Description Usage Arguments Details Value References Examples
This function is used to fit linear models considering heavy-tailed errors. It can be used to carry out univariate or multivariate regression.
1 2 |
formula |
an object of class |
data |
an optional data frame containing the variables in the model. If
not found in |
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 |
model, x, y |
logicals. If |
contrasts |
an optional list. See the |
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.
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 |
family |
the |
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 |
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. |
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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | # 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
# fixing the degrees of freedom at df = 5
fit <- heavyLm(m.marietta ~ CRSP, data = ereturns, family = Student(df = 5),
control = heavy.control(fix.shape = TRUE))
summary(fit)
|
Linear model under heavy-tailed distributions
Data: ereturns; Family: Student(df = 2.83727)
Residuals:
Min 1Q Median 3Q Max
-0.142237 -0.036156 0.003433 0.041310 0.546533
Coefficients:
Estimate Std.Error Z value p-value
(Intercept) -0.0072 0.0082 -0.8876 0.3748
CRSP 1.2637 0.1902 6.6459 0.0000
Degrees of freedom: 60 total; 58 residual
Scale estimate: 0.002520786
Log-likelihood: 71.81295 on 3 degrees of freedom
Call:
heavyLm(formula = cbind(y1, y2, y3, y4) ~ -1 + centre, data = dialyzer,
family = slash(df = 1.2294))
Converged in 71 iterations
Coefficients:
y1 y2 y3 y4
centre1 540.0177 971.5955 1404.2510 1876.3671
centre2 464.4656 845.0920 1259.5509 1683.8693
centre3 590.9750 856.7526 1273.4876 1660.6286
Degrees of freedom: 40 total; 37 residual
Linear model under heavy-tailed distributions
Data: ereturns; Family: Student(df = 5)
Residuals:
Min 1Q Median 3Q Max
-0.144574 -0.037252 0.002193 0.041296 0.542015
Coefficients:
Estimate Std.Error Z value p-value
(Intercept) -0.0064 0.0086 -0.7475 0.4547
CRSP 1.2951 0.2000 6.4747 0.0000
Degrees of freedom: 60 total; 58 residual
Scale estimate: 0.003182504
Log-likelihood: 70.75718 on 3 degrees of freedom
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