choose2 {skewMLRM}

Select a distribution in the MSMN, MSSMN, MSMSN or/and MSMSNC classes and perform covariates selection.

Description

choose2 select a model inside the multivariate scale mixtures of normal (MSMN), the multivariate scale mixtures of skew-normal (MSMSN), the multivariate skew scale mixtures of normal (MSSMN) or/and the multivariate scale mixtures of skew-normal-Cauchy (MSMSNC) classes. See details for supported distributions within each class. Then, implement the covariates selection based on the significance, the Akaike's information criteria (AIC) or Schwartz's information criteria (BIC).

Usage

choose2(y, X = NULL, max.iter = 1000, prec = 1e-04, class = "MSMN", 
   est.var = TRUE, criteria = "AIC", criteria.cov = "AIC", 
   significance = 0.05, cluster = FALSE)

Arguments

y

The multivariate vector of responses. The univariate case also is supported.

X

The regressor matrix.

max.iter

The maximum number of iterations.

prec

The convergence tolerance for parameters.

class

class in which will be performed a distribution: MSMN (default), MSSMN, MSMSN, MSMSNC or ALL (which consider all the mentioned classes). See details.

est.var

Logical. If TRUE the standard errors are estimated.

criteria

criteria to perform the selection model: AIC (default) or BIC.

criteria.cov

criteria to perform the covariates selection: AIC (default), BIC or significance.

significance

the level of significance to perform the covariate selection. Only used if criteria.cov="significance". By default is 0.05.

cluster

logical. If TRUE, parallel computing is used. FALSE is the default value.

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.

Value

an object of class "skewMLRM" is returned. The object returned for this functions is a list containing the following components:

coefficients

A named vector of coefficients

se

A named vector of the standard errors for the estimated coefficients. Valid if est.var is TRUE and the hessian matrix is invertible.

logLik

The log-likelihood function evaluated in the estimated parameters for the selected model

AIC

Akaike's Information Criterion for the selected model

BIC

Bayesian's Information Criterion for the selected model

iterations

the number of iterations until convergence (if attached)

conv

An integer code for the selected model. 0 indicates successful completion. 1 otherwise.

dist

The distribution for which was performed the estimation.

class

The class for which was performed the estimation.

function

a string with the name of the used function.

choose.crit

the specified criteria to choose the distribution.

choose.crit.cov

the specified criteria to choose the covariates.

y

The multivariate vector of responses. The univariate case also is supported.

X

The regressor matrix (in a list form).

fitted.models

A vector with the fitted models

selected.model

Selected model based on the specified criteria.

fitted.class

Selected class based on the specified criteria.

comment

A comment indicating how many coefficients were eliminated

Author(s)

Clecio Ferreira, Diego Gallardo and Camila Zeller

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

##Select a distribution within the MSMN class. Then, perform covariate 
##selection based on the significance
fit.MSMN=choose2(y, X, class="MSMN")
summary(fit.MSMN)
##Identical process within the MSSMN class.
##may take some time on some systems
fit.MSSMN=choose2(y, X, class="MSSMN")
summary(fit.MSSMN)