pseMer {MixedPsy}

PSE/JND from GLMM Estimates Using Bootstrap Method

Description

Estimates the Point of Subjective Equivalence (PSE), the Just Noticeable Difference (JND) and the related Standard Errors by means of Bootstrap Method, given an object of class merMod.

Usage

pseMer(
  mer.obj,
  B = 200,
  FUN = NULL,
  alpha = 0.05,
  ci.type = c("norm", "basic", "perc"),
  beep = F
)

Arguments

mer.obj

an object of class merMod.

B

integer. Number of bootstrap samples.

FUN

an optional, custom made function to specify the required parameters to be estimated. If NULL, pseMer estimates PSE and 50%JND of a univariable GLMM with a single intercept and slope.

alpha

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

ci.type

vector of character strings representing the type of intervals required. The value should be any subset of the values accepted by boot.ci: c("norm","basic", "stud", "perc", "bca"). Specify "all" for all five types of intervals. "perc" should be always included for the summary table.

beep

logical. If TRUE, a "ping" sound alerts that the simulation is complete. Default is FALSE.

Details

pseMer estimates PSE and JND (and additional user defined parameters) from a fitted GLMM model (class merMod).

Value

pseMer returns a list of length 3 including a summary table (estimate, inferior and superior bounds of the confidence interval), the output of bootMer, and that of boot.ci, for further analyses. Confidence intervals in the summary table are based on the percentile method.

Note

A first custom function was written in 2012 for the non-CRAN package MERpsychophisics, based on the algorithm in Moscatelli et al. (2012). The current function is a wrapper of function bootMer and boot.ci.

Increasing the number of bootstrap samples (B) makes the estimate more reliable. However, this will also increase the duration of the computation.

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

Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015). Fitting Linear Mixed-Effects Models Using lme4. Journal of Statistical Software, 67(1), 51. https://doi.org/10.18637/jss.v067.i01

See Also

bootMer and boot.ci for estimation of confidence intervals with the bootstrap method. MixDelta for confidence intervals with delta method.

Examples

library(lme4)
#example 1: univariable GLMM
mod.uni = glmer(formula = cbind(Longer, Total - Longer) ~ X + (1 | Subject),
family = binomial(link = "probit"), data = simul_data)

BootEstim.uni <- pseMer(mod.uni, B = 100, ci.type = c("perc"))

#example 2: specify custom parameters for multivariable model
mod.multi <- glmer(cbind(faster, slower) ~ speed * vibration + (1 + speed| subject), 
family = binomial(link = "probit"), data = vibro_exp3)
              
fun2mod = function(mer.obj){
#allocate space: 4 parameters (jnd_A, jnd_B, pse_A, pse_B)
jndpse = vector(mode = "numeric", length = 4)
names(jndpse) = c("pse_0", "pse_32","jnd_0", "jnd_32")
jndpse[1] = -fixef(mer.obj)[1]/fixef(mer.obj)[2] #pse_0
jndpse[2] = -(fixef(mer.obj)[1]+fixef(mer.obj)[3])/(fixef(mer.obj)[2]+ fixef(mer.obj)[4]) #pse_0
jndpse[3] = qnorm(0.75)/fixef(mer.obj)[2] #jnd_0
jndpse[4] = qnorm(0.75)/(fixef(mer.obj)[2]+ fixef(mer.obj)[4]) #jnd_32
return(jndpse)
}
 
BootEstim.multi = pseMer(mod.multi, B = 100, FUN = fun2mod)