Summarising Multi-Parameter Regression (MPR) Fits

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Description

summary method for class “mpr

Usage

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## 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:

g1(λ) = x' β

g2(γ) = z' α

g3(ρ) = w' τ

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 β coefficients, “.a” for α coefficients and “.t” for τ coefficients to avoid ambiguity.

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

H0: β_c = 0

H0: α_c = 0

where β_c and α_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 β and α effects are jointly zero:

H0: β_c = α_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

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# Veterans' administration lung cancer data
data(veteran, package="survival")
head(veteran)

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

summary(mod1)