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

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.

See Also

glm, family.elliptical, summary.elliptical

Examples

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)

gwer documentation built on April 28, 2021, 9:07 a.m.