| Title: | Determine and Test the Fixed-Point Property in Binary Mixture Data |
|---|---|
| Description: | Determine and test the fixed-point property in binary mixture data. This package was originally developed in the context of detecting mixture of cognitive processing strategies, based on observed response time distributions. The method is explain in more detail by Van Maanen, De Jong, Van Rijn (2014) <doi:10.1371/journal.pone.0106113> and Van Maanen, Couto, Lebreton, (2016) <doi:10.1371/journal.pone.0167377>. |
| Authors: | Leendert Van Maanen [aut, cre], Joaquina Couto [ctb], Hedderik Van Rijn [ctb], Mael Lebreton [ctb] |
| Maintainer: | Leendert Van Maanen <[email protected]> |
| License: | GPL-2 |
| Version: | 1.0 |
| Built: | 2024-12-11 07:11:19 UTC |
| Source: | CRAN |
This function computes Bayes Factors and p-values for within-subjects ANOVA designs, encoded as fp objects.
fpAnova(object, stat = "BF", na.rm = TRUE, check = TRUE)fpAnova(object, stat = "BF", na.rm = TRUE, check = TRUE)
object |
a list of objects from class fpp. |
stat |
Either "BF" (default), "p", or "both", specificying what statistic to report. |
na.rm |
Are |
check |
Should the data be checked for suitability? A warning will be provided if a check is failed. |
The function expects the output of fpGet, but in a list.
A list containing the results of either the Bayesian or frequentist analysis, or both:
BF |
The output of |
p |
The output of |
If check=TRUE, then warnings will be provided if the data are not suitable for correct inferences.
Leendert van Maanen ([email protected])
Van Maanen, L., De Jong, R., Van Rijn, H (2014). How to assess the existence of competing strategies in cognitive tasks: A primer on the fixed-point property. PLOS One, 9, e106113
Van Maanen, L. Couto, J. & Lebetron, M. (2016). Three boundary conditions for computing the fixed-point property in binary mixture data. PLOS One, 11, e0167377.
fpGet, anovaBF, fpConditionCheck, summary.aov.
## generate data p <- c(.1,.5,.9) rt <- sapply(1:3, function(i) {rnormMix(10000, c(1,2), c(1,1), p[i])}) dat <- data.frame(rt=c(rt), cond=rep(1:3, each=10000), pp=rep(1:50, each=200, times=3)) ## compute the list of fpp objects res <- tapply(1:nrow(dat), dat$pp, function(X) {fpGet(dat[X,], 1000, bw=.75)}) ## call fpAnova, with stat="both" to do both a Bayesian and a frequentist test fpAnova(res, stat="both")## generate data p <- c(.1,.5,.9) rt <- sapply(1:3, function(i) {rnormMix(10000, c(1,2), c(1,1), p[i])}) dat <- data.frame(rt=c(rt), cond=rep(1:3, each=10000), pp=rep(1:50, each=200, times=3)) ## compute the list of fpp objects res <- tapply(1:nrow(dat), dat$pp, function(X) {fpGet(dat[X,], 1000, bw=.75)}) ## call fpAnova, with stat="both" to do both a Bayesian and a frequentist test fpAnova(res, stat="both")
This function checks whether two conditions are met before performing fpANOVA.
fpConditionCheck(object)fpConditionCheck(object)
object |
a list of objects from class fpp. |
Finding support for the fixed-point property will be mute if there is no significant
difference between experimental conditions. Whether all conditions differ can be tested
using fpConditionCheck1, which performs pairwise t-tests. A warning is provided if
at least one paire of conditions does not significantly differ (default settings of
pairwise.t.test are used).
Finding support for the fixed-point property is difficult if the bandwidth of the density
estimation is chosen too small. In that case, multiple crossing points of pairs of densities
will preclude a precise estimate of the fixed point. fpConditionCheck2 tests the number
of crossing points for each pair of conditions, and provides a warning if more crossing points
are detected.
No return value, called for warnings generated by fpConditionCheck1 and fpConditionCheck2
Leendert van Maanen ([email protected])
Van Maanen, L., De Jong, R., Van Rijn, H (2014). How to assess the existence of competing strategies in cognitive tasks: A primer on the fixed-point property. PLOS One, 9, e106113
Van Maanen, L. Couto, J. & Lebetron, M. (2016). Three boundary conditions for computing the fixed-point property in binary mixture data. PLOS One, 11, e0167377.
N <- 200 # nr of observations per condition M <- 50 # nr of participants p <- seq(0.1, 0.9, 0.4) # mixture proportions means <- c(0.3, 0.3) # means of base distributions are equal, yielding a warning if check=TRUE sigma <- 5 # scale of base distributions bw <- 0.01 # kernel bandwidth of the density estimation. Too small values yield a warning if check=TRUE ### generate data rt <- NULL for (i in 1:length(p)) { rt <- c(rt, ifelse(sample(0:1, N * M, replace = TRUE, prob = c(p[i], 1 - p[i])), rnorm(N * M, means[1], sigma), rnorm(N * M, means[2], sigma))) } rt <- rt + rep(rnorm(M, sd = 0.1), times = N) # normally distributed pp random effect dat <- data.frame(rt = rt, cond = rep(1:length(p), each = N * M), pp = rep(1:M, each = N)) ### compute crossing points res <- tapply(1:nrow(dat), dat$pp, function(X) { fpGet(dat[X, ], 1000, bw = bw) }) ### test fixed point fpAnova(res, stat = "both", check=TRUE) # this provides both warningsN <- 200 # nr of observations per condition M <- 50 # nr of participants p <- seq(0.1, 0.9, 0.4) # mixture proportions means <- c(0.3, 0.3) # means of base distributions are equal, yielding a warning if check=TRUE sigma <- 5 # scale of base distributions bw <- 0.01 # kernel bandwidth of the density estimation. Too small values yield a warning if check=TRUE ### generate data rt <- NULL for (i in 1:length(p)) { rt <- c(rt, ifelse(sample(0:1, N * M, replace = TRUE, prob = c(p[i], 1 - p[i])), rnorm(N * M, means[1], sigma), rnorm(N * M, means[2], sigma))) } rt <- rt + rep(rnorm(M, sd = 0.1), times = N) # normally distributed pp random effect dat <- data.frame(rt = rt, cond = rep(1:length(p), each = N * M), pp = rep(1:M, each = N)) ### compute crossing points res <- tapply(1:nrow(dat), dat$pp, function(X) { fpGet(dat[X, ], 1000, bw = bw) }) ### test fixed point fpAnova(res, stat = "both", check=TRUE) # this provides both warnings
This function takes a list of fpp objects, and computes at which point the distributions cross each other.
fpDensDiff(object)fpDensDiff(object)
object |
a list of |
An m * n-array containing the crossing points of the pairs of distributions, with n the length of the list of fpp objects, and m the number of pairs of distributions.
Leendert van Maanen ([email protected])
Van Maanen, L., De Jong, R., Van Rijn, H (2014). How to assess the existence of competing strategies in cognitive tasks: A primer on the fixed-point property. PLOS One, 9, e106113
Van Maanen, L. Couto, J. & Lebetron, M. (2016). Three boundary conditions for computing the fixed-point property in binary mixture data. PLOS One, 11, e0167377.
## generate data p <- c(.1,.5,.9) rt <- sapply(1:3, function(i) {rnormMix(10000, c(1,2), c(1,1), p[i])}) dat <- data.frame(rt=c(rt), cond=rep(1:3, each=10000), pp=rep(1:50, each=200, times=3)) ## compute the list of fpp objects res <- tapply(1:nrow(dat), dat$pp, function(X) {fpGet(dat[X,], 1000, bw=.75)}) ## get the crossing points crosses=fpDensDiff(res) boxplot(t(crosses), frame.plot=FALSE,xlab="Crossing point", ylab="Condition pair", names=c("1-2","2-3","1-3"), horizontal=TRUE)## generate data p <- c(.1,.5,.9) rt <- sapply(1:3, function(i) {rnormMix(10000, c(1,2), c(1,1), p[i])}) dat <- data.frame(rt=c(rt), cond=rep(1:3, each=10000), pp=rep(1:50, each=200, times=3)) ## compute the list of fpp objects res <- tapply(1:nrow(dat), dat$pp, function(X) {fpGet(dat[X,], 1000, bw=.75)}) ## get the crossing points crosses=fpDensDiff(res) boxplot(t(crosses), frame.plot=FALSE,xlab="Crossing point", ylab="Condition pair", names=c("1-2","2-3","1-3"), horizontal=TRUE)
This function computes standard kernel-based density functions for a response time data set with three or more conditions. In addition, it computes the pairwise differences for each pair of density functions.
fpGet(dat, n = 512, bw = "nrd0")fpGet(dat, n = 512, bw = "nrd0")
dat |
n*2 dataframe or matrix with in col 1: RT (the values for which to compute the density); col 2: condition (an index) |
n |
the number of equally spaced points at which the density is to be estimated. See |
bw |
the smoothing bandwidth to be used. See |
an object of class fpp, with the following components.
dens |
list of objects from class |
diff |
dataframe of the density differences |
dat |
dataframe with the input data |
Leendert van Maanen ([email protected])
Van Maanen, L., De Jong, R., Van Rijn, H (2014). How to assess the existence of competing strategies in cognitive tasks: A primer on the fixed-point property. PLOS One, 9, e106113
Van Maanen, L. Couto, J. & Lebetron, M. (2016). Three boundary conditions for computing the fixed-point property in binary mixture data. PLOS One, 11, e0167377.
### one data set or participant ## generate data p <- c(.1,.5,.9) rt <- sapply(1:3, function(i) {rnormMix(1000, c(1,2), c(1,1), p[i])}) dat <- data.frame(rt=c(rt), cond=rep(1:3, each=1000)) ## compute one fp object fpobject <- fpGet(dat, 1000, bw=.75) ### multiple participants ## generate data p <- c(.1,.5,.9) rt <- sapply(1:3, function(i) {rnormMix(10000, c(1,2), c(1,1), p[i])}) dat <- data.frame(rt=c(rt), cond=rep(1:3, each=10000), pp=rep(1:50, each=200, times=3)) ## compute the list of fpp objects res <- tapply(1:nrow(dat), dat$pp, function(X) {fpGet(dat[X,], 1000, bw=.75)})### one data set or participant ## generate data p <- c(.1,.5,.9) rt <- sapply(1:3, function(i) {rnormMix(1000, c(1,2), c(1,1), p[i])}) dat <- data.frame(rt=c(rt), cond=rep(1:3, each=1000)) ## compute one fp object fpobject <- fpGet(dat, 1000, bw=.75) ### multiple participants ## generate data p <- c(.1,.5,.9) rt <- sapply(1:3, function(i) {rnormMix(10000, c(1,2), c(1,1), p[i])}) dat <- data.frame(rt=c(rt), cond=rep(1:3, each=10000), pp=rep(1:50, each=200, times=3)) ## compute the list of fpp objects res <- tapply(1:nrow(dat), dat$pp, function(X) {fpGet(dat[X,], 1000, bw=.75)})
"fpp"
Objects of the fpp class are used by methods and functions of the fp package, to visualize and compute the fixed-point property in response time data.
Objects can be created by calls of the form new("fpp", ...).
dens:Object of class "array". This is an array of objects of class "density".
diff:Object of class "data.frame". This is a dataframe with the paired differences between densities.
dat:Object of class "data.frame". This is a dataframe with the input data.
signature(x = "fpp"): ...
Leendert van Maanen ([email protected])
Van Maanen, L., De Jong, R., Van Rijn, H (2014). How to assess the existence of competing strategies in cognitive tasks: A primer on the fixed-point property. PLOS One, 9, e106113
Van Maanen, L. Couto, J. & Lebetron, M. (2016). Three boundary conditions for computing the fixed-point property in binary mixture data. PLOS One, 11, e0167377.
showClass("fpp")showClass("fpp")
Density, distribution, function, quantile function, and random generation for the mixture of two Gaussian distributions with mixture proportion p and 1-p.
dnormMix(x, mean=c(0,1), sd=c(1,1), p=1) pnormMix(x, mean=c(0,1), sd=c(1,1), p=1) qnormMix(x, mean=c(0,1), sd=c(1,1), p=1) rnormMix(n, mean=c(0,1), sd=c(1,1), p=1)dnormMix(x, mean=c(0,1), sd=c(1,1), p=1) pnormMix(x, mean=c(0,1), sd=c(1,1), p=1) qnormMix(x, mean=c(0,1), sd=c(1,1), p=1) rnormMix(n, mean=c(0,1), sd=c(1,1), p=1)
x |
vector of quantiles or probabilities. |
n |
number of observations. |
mean |
vector of two means. |
sd |
vector of standard deviations. |
p |
mixture proportion of the first distribution (the second has proportion 1-p). |
dnormMix gives the density, pnormMix gives the distribution function, qnormMix gives the quantile function, and rnormMix generates random deviates.
Leendert van Maanen ([email protected])
Van Maanen, L., De Jong, R., Van Rijn, H (2014). How to assess the existence of competing strategies in cognitive tasks: A primer on the fixed-point property. PLOS One, 9, e106113
Van Maanen, L. Couto, J. & Lebetron, M. (2016). Three boundary conditions for computing the fixed-point property in binary mixture data. PLOS One, 11, e0167377.
## the default value for p reduces this function to a normal distribution dnormMix(1) == dnorm(1) ## plot that illustrates the fixed-point property p <- c(.8,.5,.2) m <- c(0,1); s <- c(1,2) plot(function(X) {dnormMix(X, m, s, p[1])}, -5,10, ylab="Density",xlab="x", bty='L') for (i in 2:3) { plot(function(X) {dnormMix(X, m, s, p[i])},-5,10, add=TRUE, lty=i, lwd=2) } legend("topright", legend=paste("p=",p,sep=''), lty=1:3, lwd=2, bty='n')## the default value for p reduces this function to a normal distribution dnormMix(1) == dnorm(1) ## plot that illustrates the fixed-point property p <- c(.8,.5,.2) m <- c(0,1); s <- c(1,2) plot(function(X) {dnormMix(X, m, s, p[1])}, -5,10, ylab="Density",xlab="x", bty='L') for (i in 2:3) { plot(function(X) {dnormMix(X, m, s, p[i])},-5,10, add=TRUE, lty=i, lwd=2) } legend("topright", legend=paste("p=",p,sep=''), lty=1:3, lwd=2, bty='n')
This function plots kernel-based densities as well as density differences for three or more data sets (fpp objects).
## S3 method for class 'fpp' plot(x, ylab = c("Density", "Density difference"), xlim = NULL, ...)## S3 method for class 'fpp' plot(x, ylab = c("Density", "Density difference"), xlim = NULL, ...)
x |
an fpp object |
ylab |
y-axis labels of the two plots |
xlim |
the x limits (x1, x2) of the two plots |
... |
additional arguments to pass to both |
Generates two plots, one showing the estimated densities (based on plot.density) and
one showing the density differences (based on matplot)
No return value, called for side effects
Leendert van Maanen ([email protected])
Van Maanen, L., De Jong, R., Van Rijn, H (2014). How to assess the existence of competing strategies in cognitive tasks: A primer on the fixed-point property. PLOS One, 9, e106113
Van Maanen, L. Couto, J. & Lebetron, M. (2016). Three boundary conditions for computing the fixed-point property in binary mixture data. PLOS One, 11, e0167377.
fpGet,fpDensDiff,plot.density,matplot
## generate data p <- c(.1,.5,.9) rt <- sapply(1:3, function(i) {rnormMix(1000, c(1,2), c(1,1), p[i])}) dat <- data.frame(rt=c(rt), cond=rep(1:3, each=1000)) ## compute fpp object fpobject <- fpGet(dat, 1000, bw=.75) ## plot it op <- par(mfrow=c(1,2)) plot(fpobject) par(op)## generate data p <- c(.1,.5,.9) rt <- sapply(1:3, function(i) {rnormMix(1000, c(1,2), c(1,1), p[i])}) dat <- data.frame(rt=c(rt), cond=rep(1:3, each=1000)) ## compute fpp object fpobject <- fpGet(dat, 1000, bw=.75) ## plot it op <- par(mfrow=c(1,2)) plot(fpobject) par(op)