mbacksign: Multivariate Backward Based on Significance
In skewMLRM: Estimation for Scale-Shape Mixtures of Skew-Normal Distributions

Description Usage Arguments Details Value Author(s) References Examples

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.

1 2	mbacksign(y, X = NULL, max.iter = 1000, prec = 1e-04, dist = "MN", significance = 0.05, ...)

`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.

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.

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.

Clecio Ferreira, Diego Gallardo and Camila Zeller.

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.

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% 

##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)