Multilevel logistic regression guessing parameter

Dear everybody, thank you for your ideas and messages!

First, Philipp, yes, you are right. We have a simple two-choice
recognition task. Participants were learning some stimuli,  and after some
the recognition phase started. Always one stimuli per screen, and they have
to say whether it is one of the learnt ones or not. B is therefore coded as
response1 and response2 and afterwards coded in correct/incorrect.
The problem that might have appeared is that some distractors may have
been very similar to some well learnt items, and were simultaneously paired
with a poorly learnt target. That might produce the effect of correctness
below 0.5 We searched for such tasks and deleted them from further analysis.

My problem is that when I try to plot probability functions (x - predictor
variable, y - Accuracy from 0 to 1) for domains, they go below 0.5 which
doesn?t make sense, as this was a two-choice task. Their lower asymptote
should be on 0.5 not on 0. That?s why I am asking.

@Paul: Thanks for recommendation, but what do you mean by "Stan under the
hood"? I basically need a typical multilevel logistic regression (with
random effects for 2 crossed levels) but with lower asymptote being 0.5 and
not 0.

I will take a look at the functions!

Best,
Dominik

On Fri, May 12, 2017 at 9:36 AM, Paul Buerkner <paul.buerkner at gmail.com>
wrote:

Hi Dominik,

in addition to what Jake said, you can do this with the brms package
(using Stan under the hood). After installing brms, you can learn how to
fit such models in the "brms_nonlinear" vignette: Type
vignette("brms_nonlinear") in R.

Best,
Paul

2017-05-11 13:00 GMT+02:00 Dominik ?epuli? <dcepulic at gmail.com>:

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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