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

[Reinhold Kliegl]

Line 1 in the paragraph 2 below should read: "Then, indeed, the
distribution of errors matters. ..."
Reinhold Kliegl

On Mon, Dec 22, 2008 at 5:25 PM, Reinhold Kliegl
<reinhold.kliegl at gmail.com> wrote:
> The VR paragraphs I was referring to are on page 199.   Anyway, if one
> is willing to make the assumption of linear spacing, then responses 1,
> 2, 3, 4 can surely also be interpreted as count data; sort of the
> number of latent pieces of evidence you need to move up one  response
> category; subtract 1 if you want "0" as part of the scale.
>
> Then, indeed, the distribution or responses matters. If the
> distribution looks roughly "normal" (e.g., if categories 2 and 3 are
> more frequent than 1 and 4), it probably does not matter whether you
> use the Gaussian or the Poisson family. If they are bi-modal, I would
> definitely prefer the latter. (Of course, it does matter if you have a
> substantive theory.)
>
> Reinhold Kliegl
>
> On Mon, Dec 22, 2008 at 4:06 PM, Jonathan Baron <baron at psych.upenn.edu> wrote:
>> 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
>>> >>>
>>> >>
>>> >
>>>
>>> _______________________________________________
>>> R-sig-mixed-models at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>> --
>> 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)
>>
>