skewMLRM (version 1.6)

vcov.skewMLRM: Calculate Variance-Covariance Matrix for a Fitted Model Object

Description

Returns the variance-covariance matrix of the parameters of a fitted model object of the class "skewMLRM".

Usage

# S3 method for skewMLRM
vcov(object, ...)

Value

A matrix of the estimated covariances between the parameter estimates in the linear or non-linear predictor of the model. This should have row and column names corresponding to the parameter names given by the coef method.

Arguments

object

an object of the class "skewMLRM". See details for supported models.

...

for extra arguments

Author

Clecio Ferreira, Diego Gallardo and Camila Zeller

Details

Supported models are:

In MSMN class: multivariate normal (MN), multivariate Student t (MT), multivariate slash (MSL), multivariate contaminated normal (MCN). See Lange and Sinsheimer (1993) for details.

In MSMSN class: multivariate skew-normal (MSN), multivariate skew-T (MSTT), multivariate skew-slash (MSSL2), multivariate skew-contaminated normal (MSCN2). See Zeller, Lachos and Vilca-Labra (2011) for details.

In MSSMN class: MSN, multivariate skew-t-normal (MSTN), multivariate skew-slash normal (MSSL), multivariate skew-contaminated normal (MSCN). See Louredo, Zeller and Ferreira (2021) for details.

In MSMSNC class: multivariate skew-normal-Cauchy (MSNC), multivariate skew-t-Expected-Cauchy (MSTEC), multivariate skew-slash-Expected-Cauchy (MSSLEC), multivariate skew-contaminated-Expected-Cauchy (MSCEC). See Kahrari et al. (2020) for details.

Note: the MSN distribution belongs to both, MSMSN and MSSMN classes.

The functions which generate an object of the class "skewMLRM" compatible with vcov are

estimate.xxx: where xxx can be MN, MT, MSL, MCN, MSN, MSTN, MSSL, MSCN, MSTT, MSSL2, MSCN2, MSNC, MSTEC, MSSLEC or MSCEC.

choose.yyy: where yyy can be MSMN, MSSMN, MSMSN, MSMSNC or models.

choose2, mbackcrit and mbacksign.

References

Kahrari, F., Arellano-Valle, R.B., Ferreira, C.S., Gallardo, D.I. (2020) Some Simulation/computation in multivariate linear models of scale mixtures of skew-normal-Cauchy distributions. Communications in Statistics - Simulation and Computation. In press. DOI: 10.1080/03610918.2020.1804582

Lange, K., Sinsheimer, J.S. (1993). Normal/independent distributions and their applications in robust regression. Journal of Computational and Graphical Statistics 2, 175-198.

Louredo, G.M.S., Zeller, C.B., Ferreira, C.S. (2021). Estimation and influence diagnostics for the multivariate linear regression models with skew scale mixtures of normal distributions. Sankhya B. In press. DOI: 10.1007/s13571-021-00257-y

Zeller, C.B., Lachos, V.H., Vilca-Labra, F.E. (2011). Local influence analysis for regression models with scale mixtures of skew-normal distributions. Journal of Applied Statistics 38, 343-368.

Examples

data(ais, package="sn") ##Australian Institute of Sport data set
attach(ais)
##It is considered a bivariate regression model
##with Hg and SSF as response variables and
##Hc, Fe, Bfat and LBM as covariates
y<-cbind(Hg,SSF)
n<-nrow(y); m<-ncol(y)
X.aux=model.matrix(~Hc+Fe+Bfat+LBM)
p<-ncol(X.aux)
X<-array(0,dim=c(2*p,m,n))
for(i in 1:n) {
    X[1:p,1,i]=X.aux[i,,drop=FALSE]
    X[p+1:p,2,i]=X.aux[i,,drop=FALSE]
}
##See the covariate matrix X
##X
# \donttest{
fit.MN=estimate.MN(y, X)     #fit the MN distribution
vcov(fit.MN)                 #variance-covariance matrix
fit.MSN=estimate.MSN(y, X)   #fit the MSN distribution
vcov(fit.MSN)                #variance-covariance matrix
# }