summary.mpr: Summarising Multi-Parameter Regression (MPR) Fits

Description

summary method for class “mpr”

Usage

# S3 method for 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.

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”.

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”.

Examples

Run this code

# NOT RUN {
# 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)
# }