Package 'FMsmsnReg'

Linear Regression Models with Finite Mixtures of Skew Heavy-Tailed Errors

Description

This package contains a principal function that performs to estimate the parameters of a regression model considering an error that follows a finite mixture of Skew Heavy-Tailed Errors, using an analytically simple and efficient EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters.

Details

Package:	FMsmsnsReg
Type:	Package
Version:	1.0
Date:	2016-03-30
License:	GPL (>=2)

Author(s)

Luis Benites Sanchez [email protected], Rocio Paola Maehara [email protected] and Victor Hugo Lachos [email protected]

References

Basso, R. M., Lachos, V. H., Cabral, C. R., Ghosh, P., 2010. Robust mixture modeling based on scale mixtures of skew - normal distributions. Computational Statistics & Data Analysis.

Lachos, V. H., Ghosh, P., Arellano-Valle, R. B., 2010. Likelihood based inference for skew-normal independent linear mixed models. Statistica Sinica 20, 303 - 322.

See Also

FMsmsnReg

Examples

#See examples for the FMsmsnReg function linked above.

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Australian institute of sport data

Description

Data on 102 male and 100 female athletes collected at the Australian Institute of Sport.

Format

This data frame contains the following columns:

Sex

(0 = male or 1 = female)

Ht

height (cm)

Wt

weight (kg)

LBM

lean body mass

RCC

red cell count

WCC

white cell count

Hc

Hematocrit

Hg

Hemoglobin

Ferr

plasma ferritin concentration

BMI

body mass index, weight/height^2

SSF

sum of skin folds

Bfat

Percent body fat

Label

Case Labels

Sport

Sport

References

S. Weisberg (2005). Applied Linear Regression, 3rd edition. New York: Wiley, Section 6.4

Examples

##Load the data
 library(FMsmsnReg)
 data(ais)
 attach(ais)
#Set the response y and covariate x
 x1    <- cbind(1,SSF,Ht)
 y     <- Bfat

##Fits a linear Regression Model with Finite Mixtures of Skew t
 parST <- FMsmsnReg(y, x1, g=2, get.init = TRUE, criteria = TRUE,
          group = FALSE,family = "Skew.t", error = 10^-4,
          iter.max = 2000,obs.prob= FALSE, kmeans.param = NULL,show.converge=FALSE,cp=0.5)

##Fits a linear Regression Models with Finite Mixtures of Skew normal
 parSN <- FMsmsnReg(y, x1, g=2, get.init = TRUE, criteria = TRUE,
          group = FALSE,family = "Skew.normal", error = 10^-4,
          iter.max = 5000,obs.prob= FALSE, kmeans.param = NULL,show.converge=FALSE,cp=0.5)

##Fits a linear Regression Models with Finite Mixtures of Skew Contaminated Normal
 parCN <- FMsmsnReg(y, x1, g=2, get.init = TRUE, criteria = TRUE,
          group = FALSE,family = "Skew.cn", error = 10^-4,
          iter.max = 5000,obs.prob= FALSE, kmeans.param = NULL,show.converge=FALSE,cp=0.5)

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Linear Regression Models with Finite Mixtures of Skew Heavy-Tailed Errors

Description

Performs a Finite Mixture of Scale Mixture Skew Normal Regression Model using EM-type algorithm (ECME) for iteratively computing maximum likelihood estimates of the parameters.

Usage

FMsmsnReg(y, x1, Abetas = NULL, medj= NULL, sigma2 = NULL, shape = NULL,
pii = NULL, g = NULL, get.init = TRUE, criteria = TRUE, group = FALSE,
family = "Skew.normal", error = 0.00001, iter.max = 100, obs.prob= FALSE,
kmeans.param = NULL, show.convergence=TRUE, cp=0.4)

Arguments

y	the response matrix (dimension nx1)
x1	Matrix or vector of covariates.
Abetas	Parameters of vector regression dimension $(p + 1)$ include intercept
medj	a list of g arguments of vectors of initial values (dimension p) for the location parameters
sigma2	a list of g arguments of matrices of initial values (dimension pxp) for the scale parameters
shape	a list of g arguments of vectors of initial values (dimension p) for the skewness parameters
pii	Initial value for the EM algorithm. Each of them must be a vector of length g. (the algorithm considers the number of components to be adjusted based on the size of these vectors)
g	the number of cluster to be considered in fitting
get.init	if TRUE, the initial values are generated via k-means
criteria	It indicates if are calculated the criterion selection methods (AIC, BIC, EDC and ICL)
group	if TRUE, the vector with the classification of the response is returned
family	distribution famility to be used in fitting (Skew.t", "Skew.cn", "Skew.slash", "Skew.normal")
error	define the stopping criterion of the algorithm
iter.max	the maximum number of iterations of the EM algorithm
obs.prob	if TRUE, the posterior probability of each observation belonging to one of the g groups is reported
kmeans.param	a list with alternative parameters for the kmeans function when generating initial values, list(iter.max = 10, n.start = 1, algorithm = "Hartigan-Wong")
show.convergence	graphics of convergence for the parameters
cp	Cut Point

Value

The function returns a list with 16 elements detailed as

iter	Number of iterations.
criteria	Attained criteria value.
convergence	Convergence reached or not.
mu	Location parameter estimate.
sigma2	Scale parameter estimate.
lambda	Shape parameter estimate.
pii	Weight parameter estimate.
nu	Estimated degrees of freedom parameter.
SE	Standard Error estimates, if the output shows NA the function does not provide the standard error for this parameter.
table	Table containing the inference for the estimated parameters.
loglik	Log-likelihood value.
AIC	Akaike information criterion.
BIC	Bayesian information criterion.
EDC	Efficient Determination Criterion.
ICL	Information Completed Likelihood.
time	Processing time.

Author(s)

Luis Benites Sanchez [email protected] and Rocio Paola Maehara [email protected] and Victor Hugo Lachos [email protected]

References

Basso, R. . M., Lachos, V. H., Cabral, C. R., Ghosh, P., 2010. Robust mixture modeling based on scale mixtures of skew-normal distributions. Computational Statistics & Data Analysis doi:10.1016/j.csda.2009.09.031.

Lachos, V. H., Ghosh, P., Arellano-Valle, R. B., 2010. Likelihood based inference for skew - normal independent linear mixed models. Statistica Sinica 20, 303 - 322.

See Also

FMsmsnReg, ais, horses

Examples

#See examples for the FMsmsnReg function linked above.

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Horse Racing at Eagle Farm data

Description

Results of horse races at Eagle Farm, Brisbane, on 31 August 1998. The data, collected by Donald Forbes for his MS305 Data Analysis Project, give results for each horse in a sequence of 8 races.

Format

This data frame contains the following columns:

Position

(Finishing position)

Starters

Number of horses in race

Last

Finishing position in last race

Since

Days since last race

Number

Identifying number of horse in race

Carried

Weight carried

Weight

Handicap weight

Barrier

Barrier position at start of race

Distance

Length of race

Lengths

Number of lengths that horse finished from winner

Odds

Starting odds

Starts

Number of races previously started in

Age

Age of horse in years

Ratio

Proportion of wins in previous starts

References

Forbes, D. (1998). A Day at the Races. MS305 Data Analysis Project, Department of Mathematics, University of Queensland.

Examples

##Load the data
 library(FMsmsnReg)
 data(horses)
 attach(horses)

#Set the response y and covariate x
 x1 <- cbind(1,Last,Carried)
 y  <- Position

##Fits a linear Regression Model with Finite Mixtures of Skew Contaminated Normal

parCN  <- FMsmsnReg(y, x1, g=2, get.init = TRUE, criteria = TRUE, group = FALSE,
         family = "Skew.cn", error = 10^-4, iter.max = 5000,obs.prob= FALSE,
         kmeans.param = NULL,show.converge=FALSE,cp=0.5)

##Fits a linear Regression Model with Finite Mixtures of Skew normal
 parSN <- FMsmsnReg(y, x1, g=2, get.init = TRUE, criteria = TRUE,
          group = FALSE,family = "Skew.normal", error = 10^-4,
          iter.max = 5000,obs.prob= FALSE, kmeans.param = NULL,show.converge=FALSE,cp=0.5)

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