distMahal | R Documentation |
Compute and plot the Mahalanobis distance for any supported 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 supported distributions.
distMahal(object, alpha = 0.95, ...)
object |
an object of class "skewMLRM" returned by one of the following functions: estimate.xxx, choose.yyy, choose2, mbackcrit or mbacksign. See details for supported distributions. |
alpha |
significance level (0.05 by default). |
... |
aditional graphical parameters |
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.
distMahal provides an object of class skewMLRM related to compute the Mahalanobis distance for all the observations and a cut-off to detect possible influent observations based on the specified significance (0.05 by default).
an object of class "skewMLRM" is returned. The object returned for this functions is a list containing the following components:
Mahal |
the Mahalanobis distance for all the observations |
function |
a string with the name of the used function. |
dist |
The distribution for which was performed the estimation. |
class |
The class for which was performed the estimation. |
alpha |
specified level of significance (0.05 by default). |
cut |
the cut-off to detect possible influent observations based on the specified significance. |
y |
The multivariate vector of responses. The univariate case also is supported. |
X |
The regressor matrix (in a list form). |
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.
set.seed(2020)
n=200 # length of the sample
nv<-3 # number of explanatory variables
p<-nv+1 # nv + intercept
m<-4 # dimension of Y
q0=p*m
X<-array(0,c(q0,m,n))
for(i in 1:n) {
aux=rep(1,p)
aux[2:p]<-rMN(1,mu=rnorm(nv),Sigma=diag(nv)) ##simulating covariates
mi=matrix(0,q0,m)
for (j in 1:m) mi[((j-1)*p+1):(j*p),j]=aux
X[,,i]<-mi
} ##X is the simulated regressor matrix
betas<-matrix(rnorm(q0),ncol=1) ##True betas
Sigmas <- clusterGeneration::genPositiveDefMat(m,rangeVar=c(1,3),
lambdaLow=1, ratioLambda=3)$Sigma ##True Sigma
y=matrix(0,n,m)
for(i in 1:n) {
mui<-t(X[,,i])%*%betas
y[i,]<-rMN(n=1,c(mui),Sigmas) ## simulating the response vector
}
fit.MN=estimate.MN(y,X) #fit the MN model
mahal.MN=distMahal(fit.MN) #compute the Mahalanobis distances for MN model
plot(mahal.MN) #plot the Mahalanobis distances for MN model
mahal.MN$Mahal #presents the Malahanobis distances
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