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

## Description

`summary` method for class “`mpr`

## Usage

 ```1 2``` ```## 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.

`mpr`, `predict.mpr`.
 ```1 2 3 4 5 6 7 8``` ```# 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) ```