msn_mle(X, y, freq, start, traceout, iter_max, x_tol)
y
|
a matrix or a vector. In y is a matrix, rows refer to
observations, and columns to components of the multivariate
distribution. In 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.
|
traceout
|
logical value which controls printing of the algorithm convergence.
If traceout=1 , details are printed. Default value is 0 .
|
iter_max
| maximum number of iterations of the optimisation routine. Default is 150. |
x_tol
| tolerance (default is 1e-8). |
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*log-likelihood)
for this parameter is actually used;
see Azzalini and Capitanio (1998) for details.
The optimizer routine is called, supplying the gradient of the
profile deviance. PP Although the function accepts a vector y as input,
the use of sn.mle
is recommended in the scalar case.
dp
|
a list containing the direct parameters beta , Omega , alpha .
Here, beta is a matrix of regression coefficients with
size(beta)=[size(X,1),size(y,2)) , Omega is a covariance matrix of
order size(y,2) , alpha is a vector of shape parameters of length size(y,2) .
|
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.
|
options
|
messages from the optimisation routine; see the documentation
of foptions for explanation of its components.
|
(Omega,alpha)
parametrization
adopted here is the one of Azzalini and Capitanio (1998).Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, part 3.
dmsn
, sn_mle
, msn_fit
, foptions
# a simple case b = msn_mle(NaN,[lbm,bmi,ssf]) # # a regressione case a = msn_mle([ones(length)lbm),1),lbm], bmi, NaN, NaN, NaN, NaN,1e-6) # # refine the previous outcome a1 = msn.mle([ones(length)lbm),1),lbm], bmi, NaN, a_dp, NaN, NaN,1e-9)