skewMLRM (version 1.7)

mbacksign: Multivariate Backward Based on Significance

Description

mbacksign implements the covariates selection based on the significance of the covariates in a specified multivariate model in the multivariate scale mixtures of normal (MSMN), multivariate scale mixtures of skew-normal (MSMSN), multivariate skew scale mixtures of normal (MSSMN) or multivariate scale mixtures of skew-normal-Cauchy (MSMSNC) classes. See details for avaliable distributions.

Usage

mbacksign(y, X = NULL, max.iter = 1000, prec = 1e-04, dist = "MN", 
     significance = 0.05, ...)

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.

choose.crit

the specified criteria to choose the distribution.

comment

A comment indicating how many coefficients were eliminated

eliminated

An string vector with the eliminated betas (in order of elimination).

y

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

X

The regressor matrix (in a list form).

significance

The specified level of significance (0.05 by default).

function

a string with the name of the used function.

Arguments

y

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

X

The regressor matrix. It should include intercept term for all the variates.

max.iter

The maximum number of iterations.

prec

The convergence tolerance for parameters.

dist

the multivariate distribution in which the covariates selection will be implemented.

significance

the level of significance to perform the covariate selection. By default is 0.05.

...

Possible aditional arguments. For instance, for MSTT, MSSL2, MSTEC and MSSLEC distributions should be added nu.min and nu.fixed related to specifications for the nu parameter.

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.

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 regressor matrix X
##X
##Perform covariates selection in the MN distribution
##based on a significance level of 1%, 5% and 10% 
# \donttest{
##may take some time on some systems
fit.MN.01=mbacksign(y, X, dist="MN", sign=0.01)
fit.MN.05=mbacksign(y, X, dist="MN", sign=0.05)
fit.MN.10=mbacksign(y, X, dist="MN", sign=0.10)
summary(fit.MN.01)
summary(fit.MN.05)
summary(fit.MN.10)
##identical process in the MCN model with 
##significance level of 5%
fit.MCN=mbacksign(y, X, dist="MCN")
summary(fit.MCN)
##for MSSL model
fit.MSSL=mbacksign(y, X, dist="MSSL")
summary(fit.MSSL)
##for MSNC model
fit.MSNC=mbacksign(y, X, dist="MSNC")
summary(fit.MSNC)
# }