This function is used to fit linear models considering heavy-tailed errors. It can be used to carry out univariate or multivariate regression.
heavyLm(formula, data, family = Student(df = 4), subset, na.action,
control, model = TRUE, x = FALSE, y = FALSE, contrasts = NULL)
an object of class "formula"
: a symbolic description of
the model to be fitted.
an optional data frame containing the variables in the model. If
not found in data
, the variables are taken from environment(formula)
,
typically the environment from which heavyLm
is called.
a description of the error distribution to be used in the model. By default the Student-t distribution with 4 degrees of freedom is considered.
an optional expression indicating the subset of the rows of data that should be used in the fitting process.
a function that indicates what should happen when the data contain NAs.
a list of control values for the estimation algorithm to replace
the default values returned by the function heavy.control
.
logicals. If TRUE
the corresponding components of
the fit (the model frame, the model matrix, the response) are returned.
an optional list. See the contrasts.arg
of model.matrix.default
.
An object of class "heavyLm"
or "heavyMLm"
for multiple responses
which represents the fitted model. Generic functions print
and summary
,
show the results of the fit.
The following components must be included in a legitimate "heavyLm"
object.
a list containing an image of the heavyLm
call that produced the object.
the heavy.family
object used, with the estimated shape parameters (if requested).
final estimate of the coefficients vector.
final scale estimate of the random error (only available for univariate regression models).
estimate of scatter matrix for each row of the response matrix (only available for objects of class "heavyMLm"
).
the fitted mean values.
the residuals, that is response minus fitted values.
the log-likelihood at convergence.
the number of iterations used in the iterative algorithm.
estimated weights corresponding to the assumed heavy-tailed distribution.
squared of scaled residuals or Mahalanobis distances.
asymptotic covariance matrix of the coefficients estimates.
Models for heavyLm
are specified symbolically (for additional information see the "Details"
section from lm
function). If response
is a matrix, then a multivariate linear
model is fitted.
Dempster, A.P., Laird, N.M., and Rubin, D.B. (1980). Iteratively reweighted least squares for linear regression when errors are Normal/Independent distributed. In P.R. Krishnaiah (Ed.), Multivariate Analysis V, p. 35-57. North-Holland.
Lange, K., and Sinsheimer, J.S. (1993). Normal/Independent distributions and their applications in robust regression. Journal of Computational and Graphical Statistics 2, 175-198.
# NOT RUN {
# univariate linear regression
data(ereturns)
fit <- heavyLm(m.marietta ~ CRSP, data = ereturns, family = Student(df = 5))
summary(fit)
# multivariate linear regression
data(dialyzer)
fit <- heavyLm(cbind(y1,y2,y3,y4) ~ -1 + centre, data = dialyzer, family = slash(df = 4))
fit
# }
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