gamlss (version 4.3-4)

quantSheets: Quantile Sheets

Description

The quantile sheets function quantSheets() is based on the work of Sabine Schnabe and Paul Eiler (see references below). The estimation of the quantile curves is done simultaneously by also smoothing in the direction of y as well as x. This avoids (but do not eliminate completely) the problem of crossing quantiles.

Usage

quantSheets(y, x, x.lambda = 1, p.lambda = 1, data = NULL, 
            cent = 100 * pnorm((-4:4) * 2/3), 
            control = quantSheets.control(...), print = TRUE,  ...)
quantSheets.control(x.inter = 10, p.inter = 10, degree = 3, logit = FALSE, 
            order = 2, kappa = 0, n.cyc = 100, c.crit = 1e-05, plot = TRUE, 
            power = NULL, ...)
findPower(y, x, data = NULL, lim.trans = c(0, 1.5), prof = FALSE, 
            k = 2, c.crit = 0.01, step = 0.1)
z.scoresQS(object, y, x, plot = FALSE, tol = NULL)

Arguments

y

the y variable

x

the x variable

x.lambda

smoothing parameter in the direction of x

p.lambda

smoothing parameter in the direction of y (probabilities)

data

the data frame

cent

the centile values where the quantile sheets is evaluated

control

for the parameters controlling the algorithm

print

whether to print the sample percentages

x.inter

number of intervals in the x direction for the B-splines

p.inter

number of intervals in the probabilities (y-direction) for the B-splines

degree

the degree for the B-splines

logit

whether to use logit(p) instead of p (probabilities) for the y-axis

order

the order of the penalty

kappa

is a ridge parameter set to zero (for no ridge effect)

n.cyc

number of cycles of the algorithm

c.crit

convergence criterion of the algorithm

plot

whether to plot the resulting quantile sheets

power

The value of the power transformation in the x axis if needed

lim.trans

the limits for looking for the power transformation parameter using findPower()

prof

whether to use the profile GAIC or optim() to the parameter the power transformation

k

the GAIC penalty

step

the steps for the profile GAIC if the argument prof of findPower() is TRUE

object

a fitted quantSheets object

tol

how far out from the range of the y variable should go for estimating the distribution of y using the flexDist() function

...

for further arguments

Value

• Using the function quantSheets() a quantSheets object is returned having the following methods: print(), fitted(), predict() and resid().

  Using findPower() a single values of the power parameter is returned.

  Using z.scoresQS a vector of z-scores is returned.

Details

The advantage of quantile sheets is that they estimates simultaneously all the quantiles. This almost eliminates the problem of crossing quantiles. The method is very fast and useful for exploratory tool. The function needs two smoothing parameters. Those two parameters have to specified by the user. They are not estimated automatically. They can be selected by visual inspection.

The disadvantages of quantile sheets comes from the fact that like all non-parametric techniques do not have a goodness of fit measure to change how good is the models and the residuals based diagnostics are not existence since it is difficult to define residuals in this set up.

In this implementation we do provide residuals by using the flexDist() function from package gamlss.dist. This is based on the idea that by knowing the quantiles of the distribution we can reconstruct non parametrically the distribution itself and this is what flexDist() is doing. As a word of caution, such a construct is based on several assumptions and depends on several smoothing parameters. Treat those residuals with caution. The same caution should apply to the function z.scoresQS().

References

Schnabel, S.K. (2011) Expectile smoothing: new perspectives on asymmetric least squares. An application to life expectancy, Utrecht University.

Schnabel, S. K and Eilers, P. H. C.(2013) Simultaneous estimation of quantile curves using quantile sheets, AStA Advances in Statistical Analysis, 97, 1, pp 77-87, Springer.

Schnabel, S. K and Eilers, P. H. (2013) A location-scale model for non-crossing expectile curves, Stat, 2, 1, pp 171-183.

See Also

lms: for a parametric equivalent results.

Examples

data(abdom)
m1 <- quantSheets(y,x, data=abdom)
head(fitted(m1))
p1 <- predict(m1, newdata=c(20,30,40))
matpoints(c(20,30,40), p1)
z.scoresQS(m1,y=c(150, 300),x=c(20, 30) )
# If we needed a power transformation not appropriate for this data
findPower(y,x, data=abdom)