Summarising Multi-Parameter Regression (MPR) Fits
summary method for class “
an object of class “
further arguments passed to or from other methods.
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 “
β coefficients, “
.a” for α coefficients and “
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
print.summary.lm displays a table of such “overall p-values”.
summary.mpr returns a
list containing the following components:
the matched call from the
a typical coefficient matrix whose columns are the estimated regression coefficients, standard errors and p-values.
a matrix containing the overall p-values as described above in “Details”.
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