# MixTreatment: PSE/JND for Multivariable GLMM Using Delta Methods In MixedPsy: Statistical Tools for the Analysis of Psychophysical Data

## Description

Estimate the Point of Subjective Equivalence (PSE), the Just Noticeable Difference (JND) and the related Standard Errors for a multivariate distribution by means of Delta Method. The method applies to multivariable GLMM having a probit link function. The function is based on a recursive use of `glmer` and `MixDelta`

## Usage

 `1` ```MixTreatment(xplode.obj, datafr) ```

## Arguments

 `xplode.obj` an object of class `xplode.obj`. The fitted model (object of class `"merMod"`) from `xplode.obj` includes one continuous predictor and one factorial predictor. `datafr` the data frame fitted with the GLMM model

## Details

The function `MixTreatment` is based on a recursive use of `glmer` and `PsychDelta` to multivariable GLMM including continuous and factorial predictors. The same caveats of `PsychDelta` apply (e.g., confidence interval based on normality assumption).

## Value

A list, whose lenght is equal to the levels of the factorial predictor, i. Each cell of the list is equal to the output of `delta.psy.probit` applied to a multivariable model whose baseline is level i of the factorial predictor.

## References

Moscatelli, A., Mezzetti, M., & Lacquaniti, F. (2012). Modeling psychophysical data at the population-level: The generalized linear mixed model. Journal of Vision, 12(11):26, 1-17. https://doi.org/10.1167/12.11.26

`glmer` for Generalized Linear Mixed Models (including random effects).`MixDelta` for univariable model with delta method. `pseMer` for bootstrap-based confidence intervals.
 ```1 2 3 4 5 6``` ```library(lme4) data(vibro_exp3) formula.mod <- cbind(faster, slower) ~ speed * vibration + (1 + speed| subject) mod <- glmer(formula = formula.mod, family = binomial(link = "probit"), data = vibro_exp3) xplode.mod <- xplode(model = mod, name.cont = "speed", name.factor = "vibration") MixTreatment(xplode.mod, vibro_exp3) ```