# heavyLm {heavy}

### Description

This function is used to fit linear models considering heavy-tailed errors. It can be used to carry out univariate or multivariate regression.

### Usage

heavyLm(formula, data, family = Student(df = 4), subset, na.action, control, model = TRUE, x = FALSE, y = FALSE, contrasts = NULL)

### Arguments

- formula
- an object of class
`"formula"`

: a symbolic description of the model to be fitted. - data
- 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. - family
- 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.
- subset
- an optional expression indicating the subset of the rows of data that should be used in the fitting process.
- na.action
- a function that indicates what should happen when the data contain NAs.
- control
- a list of control values for the estimation algorithm to replace the default values returned by the function
`heavy.control`

. - model, x, y
- logicals. If
`TRUE`

the corresponding components of the fit (the model frame, the model matrix, the response) are returned. - contrasts
- an optional list. See the
`contrasts.arg`

of`model.matrix.default`

.

### Details

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.

### Values

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.

- call
- a list containing an image of the
`heavyLm`

call that produced the object. - family
- the
`heavy.family`

object used, with the estimated shape parameters (if requested). - coefficients
- final estimate of the coefficients vector.
- sigma2
- final scale estimate of the random error (only available for univariate regression models).
- Sigma
- estimate of scatter matrix for each row of the response matrix (only available for objects of class
`"heavyMLm"`

). - fitted.values
- the fitted mean values.
- residuals
- the residuals, that is response minus fitted values.
- logLik
- the log-likelihood at convergence.
- numIter
- the number of iterations used in the iterative algorithm.
- weights
- estimated weights corresponding to the assumed heavy-tailed distribution.
- distances
- squared of scaled residuals or Mahalanobis distances.
- acov
- asymptotic covariance matrix of the coefficients estimates.

### References

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.

### Examples

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