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.
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 (only 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.
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.
Documentation reproduced from package heavy, version 0.38. License: GPL (>= 2)