# MixDelta: PSE/JND for Univariable 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 an univariate distribution by means of Delta Method.

## Usage

 `1` ```MixDelta(xplode.obj, alpha = 0.05) ```

## Arguments

 `xplode.obj` an object of class `xplode.obj` (univariable GLMMs). `alpha` significance level of the confidence interval. Default is 0.05.

## Details

`MixDelta` estimates PSE and JND of a univariable psychometric function (object of class `"glm"`).The method only applies to univariable GLMMs having a probit link function. Use `MixTreatment` for multivariable GLMMs.

## Value

`MixDelta` returns a list of length 1 including Estimate, Standard Error, Inferior and Superior Confidence Interval of PSE and JND. Confidence Intervals are computed as: Estimate +/- z(1-(α/2)) * Std.Error.

## Note

The function assumes that the first model coefficient is the intercept and the second is the slope. The estimate of the JND assumes a probit link function.

## 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

Casella, G., & Berger, R. L. (2002). Statistical inference (2nd ed.). Pacific Grove, CA: Duxbury Press

`MixTreatment` for univarible and multivariable GLMM. `pseMer` for bootstrap-based confidence intervals. `xplode` objects of class `xplode.obj`.
 ```1 2 3 4 5 6 7 8``` ```library(lme4) data(vibro_exp3) formula.mod <- cbind(faster, slower) ~ speed + (1 + speed| subject) mod <- glmer(formula = formula.mod, family = binomial(link = "probit"), data = vibro_exp3[vibro_exp3\$vibration == 0,]) define.mod <- list(pf = list(intercept = 1, slope = 2)) xplode.mod <- xplode(model = mod, name.cont = "speed", define.pf = define.mod) pse.jnd <- MixDelta(xplode.mod) ```