The function implements linear elliptical regression models, specified by giving a symbolic description of the systematic and stochastic components.
elliptical(formula = formula(data), family = Normal,
data = sys.parent(), 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 vector of weights to be used in the fitting process.
an optional 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 egwr.fit this is passed to glm.control.
a logical value indicating whether model frame should be included as a component of the returned value.
a logical value indicating whether the response vector used in the fitting process should be returned as components of the returned value.
a logical value indicating whether model matrix used in the fitting process should be returned as components of the returned value.
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.
A list of class “elliptical”:
coefficients of location of the model fit.
coefficients of dispersion of the model fit.
the standardized residuals, that is the residuals in the final iteration of the optimization process.
the fitted mean values.
the likelihood logarithm value of the adjusted model's.
the values of the function W_g(u).
the values of the function W^'_g(u).
the values of the function V(u).
the numeric rank of the fitted linear model.
the number of iterations of optimization process.
the values of the 4d_g for the specified distribution.
the values of the 4f_g for the specified distribution.
the values of the scale variance for the specified distribution.
the degrees of freedom for fitted model.
is 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 thecontrol 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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