# elliptical: Fitting Elliptical Regression Models In gwer: Geographically Weighted Elliptical Regression

## Description

The function `elliptical` is used to fit linear elliptical regression models. This models is specified giving a symbolic description of the systematic and stochastic components.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```elliptical( formula = formula(data), family = Normal, data, dispersion = NULL, weights, subset, na.action = "na.fail", method = "elliptical.fit", control = glm.control(epsilon = 1e-04, maxit = 100, trace = F), model = F, x = F, y = T, contrasts = NULL, offset, ... ) ```

## Arguments

 `formula` regression model formula of a formula `object`. `family` a description of the error distribution to be used in the model (see `family.elliptical` for details of elliptical distribution). `data` an optional data frame, list or environment containing the variables in the model. `dispersion` an optional fixed value for dispersion parameter. `weights` an optional numeric vector of “prior weights” to be used in the fitting process. `subset` an optional numeric vector specifying a subset of observations to be used in the fitting process. `na.action` a function which indicates what should happen when the data contain NAs (see `glm`). `method` optimization method used to estimate the model parameters. The default method "elliptical.fit" uses Fisher's scoring method. The alternative "model.frame" returns the model frame and does no fitting. `control` a list of parameters for controlling the fitting process. This is passed by `glm.control`. `model` a logical value indicating whether model frame should be included as a component of the return. `x` a logical value indicating whether the response vector used in the fitting process should be returned as components of the return. `y` a logical value indicating whether model matrix used in the fitting process should be returned as components of the return. `contrasts` an optional list. See the `contrasts.arg` of `model.matrix.default`. `offset` this can be used to specify a “prior known component” to be included in the linear predictor during fitting (as in `glm`). `...` arguments to be used to form the default control argument if it is not supplied directly.

## Value

returns an object of class “elliptical”, a list with follow components:

 `coefficients` coefficients of location parameters. `dispersion` coefficient of dispersion parameter. `residuals` standardized residuals. `fitted.values` the fitted mean values. `loglik` the likelihood logarithm value for the fitted model. `Wg` values of the function `W_g(u)`. `Wgder` values for the function `W^{(1)}_g(u)`. `v` values for the function `V(u)`. `rank` the numeric rank for the fitted model. `R` the matrix of correlation for the estimated parameters. `inter` number of iterations of optimization process. `scale` values of the `4d_g` for the specified distribution. `scaledispersion` values of the `4f_g` for the specified distribution. `scalevariance` values of the scale variance for the specified distribution. `df` degree of freedom for t-student distribution. `s, r` shape parameters for generalized t-student distribution. `alpha` shape parameter for contaminated normal and generalized logistic distributions. `mp` shape parameter for generalized logistic distribution. `epsi,sigmap` dispersion parameters for contaminated normal distribution. `k` shape parameter for power exponential distribution. `Xmodel` the model matrix. `weights` the working weights, that is the weights in the final iteration of optimization process `df.residuals` the residual degrees of freedom. `family` the `family` object used. `formula` the `formula` supplied. `terms` the `terms` object used. `contrasts` (where relevant) the contrasts used. `control` the value of the `control` argument used. `call` the matched call. `y` the response variable used.

## References

Cysneiros, F. J. A., Paula, G. A., and Galea, M. (2007). Heteroscedastic symmetrical linear models. Statistics & probability letters, 77(11), 1084-1090. doi: 10.1016/j.spl.2007.01.012

Fang, K. T., Kotz, S. and NG, K. W. (1990, ISBN:9781315897943). Symmetric Multivariate and Related Distributions. London: Chapman and Hall.

`glm`, `family.elliptical`, `summary.elliptical`
 ``` 1 2 3 4 5 6 7 8 9 10``` ```data(luzdat) y <- luzdat\$y x1 <- luzdat\$x1 ; x1 <- factor(x1) ; x1 <- C(x1,treatment) x2 <- luzdat\$x2 x3 <- (luzdat\$x2)^2 luz <- data.frame(y,x1,x2,x3) elliptical.fitt <- elliptical(y ~ x1+x2+x3, family = Student(df=5) ,data=luz) elliptical.fitLII <- elliptical(y ~ x1+x2+x3, family = LogisII() ,data=luz) ```