FMshnReg {bssn} R Documentation

## Linear regression models using finite mixture of Sinh-normal distribution

### Description

Performs the EM-type algorithm with conditonal maximation to perform maximum likelihood inference of the parameters of the proposed model based on the assumption that the error term follows a finite mixture of Sinh-normal distributions.

### Usage

```FMshnReg(y, x1, alpha = NULL, Abetas = NULL, medj=NULL,
pii = NULL, g = NULL, get.init = TRUE,algorithm = "K-means",
accuracy = 10^-6, show.envelope="FALSE", iter.max = 100)
```

### Arguments

 `y` the response matrix (dimension nx1). `x1` Matrix or vector of covariates. `alpha` Value of the shape parameter 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). `Abetas` Parameters of vector regression dimension (p + 1) include intercept. `medj` a list of `g` arguments of vectors of values (dimension p) for the location parameters. `pii` 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. `algorithm` clustering procedure of a series of vectors according to a criterion. The clustering algorithms may classified in 4 main categories: exclusive, overlapping, hierarchical and probabilistic. `accuracy` The convergence maximum error. `show.envelope` Logical; if TRUE, show the simulated envelope for the fitted model. `iter.max` The maximum number of iterations of the EM algorithm

### Value

The function returns a list with 10 elements detailed as

 `iter` Number of iterations. `criteria` Attained criteria value. `convergence` Convergence reached or not. `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. `LK` log-likelihood. `AIC` Akaike information criterion. `BIC` Bayesian information criterion. `EDC` Efficient Determination criterion. `time` Processing time.

### Author(s)

Rocio Maehara rmaeharaa@gmail.com and Luis Benites lbenitesanchez@gmail.com

### References

Maehara, R. and Benites, L. (2020). Linear regression models using finite mixture of Sinh-normal distribution. In Progress.

Bartolucci, F. and Scaccia, L. (2005). The use of mixtures for dealing with non-normal regression errors, Computational Statistics & Data Analysis 48(4): 821-834.

### Examples

```## Not run:
#Using the AIS data

library(FMsmsnReg)
data(ais)

#################################
#The model
x1    <- cbind(1,ais\$SSF,ais\$Ht)
y     <- ais\$Bfat

library(ClusterR) #This library is useful for using the k-medoids algorithm.

FMshnReg(y, x1, get.init = TRUE, g=2, algorithm="k-medoids",
accuracy = 10^-6, show.envelope="FALSE", iter.max = 1000)

#########################################
#A simple output example

------------------------------------------------------------
Finite Mixture of Sinh Normal Regression Model
------------------------------------------------------------

Observations = 202

-----------
Estimates
-----------

Estimate      SE
alpha1  0.81346 0.10013
alpha2  3.04894 0.32140
beta0  15.08998 1.70024
beta1   0.17708 0.00242
beta2  -0.07687 0.00934
mu1    -0.25422 0.18069
mu2     0.37944 0.38802
pii1    0.59881 0.41006

------------------------
Model selection criteria
------------------------

Loglik    AIC     BIC     EDC
Value -355.625 721.25 737.791 725.463

-------
Details
-------

Convergence reached? = TRUE
EM iterations = 39 / 1000
Criteria = 6.58e-07
Processing time = 0.725559 secs

## End(Not run)
```

[Package bssn version 1.0 Index]