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

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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

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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 lbenitesanchez@gmail.com and Rocio Paola Maehara rmaeharaa@gmail.com and Victor Hugo Lachos hlachos@ime.unicamp.br

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

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#See examples for the FMsmsnReg function linked above.