summary.lts: Summary Method for LTS objects

Description

summary method for class "lts".

Usage

# S3 method for lts
summary(object, correlation = FALSE, …)
# S3 method for summary.lts
print(x, digits = max(3, getOption("digits") - 3),
     signif.stars = getOption("show.signif.stars"), …)

Arguments

object

an object of class "lts", usually, a result of a call to ltsReg.

correlation

logical; if TRUE, the correlation matrix of the estimated parameters is returned and printed.

an object of class "summary.lts", usually, a result of a call to summary.lts.

digits

the number of significant digits to use when printing.

signif.stars

logical indicating if “significance stars” should be printer, see printCoefmat.

…

further arguments passed to or from other methods.

Value

The function summary.lts computes and returns a list of summary statistics of the fitted linear model given in object, using the components of this object (list elements).

residuals

the residuals - a vector like the response y containing the residuals from the weighted least squares regression.

coefficients

a $p \times 4$ matrix with columns for the estimated coefficient, its standard error, t-statistic and corresponding (two-sided) p-value.

sigma

the estimated scale of the reweighted residuals $$\hat\sigma^2 = \frac{1}{n-p}\sum_i{R_i^2},$$ where $R_i$ is the $i$-th residual, residuals[i].

degrees of freedom, a 3-vector $(p, n-p, p*)$, the last being the number of non-aliased coefficients.

fstatistic

(for models including non-intercept terms) a 3-vector with the value of the F-statistic with its numerator and denominator degrees of freedom.

r.squared

$R^2$, the “fraction of variance explained by the model”, $$R^2 = 1 - \frac{\sum_i{R_i^2}}{\sum_i(y_i- y^*)^2},$$ where $y^*$ is the mean of $y_i$ if there is an intercept and zero otherwise.

adj.r.squared

the above $R^2$ statistic “adjusted”, penalizing for higher $p$.

cov.unscaled

a $p \times p$ matrix of (unscaled) covariances of the $\hat\beta_j$, $j=1, \dots, p$.

correlation

the correlation matrix corresponding to the above cov.unscaled, if correlation = TRUE is specified.

Details

These functions compute and print summary statistics for weighted least square estimates with weights based on LTS estimates. Therefore the statistics are similar to those for LS but all terms are multiplied by the corresponding weight.

Correlations are printed to two decimal places: to see the actual correlations print summary(object)$correlation directly.

Examples

Run this code

# NOT RUN {
data(Animals2)
ltsA <- ltsReg(log(brain) ~ log(body), data = Animals2)
(slts <- summary(ltsA))
## non-default options for printing the summary:
print(slts, digits = 5, signif.stars = FALSE)
# }