`summary`

method for class “`mpr`

”

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`object` |
an object of class “ |

`overall` |
logical. If |

`...` |
further arguments passed to or from other methods. |

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”.

The function `summary.mpr`

returns a `list`

containing the following components:

`call` |
the matched call from the |

`model` |
a |

`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”. |

Kevin Burke.

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