st.2logL.profile {sn} | R Documentation |
Computation and plot of 1-dimensional and 2-dimensional profile (negative) twice log-likelihood function for skew-t regression models.
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, ...)
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 (NA s) 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.
|
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 NA s.
|
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.
|
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)
.
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.
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.
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)")