[R-sig-ME] how to specify the response (dependent) variable in a logistic regression model

[Greg Snow]

John,

I agree that ordering your responses does not make sense, but the
multinomial models are for unordered categorical data.  So you can
just treat your 4 possible outcomes as unordered categories.

Another option is to convert to a Poisson regression where the
response variable is the count (number of times each of the 4
combinations is selected) and then your categories become
explanitory/predictor variables.  You can either use a single
predictor with the 4 levels (and choose appropriate indicator
variables) or you can have 2 predictors (b vs w and 1 vs 2) as well as
their interaction.  That would give a different interpretation of the
model, but may be more what you are trying to accomplish.

On Thu, Jan 14, 2021 at 8:44 AM John Kingston <jkingstn using umass.edu> wrote:
>
> Dear Thierry,
> Thanks for your question. Here's the reason why I think the responses
> aren't multinomial (or ordinal).
>
> The listeners were presented with spoken strings of the form CVC, where C =
> consonant and V = vowel. The rate at which the acoustics changed at the
> beginning of the syllable was varied orthogonally with the duration of the
> vowel. The rate of acoustic change conveyed the identity of the initial
> consonant, which was expected to sound like "b" when the rate of change was
> faster and like "w" when it was slower. The duration of the vowel conveyed
> how many syllables the string consisted of, which was expected to be "1"
> when the vowel was shorter and "2" when the vowel was longer. The listeners
> were instructed to respond with "b" or "w" and "1" or "2" on every trial.
> So, unlike a truly multinomial dependent variable, such as professions or
> majors, the responses here are not unordered. They also cannot be arranged
> into a single order sensibly, because even if "b1" and "w2" responses are
> first and last in the order, there's no way of deciding *a priori* the
> order of "b2" and "w1" responses.
>
> Again, thanks for your reply.
> Best,
> John
> John Kingston
> Professor
> Linguistics Department
> University of Massachusetts
> N434 Integrative Learning Center
> 650 N. Pleasant Street
> Amherst, MA 01003
> 1-413-545-6833, fax -2792
> jkingstn using umass.edu
> https://blogs.umass.edu/jkingstn
> <https://blogs.umass.edu/jkingstn/wp-admin/>
>
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-- 
Gregory (Greg) L. Snow Ph.D.
538280 using gmail.com