[R-sig-ME] mixed model with non-continuous numeric response

[Jonathan Baron]

On 12/22/08 15:04, Reinhold Kliegl wrote:
> See Venables and Ripley (2002, p.200) for an example modeling
> three-levels of satisfaction (low, medium, high) as a surrogate
> Poisson model. They also provide the technical justification. The
> alternative is to fit it as multinomial model--not sure how, if it at
> all, this can be done with glmer in its current implementation.

Johnson (the original poster) said that the responses can be thought
of as equally spaced points, i.e., linear with the underlying variable
of interest.  I think that this is often a reasonable assumption, so
another alternative is to do what he said.  Psychologists -- perhaps
because we have read Dawes, R. M., & Corrigan, B. (1974). Linear
models in decision making. Psychological Bulletin, 81, 97–106 -- are
often willing to assume that linear models are good fits even when
they are technically wrong.

(I also couldn't find VR's rationale for the surrogate Poisson model,
but I'm not questioning that possibility.)

The question is about how serious is the violation of the assumed
error distribution when we have only 4 categories.  When I do this -
which I admit is usually when I'm using lm() and not lmer() - I look
at the error distributions (from the default plot()) and do an eyeball
test.  If the result is barely "significant" at the outset, I worry.

Jon

> Reinhold Kliegl
> 
> On Mon, Dec 22, 2008 at 1:41 PM, Daniel Ezra Johnson
> <danielezrajohnson at gmail.com> wrote:
> > I don't think this is count data, is it???
> >
> > On Mon, Dec 22, 2008 at 12:40 PM, Reinhold Kliegl
> > <reinhold.kliegl at gmail.com> wrote:
> >> ( ...,  family="poisson")  is the most used option for count data
> >>
> >> Reinhold Kliegl
> >>
> >> On Mon, Dec 22, 2008 at 12:54 PM, Daniel Ezra Johnson
> >> <danielezrajohnson at gmail.com> wrote:
> >>> Dear all,
> >>>
> >>> I have survey results where the response is 1, 2, 3, or 4. These can
> >>> be thought of as equally-spaced points on a scale, I don't have a
> >>> problem with that. (They're actually more like "not at all", "some",
> >>> "mostly", "totally"; the subject is judging a stimulus.)
> >>>
> >>> I want to model crossed random effects for Subject and Item. Am I way
> >>> off base in modeling this data with a lmer(family="gaussian") model? I
> >>> know it's not perfect, but is it really bad? If so, what could I do
> >>> instead? (The error certainly wouldn't be binomial, right?)
> >>>
> >>> Thanks,
> >>> Daniel
> >>>
> >>> _______________________________________________
> >>> R-sig-mixed-models at r-project.org mailing list
> >>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>
> >>
> >
> 
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-- 
Jonathan Baron, Professor of Psychology, University of Pennsylvania
Home page: http://www.sas.upenn.edu/~baron
Editor: Judgment and Decision Making (http://journal.sjdm.org)