The function implements linear elliptical regression models. This models is specified giving a symbolic description of the systematic and stochastic components.
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,
...
)regression model formula as in glm.
a description of the error distribution to be used in the model (see elliptical.family for details of family functions).
an optional data frame, list or environment containing the variables in the model.
an optional fixed value for dispersion parameter.
an optional numeric vector of weights to be used in the fitting process.
an optional numeric vector specifying a subset of observations to be used in the fitting process.
a function which indicates what should happen when the data contain NAs (see glm).
optimization method used to estimate the parameters. The default method "elliptical.fit" uses Fisher's scoring method. The alternative "model.frame" returns the model frame and does no fitting.
a list of parameters for controlling the fitting process. For elliptical this is passed by glm.control.
a logical value indicating whether model frame should be included as a component of the return.
a logical value indicating whether the response vector used in the fitting process should be returned as components of the return.
a logical value indicating whether model matrix used in the fitting process should be returned as components of the return.
an optional list. See the contrasts.arg of model.matrix.default.
this can be used to specify an a priori 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.
returns an object of class “elliptical”, a list with follow components:
coefficients of location parameters.
coefficient of dispersion parameter.
standardized residuals.
the fitted mean values.
the likelihood logarithm value for the fitted model.
values of the function W_g(u).
values for the function W^{(1)}_g(u).
values for the function V(u).
the numeric rank for the fitted model.
the matrix of correlation for the estimated parameters.
number of iterations of optimization process.
values of the 4d_g for the specified distribution.
values of the 4f_g for the specified distribution.
values of the scale variance for the specified distribution.
degree of freedom for t-student distribution.
shape parameters for generalized t-student distribution.
shape parameter for contaminated normal and generalized logistic distributions.
shape parameter for generalized logistic distribution.
dispersion parameters for contaminated normal distribution.
shape parameter for power exponential distribution.
the model matrix.
the working weights, that is the weights in the final iteration of optimization process
the residual degrees of freedom.
the family object used.
the formula supplied.
the terms object used.
(where relevant) the contrasts used.
the value of the control argument used.
the matched call.
the response variable used.
Cysneiros, F. J. A., Paula, G. A., and Galea, M. (2007). Heteroscedastic symmetrical linear models. Statistics & probability letters, 77(11), 1084-1090. https://doi.org/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.
# NOT RUN {
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)
# }
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