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

[Thierry Onkelinx]

Dear all,

IMHO, Phillip's suggestion matches best with the data generating model.
Greg's suggestions are simpler but usable models too.

Given that different subjects respond to the same questions and we can rule
out that one subject is more likely to respond "b" over "w" than another
subject, we need to add the subject as a random effect.

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx using inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

///////////////////////////////////////////////////////////////////////////////////////////
To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey
///////////////////////////////////////////////////////////////////////////////////////////

<https://www.inbo.be>


Op vr 15 jan. 2021 om 10:09 schreef Juho Kristian Ruohonen <
juho.kristian.ruohonen using gmail.com>:

> Another fellow linguist here, albeit a junior one.
>
> It sounds to me like:
>
>    1. You have two binary outcomes, the 1st always occurring before the
> 2nd.
>    2. For each subject, you have exactly one response per binary outcome.
>
> This being the case, I struggle to see why a complex model such as a
> multinomial, multi-response or GLMM is even necessary.
>
> If each subject makes the same number of responses, their idiosyncrasies
> can be expected to cancel each other out overall, no?. Therefore, we don't
> need random effects. We can fit a standard logistic fixed-effects model
> whose interpretation is 'A random individual makes a binary choice'.
>
> And since the binary responses have a fixed order, the first one can simply
> be used as a covariate in the analysis of the second one.
>
> Thus, I struggle to see why we could not simply:
>
>    1. First fit a standard logistic regression for Response 1 with all
>    covariates of interest.
>    2. Then fit a standard logistic regression for Response 2 with all
>    covariates of interest PLUS the subject's observed Response 1 as an
> added
>    covariate. Its addition will address the question of possible
> correlation
>    between the two responses.
>
> Experts, please do tell me why I'm wrong.
>
> Best,
>
> Juho
>
>
>
> pe 15. tammik. 2021 klo 1.27 John Kingston (jkingstn using umass.edu) kirjoitti:
>
> > Dear Phillip and Greg,
> > Thank you both very much.
> >
> > I don't have experience yet beyond lme4, but you've both given me useful
> > directions to pursue.
> >
> > I'll come back with results once they're in hand.
> > 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/>
> >
> >
> > On Thu, Jan 14, 2021 at 11:41 AM Phillip Alday <me using phillipalday.com>
> > wrote:
> >
> > > John,
> > >
> > > How comfortable are you with mixed models software beyond lme4? This
> > > seems like a perfect case for a multivariate mixed model (which you can
> > > do with e.g. brms or MCMCglmm). The basic idea is that you do create a
> > > single mixed model that can be thought of doing two GLMMs
> > > simultaneously. Here's the basic syntax for doing this in brms:
> > >
> > >
> > > brm(mvbind(Resp1, Resp2) ~ preds + ..., data=your_data,
> family=binomial)
> > >
> > > You can also specify this as two formulae (which really highlights the
> > > "two models simultaneously" intuition):
> > >
> > >
> > > var1 = bf(Resp1 ~ preds + ....) + binomial()
> > > var2 = bf(Resp2 ~ preds + ....) + binomial()
> > >
> > > brm(var1 + var2, data=your_data)
> > >
> > > The advantage to doing this as a multivariate model as opposed to
> > > separate models is that you get simultaneous estimates across both
> > > models, including correlation/covariance between those estimates.  See
> > > e.g. the brms documentation
> > > (https://paul-buerkner.github.io/brms/articles/brms_multivariate.html)
> > > for more info. In particular, pay attention to the extra syntax for
> > > computing shared correlation in the random effects across sub-models.
> > >
> > > The cons for this approach are that [1] most reviewers in
> > > (psycho)linguistics will not be familiar with it (and there was recent
> a
> > > Twitter storm on this very problem) and [2] the computational costs are
> > > noticeably higher.
> > >
> > > Another alternative is to do something like "linked mixed models" (cf.
> > > Hohenstein, Matuschek and Kliegl, PBR 2016). There are a few variants
> on
> > > this, but the basic idea is that you use one response to predict the
> > > other. Given the temporal ordering here, this might make sense, e.g.
> > >
> > > mod1 = glmer(Resp1 ~ preds + ....)
> > > mod2 = glmer(Resp2 ~ preds + YYY + ....)
> > >
> > > where YYY is one of:
> > > [a] Resp1
> > > [b] fitted(mod1)
> > > [c] fitted(mod1) + resid(mod1)
> > >
> > > You can potentially omit mod1, in which case you have something like
> the
> > > Davidson and Martin (Acta Psychologia, 2016) approach to the joint
> > > analysis of reaction times and response accuracy.
> > >
> > > The downside to this approach is that the variability that's in Resp1
> > > can create problems in mod2, because standard GLMMs assume that the
> > > predictors are measured without error/variability. Variants [b] and
> > > especially [c] mitigate this a bit though. (And if you want to get even
> > > more complicated, there are  "errors-within-variables" models, which
> can
> > > handle this and are available in e.g. brms). I think the advantage to
> > > the linked model approach relative to the multivariate approach is that
> > > it's somewhat more accessible for a typical (psycho)linguistic
> reviewer.
> > >
> > > Note that I am nominally originally from linguistics and do know a bit
> > > about mixed models, so I'm a good usual suspect for a reviewer on these
> > > things.
> > >
> > > Best,
> > > Phillip
> > >
> > > PS: the multinomial models suggested by the others are also pretty
> good,
> > > but again multinomial models are usually something that require getting
> > > used to and doesn't reflect the potential covariance of Resp1 and Resp2
> > > in an obvious way.
> > >
> > >
> > >
> > > On 14/1/21 5:05 pm, Greg Snow wrote:
> > > > 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/>
> > > >>
> > > >>         [[alternative HTML version deleted]]
> > > >>
> > > >> _______________________________________________
> > > >> R-sig-mixed-models using r-project.org mailing list
> > > >> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> > > >
> > > >
> > > >
> > >
> >
> >         [[alternative HTML version deleted]]
> >
> > _______________________________________________
> > R-sig-mixed-models using r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
>
>         [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-mixed-models using r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>

	[[alternative HTML version deleted]]