MixDelta {MixedPsy}

PSE/JND from GLMM Estimates using Delta Method

Description

Estimate Points of Subjective Equivalence (PSE), Just Noticeable Differences (JND) and the related Standard Errors from a GLMM by means of delta method. The method applies to models with a probit link function, one continuous predictor, and one (optional) factorial predictor.

Usage

MixDelta(xplode.obj, alpha = 0.05, p = 0.75)

Arguments

xplode.obj

an object of class xplode.obj. The fitted model (object of class merMod, specifically of subclass glmerMod) includes one continuous predictor and one (optional) factorial predictor.

alpha

significance level of the confidence intervals. Default is 0.05 (value for 95% confidence interval).

p

probability value relative to the JND upper limit. Default is 0.75 (value for 50% JND).

Details

When the model includes a factorial predictor, the function is based on a recursive use of glmer and re-order of levels of the factorial predictor. The JND estimate assumes a probit link function.

Value

A matrix including estimate, standard error, inferior and superior bounds of the confidence interval of PSE and JND. If a factorial predictor is included in the model, the function returns a list, each item containing a matrix for the estimates relative to a level of the predictor.

Note

The delta method is based on the assumption of asymptotic normal distribution of the parameters estimates. This may result in an incorrect variance estimation. For a more reliable (but more time-consuming) estimation based on bootstrap method, use pseMer.

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. doi:10.1167/12.11.26

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

See Also

glmer for fitting Generalized Linear Mixed Models. xplode for interfacing values from a fitted GLMM to MixedPsy functions. pseMer for bootstrap-based confidence intervals of psychometric parameters.

Examples

library(lme4)

#univariable GLMM (one continuous predictor)
mod.uni = glmer(formula = cbind(Longer, Total - Longer) ~ X + (1 | Subject), 
family = binomial(link = "probit"), data = simul_data)
xplode.uni = xplode(model = mod.uni, name.cont = "X")
MixDelta(xplode.uni)

#multivariable GLMM (one continuous and one factorial predictor)
mod.multi <- glmer(cbind(faster, slower) ~ speed * vibration + (1 + speed| subject), 
family = binomial(link = "probit"), data = vibro_exp3)
xplode.multi <- xplode(model = mod.multi, name.cont = "speed", name.factor = "vibration")
MixDelta(xplode.multi)