quickpsy {quickpsy}

Fits psychometric functions

Description

quickpsy fits, by direct maximization of the likelihood (Prins and Kingdom, 2010; Knoblauch and Maloney, 2012), psychometric functions of the form

\psi(x) = \gamma + (1 - \gamma - \lambda) * fun(x)

where \gamma is the guess rate, \lambda is the lapse rate and fun is a sigmoidal-shape function with asymptotes at 0 and 1.

Usage

quickpsy(d, x = x, k = k, n = n, grouping, random, within, between,
  xmin = NULL, xmax = NULL, log = FALSE, fun = cum_normal_fun,
  parini = NULL, guess = 0, lapses = 0, prob = NULL, thresholds = T,
  bootstrap = "parametric", B = 100, ci = 0.95, optimization = "optim")

Arguments

d

Data frame with the results of a Yes-No experiment to fit. It should have a tidy form in which each column corresponds to a variable and each row is an observation.

x

Name of the explanatory variable.

k

Name of the response variable. The response variable could be the number of trials in which a yes-type response was given or a vector of 0s (or -1s; no-type response) and 1s (yes-type response) indicating the response on each trial.

n

Only necessary if k refers to the number of trials in which a yes-type response was given. It corresponds to the name of the variable indicating the total number of trials.

grouping

Name of the grouping variables. It should be specified as grouping = .(variable_name1, variable_name2).

random

Name of the random variable. It should be specified as random = .(variable_name1, variable_name2). In the current version of quickpsy, the random variable has not special treatment. It does the same as grouping.

within

Name of the within variable. It should be specified as within = .(variable_name1, variable_name2). In the current version of quickpsy, the within variable has not special treatment. It does the same as grouping.

between

Name of the between variable. It should be specified as between = .(variable_name1, variable_name2). In the current version of quickpsy, the between variable has not special treatment. It does the same as grouping.

xmin

Minimum value of the explanatory variable for which the curves should be calculated (the default is the minimum value of the explanatory variable).

xmax

Maximum value of the explanatory variable for which the curves should be calculated (the default is the maximum value of the explanatory variable).

log

If TRUE, the logarithm of the explanatory variable is used to fit the curves (default is FALSE).

fun

Name of the shape of the curve to fit. It could be a predefined shape (cum_normal_fun, logistic_fun, weibull_fun) or the name of a function introduced by the user (default is cum_normal_fun).

parini

Initial parameters. quickpsy calculates default initial parameters using probit analysis, but it is also possible to specify a vector of initial parameters or a list of the form list(c(par1min, par1max), c(par2min, par2max)) to constraint the lower and upper bounds of the parameters (when optimization = 'DE', parini should be also a list).

guess

Value indicating the guess rate \gamma (default is 0). If TRUE, the guess rate is estimated as the i + 1 paramEter where i corresponds to the number of parameters of fun. If, for example, fun is a predefined shape with parameters p1 and p2, then the guess rate corresponds to parameter p3.

lapses

Value indicating the lapse rate \lambda (default is 0). If TRUE, the lapse rate is estimated as the i + 1 parameter where i corresponds to the number of parameters of fun plus one if the guess rate is estimated. If, for example, fun is a predefined shape with parameters p1 and p2, then the lapse rate corresponds to parameter p3. If the guess rate is also estimated, p3 will be the guess rate and p4 the lapse rate.

prob

Probability to calculate the threshold (default is guess + .5 * (1 - guess)).

thresholds

If FALSE, thresholds are not calculated (default is TRUE).

bootstrap

'parametric' performs parametric bootstrap; 'nonparametric' performs non-parametric bootstrap; 'none' does not perform bootstrap (default is 'parametric').

B

number of bootstrap samples (default is 100 ONLY).

ci

Confidence intervals level based on percentiles (default is .95).

optimization

Method used for optimization. The default is 'optim' which uses the optim function. It can also be 'DE' which uses de function DEoptim from the package DEoptim, which performs differential evolution optimization. By using DEoptim, it is less likely that the optimization finishes in a local minimum, but the optimization is slow. When 'DE' is used, parini should be specified as a list with lower and upper bounds.

Value

A list containing the following components:

• x, k, n

• groups The grouping variables.

• funname String with the name of the shape of the curve.

• psyfunguesslapses Curve including guess and lapses.

• limits Limits of the curves.

• parini Initial parameters.

• optimization Method to optimize.

• pariniset FALSE if initial parameters are not given.

• ypred Predicted probabilities at the values of the explanatory variable.

• curves Curves.

• par Fitted parameters and its confidence intervals.

• curvesbootstrap Bootstrap curves.

• thresholds Thresholds.

• thresholdsci Confidence intervals for the thresholds.

• logliks Log-likelihoods of the model.

• loglikssaturated Log-likelihoods of the saturated model.

• deviance Deviance of the model and the p-value calculated by bootstraping.

• aic AIC of the model defined as

  - 2 * loglik + 2 *k

  where k is the number of parameters of the model.

References

Burnham, K. P., & Anderson, D. R. (2003). Model selection and multimodel inference: a practical information-theoretic approach. Springer Science & Business Media.

Knoblauch, K., & Maloney, L. T. (2012). Modeling Psychophysical Data in R. New York: Springer.

Prins, N., & Kingdom, F. A. A. (2016). Psychophysics: a practical introduction. London: Academic Press.

See Also

quickpsy_

Examples

# make sure that all the requires packages are installed
# and loaded; instructions at https://github.com/danilinares/quickpsy
library(MPDiR) # contains the Vernier data; use ?Vernier for the reference
fit <- quickpsy(Vernier, Phaseshift, NumUpward, N,
                grouping = .(Direction, WaveForm, TempFreq), B = 10)
plotcurves(fit)
plotpar(fit)
plotthresholds(fit, geom = 'point')