rMMSN.contour {CensMFM}

Pairwise Scatter Plots and Histograms for Finite Mixture of Multivariate Distributions.

Description

It plots the scatter plots with density contours for different multivariate distributions. Possible options are the Skew-normal (family == "SN"), Normal (family == "Normal") and Student-t (family == "t") distribution. Different colors are used by groups. Histograms are shown in the diagonal.

Usage

rMMSN.contour(model = NULL, y = NULL, mu = NULL, Sigma = NULL,
shape = NULL, nu = NULL, pii = NULL, Zij = NULL,
contour = FALSE, hist.Bin = 30, contour.Bin = 10,
slice = 100, col.names = NULL, length.x = c(0.5, 0.5),
length.y = c(0.5, 0.5), family = "SN")

Arguments

model

is an object resultant from the fit.FMMSNC function.

y

the response matrix with dimension nxp.

mu

a list with g entries, where each entry represents location parameter per group, being a vector of dimension p.

Sigma

a list with g entries, where each entry represents a scale parameter per group, a matrix with dimension pxp.

shape

a list with g entries, where each entry represents a skewness parameter, being a vector of dimension p.

nu

the degrees of freedom for the Student-t distribution case, being a vector with dimension g.

pii

a vector of weights for the mixture of dimension g, the number of clusters. It must sum to one!

Zij

a matrix of dimension nxp indicating the group for each observation.

contour

If contour == TRUE the density contour will be shown, if contour == FALSE the density contour must be not returned.

hist.Bin

number of bins in the histograms. Default is 30.

contour.Bin

creates evenly spaced contours in the range of the data. Default is 10.

slice

desired length of the sequence for the variables grid. This grid is build for the contours.

col.names

names passed to the data matrix y of dimension p.

length.x

a vector of dimension 2 with the value to be subtracted and added from the minimum and maximum observation in the x-axis respectively. Default is c(0.5,0.5).

length.y

a vector of dimension 2 with the value to be subtracted and added from the minimum and maximum observation in the y-axis respectively. Default is c(0.5,0.5).

family

distribution family to be used. Available distributions are the Skew-normal ("SN"), normal ("Normal") or Student-t ("t") distribution.

Details

If the model object is used, the user still has the option to choose the family. If the model object is not used, the user must input all other parameters. User may use the rMMSN function to generate data.

Note

This functions works well for any length of g and p, but contour densities are only shown for p = 2.

Author(s)

Francisco H. C. de Alencar [e-mail], Christian E. Galarza [e-mail], Victor Hugo Lachos [e-mail] and Larissa A. Matos [e-mail]

Maintainer: Francisco H. C. de Alencar [e-mail]

References

Cabral, C. R. B., Lachos, V. H., & Prates, M. O. (2012). Multivariate mixture modeling using skew-normal independent distributions. Computational Statistics & Data Analysis, 56(1), 126-142.

Prates, M. O., Lachos, V. H., & Cabral, C. (2013). mixsmsn: Fitting finite mixture of scale mixture of skew-normal distributions. Journal of Statistical Software, 54(12), 1-20.

C.E. Galarza, L.A. Matos, D.K. Dey & V.H. Lachos. (2019) On Moments of Folded and Truncated Multivariate Extended Skew-Normal Distributions. Technical report. ID 19-14. University of Connecticut.

F.H.C. de Alencar, C.E. Galarza, L.A. Matos & V.H. Lachos. (2019) Finite Mixture Modeling of Censored and Missing Data Using the Multivariate Skew-Normal Distribution. echnical report. ID 19-31. University of Connecticut.

See Also

fit.FMMSNC, rMMSN and fit.FMMSNC

Examples

mu          <- Sigma <- shape <- list()
mu[[1]]     <- c(-3,-4)
mu[[2]]     <- c(2,2)
Sigma[[1]]  <- matrix(c(3,1,1,4.5), 2,2)
Sigma[[2]]  <- matrix(c(2,1,1,3.5), 2,2)
shape[[1]]  <- c(-2,2)
shape[[2]]  <- c(-3,4)
nu          <- 0
pii         <- c(0.6,0.4)
percent     <- c(0.1,0.2)
n <- 100
seed <- 654678

set.seed(seed)
test = rMMSN(n = n, pii = pii,mu = mu,Sigma = Sigma,shape = shape,
percent = percent, each = TRUE, family = "SN")


## SN ##
SN.contour = rMMSN.contour(model = NULL, y = test$y, Zij = test$G
,mu = mu, Sigma = Sigma, shape = shape, pii = pii, family = "SN")

#Plotting contours may take some time...

## SN ##
SN.contour = rMMSN.contour(model = NULL, y = test$y, Zij = test$G
,mu = mu, Sigma = Sigma, shape = shape, pii = pii, contour = TRUE,
family = "SN")

## Normal ##
N.contour = rMMSN.contour(model = NULL,y = test$y, Zij = test$G
,mu = mu, Sigma = Sigma, shape = shape, pii = pii, contour = TRUE,
family = "Normal")

## t ##
t.contour = rMMSN.contour(model = NULL,y = test$y, Zij = test$G
,mu = mu, Sigma = Sigma, shape = shape, pii = pii, nu = c(4,3),
contour = TRUE, family = "t")