summary.mpr {mpr}

Summarising Multi-Parameter Regression (MPR) Fits

Description

summary method for class “mpr”

Usage

## S3 method for class 'mpr'
summary(object, overall = TRUE, ...)

Arguments

object

an object of class “mpr” which is the result of a call to mpr.

overall

logical. If TRUE, p-values testing the overall effect of a covariate are shown. See “Details” for more information.

...

further arguments passed to or from other methods.

Details

The function print.summary.lm produces a typical table of coefficients, standard errors and p-values along with “significance stars”. In addition, a table of overall p-values are shown.

Multi-Parameter Regression (MPR) models are defined by allowing mutliple distributional parameters to depend on covariates. The regression components are:

g_1(\lambda) = x^T \beta

g_2(\gamma) = z^T \alpha

g_3(\rho) = w^T \tau

and the table of coefficients displayed by print.summary.lm follows this ordering. Furthermore, the names of the coefficients in the table are proceeded by “.b” for \beta coefficients, “.a” for \alpha coefficients and “.t” for \tau coefficients to avoid ambiguity.

Let us assume that a covariate c, say, appears in both the \lambda and \gamma regression components. The standard table of coefficients provides p-values corresponding to the following null hypotheses:

H_0: \beta_c = 0

H_0: \alpha_c = 0

where \beta_c and \alpha_c are the regression coefficients of c (one for each of the two components in which c appears). However, in the context of MPR models, it may be of interest to test the hypothesis that the overall effect of c is zero, i.e., that its \beta and \alpha effects are jointly zero:

H_0: \beta_c = \alpha_c = 0

Thus, if overall=TRUE, print.summary.lm displays a table of such “overall p-values”.

Value

The function summary.mpr returns a list containing the following components:

call

the matched call from the mpr object.

model

a data.frame containing useful information about the fitted model. This is the same as the “model” element of the mpr object - see mpr for details.

coefmat

a typical coefficient matrix whose columns are the estimated regression coefficients, standard errors and p-values.

overallpmat

a matrix containing the overall p-values as described above in “Details”.

Author(s)

Kevin Burke.

See Also

mpr, predict.mpr.

Examples

# Veterans' administration lung cancer data
veteran <- survival::veteran
head(veteran)

# Weibull MPR treatment model (family = "Weibull" by default)
mod1 <- mpr(Surv(time, status) ~ list(~ trt, ~ trt), data=veteran)

summary(mod1)