[R-sig-ME] Multilevel logistic regression guessing parameter

[Jake Westfall]

Hi Dominik,

In addition to the issues Phillip raised, note that adding a guessing
parameter to the model (so that it resembled what is called the 3PL model
in item response theory;
https://en.wikipedia.org/wiki/Item_response_theory#Three_parameter_logistic_model)
would make the model inherently nonlinear in the parameters. So the model
could not be fit in glmer(). And since I don't think nlmer() supports
non-Normal response families, this would mean you can't use lme4 at all. I
would recommend fitting such a model in a fully Bayesian setting using e.g.
Stan.

Jake

On Thu, May 11, 2017 at 9:16 PM, Phillip Alday <Phillip.Alday at unisa.edu.au>
wrote:

> Dominik,
>
> You're assuming that test subjects are guessing at random -- it's quite
> possible that they believe that they incorrect answer is the correct one,
> which would make them less likely than "chance" to select the correct
> answer.
>
> "Chance" performance may also not fall at 50% if there are multiple
> possible incorrect responses but only one possible correct response.
>
> You could also simply have more incorrect than correct responses for
> certain values of your predictor for various reasons related to your
> preprocessing steps -- maybe data with a correct response is more likely to
> be excluded for various reasons (blinks, timeouts, whatever exclusion
> criteria you have for your given methods).
>
> Finally, is B really coded as correct/incorrect? Or is B coded as
> response-1/response-2, i.e. without mapping a binary response to
> correct-vs-incorrect?
>
> Best,
> Phillip
>
>
>
> > On 11 May 2017, at 20:30, Dominik Ćepulić <dcepulic at gmail.com> wrote:
> >
> > I  have a following situation:
> >
> > I want to predict variable B (which is dichotomous) from variable A
> > (continous) controlling for random effects on the level of a) Subjects;
> b)
> > Tasks.
> >
> > A -> B (1)
> >
> > The problem is that when I use model to predict the values of B from A,
> > values below probability of 0.5 get predicted, and in my case that
> doesn´t
> > make sense, because, if you guess at random, the probability of correct
> > answer on B would be 0.5.
> >
> > I want to know how I can constrain the model (1) in lme4 so that it
> doesn´t
> > predict values lower than 0.5 in variable B.
> >
> > Thank you,
> >
> > Dominik!
> >
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> >
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