get.correspondence {idr}

Compute correspondence profiles

Description

Compute the correspondence profiles (Psi and Psi') and the corresponding smoothed curve using spline

Usage

get.correspondence(x1, x2, t, spline.df = NULL)

Arguments

x1

Data values or ranks of the data values on list 1, a vector of numeric values. Large values need to be significant signals. If small values represent significant signals, rank the signals reversely (e.g. by ranking negative values) and use the rank as x1.

x2

Data values or ranks of the data values on list 2, a vector of numeric values. Large values need to be significant signals. If small values represent significant signals, rank the signals reversely (e.g. by ranking negative values) and use the rank as x1.

t

A numeric vector between 0 and 1 in ascending order. t is the right-tail percentage.

spline.df

Degree of freedom for spline, to control the smoothness of the smoothed curve.

Value

psi

the correspondence profile in terms of the scale of percentage, i.e. between (0, 1)

dpsi

the derivative of the correspondence profile in terms of the scale of percentage, i.e. between (0, 1)

psi.n

the correspondence profile in terms of the scale of the number of observations

dpsi.n

the derivative of the correspondence profile in terms of the scale of the number of observations

Each object above is a list consisting of the following items: t: upper percentage (for psi and dpsi) or number of top ranked observations (for psi.n and dpsi.n) value: psi or dpsi smoothed.line: smoothing spline ntotal: the number of observations jump.point: the index of the vector of t such that psi(t[jump.point]) jumps up due to ties at the low values. This only happends when data consists of a large number of discrete values, e.g. values imputed for observations appearing on only one replicate.

Author(s)

Qunhua Li

References

Q. Li, J. B. Brown, H. Huang and P. J. Bickel. (2011) Measuring reproducibility of high-throughput experiments. Annals of Applied Statistics, Vol. 5, No. 3, 1752-1779.

Examples

# salmon data 
data(salmon)

# get.correspondence() needs the observations with high ranks have 
# high correlation and the observations with low ranks have low correlation. 
# In this dataset, small values have high correlation and large values 
# have low correlation.
# Ranking negative values makes the data follow the structure required
# by get.correspondence().
# There are 28 observations in this data set.

rank.x <- rank(-salmon$spawners)
rank.y <- rank(-salmon$recruits)
uv <- get.correspondence(rank.x, rank.y, seq(0.01, 0.99, by=1/28)) 


# plot correspondence curve on the scale of percentage
plot(uv$psi$t, uv$psi$value, xlab="t", ylab="psi", xlim=c(0, max(uv$psi$t)), 
ylim=c(0, max(uv$psi$value)), cex.lab=2)
lines(uv$psi$smoothed.line, lwd=4)
abline(coef=c(0,1), lty=3)

# plot the derivative of correspondence curve on the scale of percentage
plot(uv$dpsi$t, uv$dpsi$value, xlab="t", ylab="psi'", xlim=c(0, max(uv$dpsi$t)),
ylim=c(0, max(uv$dpsi$value)), cex.lab=2)
lines(uv$dpsi$smoothed.line, lwd=4)
abline(h=1, lty=3)

# plot correspondence curve on the scale of the number of observations
plot(uv$psi.n$t, uv$psi.n$value, xlab="t", ylab="psi", xlim=c(0, max(uv$psi.n$t)), 
ylim=c(0, max(uv$psi.n$value)), cex.lab=2)
lines(uv$psi.n$smoothed.line, lwd=4)
abline(coef=c(0,1), lty=3)

# plot the derivative of correspondence curve on the scale of the number
# of observations
plot(uv$dpsi.n$t, uv$dpsi.n$value, xlab="t", ylab="psi'", xlim=c(0, max(uv$dpsi.n$t)), 
ylim=c(0, max(uv$dpsi.n$value)), cex.lab=2)
lines(uv$dpsi.n$smoothed.line, lwd=4)
abline(h=1, lty=3)

# If the rank lists consist of a large number of ties at the bottom
# (e.g. the same low value is imputed to the list for the observations
# that appear on only one list), it may be desirable to plot only
# observations before hitting the ties. Then it can be plotted using the
# following
plot(uv$psi$t[1:uv$psi$jump.point], uv$psi$value[1:uv$psi$jump.point], xlab="t",
ylab="psi", xlim=c(0, max(uv$psi$t[1:uv$psi$jump.point])), 
ylim=c(0, max(uv$psi$value[1:uv$psi$jump.point])), cex.lab=2)
lines(uv$psi$smoothed.line, lwd=4)
abline(coef=c(0,1), lty=3)