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) ```