summary.selm {sn} | R Documentation |
selm
fitssummary
method for class "selm"
and "mselm"
.
## S4 method for signature 'selm' summary(object, param.type = "CP", cov = FALSE, cor = FALSE) ## S4 method for signature 'mselm' summary(object, param.type = "CP", cov = FALSE, cor = FALSE)
object |
an object of class |
param.type |
a character string which indicates the required type of
parameter type; possible values are |
cov |
a logical value, to indicate if an estimate of the variance and
covariance matrix of the estimates is required (default: |
cor |
a logical value, to indicate if an estimate of the correlation
matrix of the estimates is required (default: |
An S4 object of class summary.selm
with 12 slots.
|
the calling statement. |
|
the parametric family of skew-ellitically contoured distributed (SEC) type. |
|
the maximized log-likelihood or penalized log-likelihood value |
|
estimation method ( |
|
a characer string with the chosen parameter set. |
|
table of parameters, std.errors and z-values |
|
a list of fixed parameter values |
|
residual values |
|
a list with control parameters |
|
a list of auxiliary quantities |
|
a numeric vector with various lengths and dimensions |
|
a logical value which indicates whether the estimates are on the boundary of the parameter space |
There are two reasons why the default choice of param.type
is
CP
. One is the the easier interpretation of cumulant-based quantities
such as mean value, standard deviation, coefficient of skewness. The other
reason is more technical and applies only to cases when the estimate of the
slant parameter alpha
of the SN distribution is close to the
origin: standard asymptotic distribution theory of maximum likelihood
estimates does not apply in these cases and the corresponding standard errors
are not trustworthy, especially those of alpha
and xi
or the
intercept in the regression case. The problem is especialy severe at
alpha=0
but to some extent propagates to its vicinity. For background
information, see Sections 3.1.4–6 and 5.2.3 of Azzalini and Capitanio (2014)
and references therein. This problem does not occur with the the SC
and the ST distribution (unless its tail-weight parameter nu
diverges, hence approaching the SN
case).
Adelchi Azzalini
Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monographs series.
selm
function,
selm
(and mselm
) class,
plot.selm
, dp2cp
data(wines, package="sn") m5 <- selm(acidity ~ phenols + wine, family="SN", data=wines) summary(m5) summary(m5, "dp") s5 <- summary(m5, "dp", cor=TRUE, cov=TRUE) dp.cor <- slot(s5, "aux")$param.cor cov2cor(vcov(m5, "dp")) # the same # # m6 <- selm(acidity ~ phenols + wine, family="ST", data=wines) # boundary!? # m12 <- selm(cbind(acidity, alcohol) ~ phenols + wine, family="SN", data=wines) s12 <- summary(m12) coef(m12, 'dp') coef(m12, "dp", vector=FALSE) # # see other examples at function selm