Function to perform ANOVA on fp objects

Description

This function computes Bayes Factors and p-values for within-subjects ANOVA designs, encoded as fp objects.

Usage

fpAnova(object, stat = "BF", na.rm = TRUE, check = TRUE)

Arguments

Details

The function expects the output of fpGet, but in a list.

Value

A list containing the results of either the Bayesian or frequentist analysis, or both:

Warning

If check=TRUE, then warnings will be provided if the data are not suitable for correct inferences.

Author(s)

Leendert van Maanen (l.vanmaanen@uu.nl)

References

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.

See Also

fpGet, anovaBF, fpConditionCheck, summary.aov.

Examples

## 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")

Checks preconditions before performing fpANOVA

Description

This function checks whether two conditions are met before performing fpANOVA.

Usage

fpConditionCheck(object)

Arguments

Details

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.

Value

No return value, called for warnings generated by fpConditionCheck1 and fpConditionCheck2

Author(s)

Leendert van Maanen (l.vanmaanen@uu.nl)

References

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.

See Also

fpAnova, pairwise.t.test

Examples

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 warnings

Function to compute the crossing point of two kernel-based distribution functions

Description

This function takes a list of fpp objects, and computes at which point the distributions cross each other.

Usage

fpDensDiff(object)

Arguments

Value

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.

Author(s)

Leendert van Maanen (l.vanmaanen@uu.nl)

References

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.

See Also

fpGet,fpAnova

Examples

## 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)

Function to compute densities and density differences for three or more data sets

Description

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.

Usage

fpGet(dat, n = 512, bw = "nrd0")

Arguments

Value

an object of class fpp, with the following components.

Author(s)

Leendert van Maanen (l.vanmaanen@uu.nl)

References

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.

See Also

density.

Examples

### 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)})

Class "fpp"

Description

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 from the Class

Objects can be created by calls of the form new("fpp", ...).

Slots

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.

Methods

plot

signature(x = "fpp"): ...

Author(s)

Leendert van Maanen (l.vanmaanen@uu.nl)

References

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.

Examples

showClass("fpp")

Gaussian binary mixture distribution

Description

Density, distribution, function, quantile function, and random generation for the mixture of two Gaussian distributions with mixture proportion p and 1-p.

Usage

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)

Arguments

Value

dnormMix gives the density, pnormMix gives the distribution function, qnormMix gives the quantile function, and rnormMix generates random deviates.

Author(s)

Leendert van Maanen (l.vanmaanen@uu.nl)

References

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.

Examples

## 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')

Function to plot the distributions and differences of multiple binary mixture distributions.

Description

This function plots kernel-based densities as well as density differences for three or more data sets (fpp objects).

Usage

## S3 method for class 'fpp'
plot(x, ylab = c("Density", "Density difference"), xlim = NULL, ...)

Arguments

Details

Generates two plots, one showing the estimated densities (based on plot.density) and one showing the density differences (based on matplot)

Value

No return value, called for side effects

Author(s)

Leendert van Maanen (l.vanmaanen@uu.nl)

References

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.

See Also

fpGet,fpDensDiff,plot.density,matplot

Examples

## 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)