Description Usage Arguments Details Value Author(s) References Examples

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).

1 2 3 |

`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. |

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. |

`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 |

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
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)
``` |

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