# Binomial GLMM : How to evaluate the effect of a categorical predictor for a given value of a continuous predictor?

I use a logistic mixed model to analyze binary data (accuracy) of an experiment. In this experiment, there are two types of trials (congruent and incongruent) and the stimulus exposure time is manipulated (6 levels).

Beyond global effects, I would like to estimate the exposure time necessary to be above chance level, and the exposure time necessary to observe a significant difference between congruent and incongruent trials.

The structure of the best model obtained is the following: Score~1+Cong x ExpTime+ ExpTime x Bloc for the fixed part, with by-subject random slopes for ExpTime and Cong, where

• The dependent variable is Score: 0 (incorrect); 1 (correct).
• Cong: -1 (Congruent); +1 (Incongruent) and Bloc (8levels) are categorical predictors
• ExpTime (from 0 to .833) is used as a continuous predictor:

Actually, I am facing two issues.

1°) If exposure time was used as a categorical predictor, then, Wald-tests on the intercept and on the fixed effect for Cong would reveal, respectively, whether where are above chance level and whether there is a congruency effect for the exposure time chosen as reference. However, this answer only holds for the block 1. How to test for the global experiment (i.e. the 8 blocks simultaneously) ?

2°) Here, Exposure time is used as a continuous predictor. So I can model the prediction for the logit, averaged on all the blocks, for the two types of items, as a function of TempsCont. However, if I want to make inference, I need to evaluate SE on this prediction. So, how to compute SE(TempsCont|Cong), SE(TempsCont|Incong) in order to take into consideration the variance associated with the fixed effects but also with the random effects ? And then, how to test the existence of a congruency effect as a function of TempsCont ?