msn.mle {sn} | R Documentation |
Fits a multivariate skew-normal (MSN) distribution to data, or fits a linear regression model with multivariate skew-normal errors, using maximum likelihood estimation.
msn.mle(X, y, freq, start, trace=FALSE, method="BFGS", control=list(iter.max=150) )
y |
a matrix or a vector. If y is a matrix, rows refer to
observations, and columns to components of the multivariate
distribution. If y is a vector, it is converted to a one-column
matrix, and a scalar skew-normal distribution is fitted.
|
X |
a matrix of covariate values.
If missing, a one-column matrix of 1's is created; otherwise,
it must have the same number of rows of y .
|
freq |
a vector of weights.
If missing, a one-column matrix of 1's is created; otherwise
it must have the same number of rows of y .
|
start |
a list contaning the components beta ,Omega , alpha ,
of the type described below. The dp component of the returned
list from a previous call has the required format.
|
trace |
logical value which controls printing of the algorithm convergence.
If trace=TRUE , details are printed. Default value is F .
|
method |
this parameter is just passed to the optimizer optim ;
see the documentation of this function for its usage. Default value is
"BFGS" .
|
control |
this parameter is passed to the optimizer optim ;
see the documentation of this function for its usage.
|
The parameter freq
is intended for use with grouped data,
setting the values of y
equal to the central values of the
cells; in this case the resulting estimate is an approximation
to the exact maximum likelihood estimate. If freq
is not
set, exact maximum likelihood estimation is performed.
The working parameter used in the maximization stage is
c(beta,alpha/omega)
, since a profile `deviance' -2*loglikelihood
for this parameter is actually used;
see Azzalini and Capitanio (1999) for details.
The optimizer optim
is called, supplying the gradient of
the profile deviance.
The function can take a vector y
as input; however the use of
sn.mle
is recommended in the scalar case.
A list containing the following components:
call |
a string containing the calling statement. |
dp |
a list containing the direct parameters beta , Omega , alpha .
Here, beta is a matrix of regression coefficients with
dim(beta)=c(nrow(X),ncol(y)) , Omega is a covariance matrix of
order ncol(y) , alpha is a vector of shape parameters of length
ncol(y) .
|
se |
a list containing the components beta , alpha , info .
Here, beta and alpha are the standard errors for the
corresponding point estimates;
info is the observed information matrix for the working parameter,
as explained below.
|
optim |
the list returned by the optimizer optim ; see the documentation
of this function for explanation of its components.
|
The multivariate skew-normal distribution is discussed by
Azzalini and Dalla Valle (1996); the (Omega,alpha)
parametrization
adopted here is the one of Azzalini and Capitanio (1999).
Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715–726.
Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579–602.
data(ais) attach(ais) # a simple-sample case b <- msn.mle(y=cbind(Ht,Wt)) # # a regression case: a <- msn.mle(X=cbind(1,Ht,Wt), y=bmi, control=list(x.tol=1e-6)) # # refine the previous outcome a1 <- msn.mle(X=cbind(1,Ht,Wt), y=bmi, control=list(x.tol=1e-9), start=a$dp)