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
- 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
- model, x, y
- logicals. If
TRUEthe corresponding components of the fit (the model frame, the model matrix, the response) are returned.
- an optional list. See the
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.
An object of class
"heavyMLM" for multiple responses which represents the fitted model. Generic functions
summary, show the results of the fit. The following components must be included in a legitimate
- a list containing an image of the
heavyLmcall that produced the object.
heavy.familyobject 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 (available for objects of class
- 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.
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.
Documentation reproduced from package heavy, version 0.3. License: GPL (>= 2)