# FMsmsnReg: Linear Regression Models with Finite Mixtures of Skew... In FMsmsnReg: 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

 ```1 2 3 4``` ```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.

`FMsmsnReg`, `ais`, `horses`
 `1` ```#See examples for the FMsmsnReg function linked above. ```