st.2logL.profile {sn}R Documentation

Profile twice loglikelihood for skew-t models

Description

Computation and plot of 1-dimensional and 2-dimensional profile (negative) twice log-likelihood function for skew-t regression models.

Usage

st.2logL.profile(X=matrix(rep(1, n)), y, freq, trace=FALSE,
          fixed.comp = c(ncol(X)+2, ncol(X)+3), 
          fixed.values = cbind(c(-4,4), log(c(1,25))),
          npts=51/length(fixed.comp), plot.it=TRUE, ...)

Arguments

X a matrix of explanatory variables; must have nrow(X) equal to length(y). Missing values (NA) are not allowed. If X is missing, a one-column matrix of 1's is created.
y a numeric vector. Missing values (NAs) are not allowed.
freq a vector of weights. If missing, a vector of 1's is created; otherwise it must have the same length of y.
trace logical value which controls printing of the algorithm convergence. If trace=TRUE, details are printed. Default value is FALSE.
fixed.comp a vector containing the subset of the parameters for which the profile log-likelihood function is required; it can be of length 1 or 2. The set of components of the parameters are beta, log(omega), alpha, log(df), where beta represents the regression parameters and has ncol(X) components.
fixed.values a numeric vector of values or a matrix with two columns, giving the range spanned by the selected parameters.
npts number of points on each parameter interval for which the function must be evaluated.
plot.it logical value; if plot.it=TRUE (default value) a graphical display is produced.
... graphical parameter passed either to plot or to contour, depending on whether lenght(fixed.comp) is 1 or 2.

Value

A list containing the following components:

call the matched call.
param1 vector of values of the first parameters values where the function has been evaluated.
param2 vectors of the parameters values where the function has been evaluated. If length(fixed.comp)=1, the second vector contains NAs.
deviance a vector or a matrix which represents twice the negative relative profile loglikelihood; this is in the "relative" version, i.e. setting the maximum value to be 0.
max.logL a numeric value with the maximum which has been added to obtain the "relative" version of deviance.
best a list with the output of optim at the best evaluated point, that is the one with higher log-likelihood.

Side Effects

If plot.it=TRUE, a plot of the profile twice relative loglikeliood is produced on a graphical device. If length(fixed.comp)=1, a plot of the `deviance' is produced as a function of the chosen parameter component. If length(fixed.comp)=2, this plot takes the form of a contour plot whose contour lines correspond to confidence regions of approximate probability levels c(0.25, 0.5, 0.75, 0.90,0.95, 0.99).

Background

The family of skew-t distributions is an extension of the Student's t family, via the introduction of a shape parameter which regulates skewness; when shape=0, the skew-t distribution reduces to the usual t distribution. A multivariate version of the distribution exists. See the reference below for additional information.

References

Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J.Roy. Statist. Soc. B 65, 367–389.

See Also

st.mle, sn.2logL.profile

Examples

data(ais, package="sn")
attach(ais)
a <- st.2logL.profile(y=bmi, xlab="alpha", ylab="log(df)")
a <- st.2logL.profile(y=bmi, fixed.comp=4, fixed.values=log(c(1,25)))
a <- st.2logL.profile(X=cbind(1,lbm), y=bmi, fixed.comp=5,  
         fixed.values=log(c(5,25)), xlab="log(df)", npts=50)
a <- st.2logL.profile(X=cbind(1,Ht), y=Wt, fixed.comp=c(4,5),
         fixed.values=cbind(c(-1,5), log(c(2,25))),
         xlab="alpha", ylab="log(df)")

[Package sn version 0.4-12 Index]