Profile twice loglikelihood for skew-normal models

Usage

sn_2logL_profile(X, y, param_range, use_cp, npts, plotit)

Arguments

y a numeric vector. Missing values (NaNs) are not allowed.
X a matrix of explantory variables; must have size(X,2) equal to length(y). Missing values (NaN) are not allowed. If X is missing, a one-comun matrix of 1's is created.
param_range a numeric vector of length either 2 or 4. If the length is 2, the dimensional parameter d is set to 1, and a 1-dimensional profile is computed and plotted, for the shape or skewness parameter (depending on the parametrization adopted; see below); in this case the two value represent the minimum and maximum value for the range of the parameter. If the length of param_range is 4, the first two values determine the range of the scale parameter, the last two give the range of the shape (or skewness) parameter; in this case, d=2. Default is [sqrt(var(y)) .* [0.67, 1.5], -0.95, 0.95].
use_cp logical value which selects the parametrization adopted. If use_cp=1 (default value), the centred parametrization is used, otherwise the direct parametrization is adopted.
npts number of points (in the scalar case) or grid size (in the 2-dimensional case). Default is 31/d.
plotit logical value which determines is plotting takes place; default is 1.

Description

Computation and plot of 1-dimensional and 2-dimensional profile 2*loglikelihood for skew-normal regression models.

Details

Likelihood maximization is performed by sn_em.

See the reference below for explanation of the two possible parametrizations.

Value

a list containing the following components

param1,param2 vectors of the paramters values where the function has been evaluated. If d=2, the second vector contains NaNs.
param_names a character vector of two elements with the names of the param1 and param2.
2logL a vector or a matrix which represents twice the profile loglikelihood; this is in the "relative" version, i.e. setting the maximum value to be 0.
maximum a numeric value with the maximum which has been subtracted to obtain the "relative" version of 2logL.

Side Effects

If plotit=1, a plot of the profile twice relative loglikeliood is produced on a graphical device.

References

Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, part 3.

See Also

sn_em, sn_mle

Examples

a = sn_2logL_profile(NaN,otis)
a = sn_2logL_profile(NaN,otis,NaN,0)
a = sn_2logL_profile([ones(length(lbm),1),lbm],bmi,[0,0.9],NaN,50)
a = sn_2logL_profile(NaN,frontier, [0.8,1.6,10,30],0,11)


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