/2011-01-11-Madison/5GLMM.pdf), it
is said that
"When using LMMs we assume that the response being modeled is on a
continuous scale.
Sometimes we can bend this assumption a bit if the response is an ordinal
response with a moderate to large number of levels.
For example, [...a response variable taking] integer values on the scale of
1 to 10."
=> is 5 levels too few to be treated as continuous? Or would it be ok given
residuals behave nicely?

I would appreciate any help and thoughts on this.
I checked that this was not treated in a previous post and I hope I did not
miss it (sorry if I did).

Best,
Nicolas Deguines
----------------------------------
Postdoctoral Research Associate
Laboratoire Ecologie, Systématique et Evolution
Université Paris Sud, Orsay, France
Website: http://nicolasdeguines.weebly.com/

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