summary.SemiParBIV: SemiParBIV summary

In GJRM: Generalised Joint Regression Modelling

SemiParBIV summary

Description

It takes a fitted SemiParBIV object and produces some summaries from it.

Usage

## S3 method for class 'SemiParBIV'
summary(object, n.sim = 100, prob.lev = 0.05, gm = FALSE, ...)
        
## S3 method for class 'summary.SemiParBIV'
print(x, digits = max(3, getOption("digits") - 3), 
           signif.stars = getOption("show.signif.stars"), ...)    
                      

Arguments

object	A fitted SemiParBIV object.
x	summary.SemiParBIV object produced by summary.SemiParBIV().
n.sim	The number of simulated coefficient vectors from the posterior distribution of the estimated model parameters. This is used to calculate intervals for the association parameter, dispersion coefficient and other measures (e.g., gamma measure). It may be increased if more precision is required.
prob.lev	Probability of the left and right tails of the posterior distribution used for interval calculations.
gm	If TRUE then intervals for the gamma measure and odds ratio are calculated.
digits	Number of digits printed in output.
signif.stars	By default significance stars are printed alongside output.
...	Other arguments.

Details

Using some low level functions in mgcv, based on the results of Marra and Wood (2012), ‘Bayesian p-values’ are returned for the smooth terms. These have better frequentist performance than their frequentist counterpart. See the help file of summary.gam in mgcv for further details. Covariate selection can also be achieved using a single penalty shrinkage approach as shown in Marra and Wood (2011).

Posterior simulation is used to obtain intervals of nonlinear functions of parameters, such as the association and dispersion parameters as well as the odds ratio and gamma measure discussed by Tajar et al. (2001) if gm = TRUE.

print.summary.SemiParBIV prints model term summaries.

Value

tableP1	Table containing parametric estimates, their standard errors, z-values and p-values for equation 1.
tableP2, tableP3, ...	As above but for equation 2 and equations 3 and 4 if present.
tableNP1	Table of nonparametric summaries for each smooth component including effective degrees of freedom, estimated rank, approximate Wald statistic for testing the null hypothesis that the smooth term is zero and corresponding p-value, for equation 1.
tableNP2, tableNP3, ...	As above but for equation 2 and equations 3 and 4 if present.
n	Sample size.
theta	Estimated dependence parameter linking the two equations.
formula1, formula2, formula3, ...	Formulas used for the model equations.
l.sp1, l.sp2, l.sp3, ...	Number of smooth components in model equations.
t.edf	Total degrees of freedom of the estimated bivariate model.
CItheta	Interval(s) for \theta.
n.sel	Number of selected observations in the sample selection case.
OR, CIor	Odds ratio and related CI. The odds ratio is a measure of association between binary random variables and is defined as p00p11/p10p01. In the case of independence this ratio is equal to 1. It can take values in the range (-Inf, Inf) and it does not depend on the marginal probabilities (Tajar et al., 2001). Interval is calculated using posterior simulation.
GM, CIgm	Gamma measure and related CI. This measure of association was proposed by Goodman and Kruskal (1954). It is defined as (OR - 1)/(OR + 1), can take values in the range (-1, 1) and does not depend on the marginal probabilities. Interval is calculated using posterior simulation.

WARNINGS

Note that the Kendall's tau (and related interval), as implemented here, is a valid measure of dependence for continuous margins and it will only provide a crude indication of dependence in other cases.

Author(s)

Maintainer: Giampiero Marra [e-mail]

References

Marra G. and Wood S.N. (2011), Practical Variable Selection for Generalized Additive Models. Computational Statistics and Data Analysis, 55(7), 2372-2387.

Marra G. and Wood S.N. (2012), Coverage Properties of Confidence Intervals for Generalized Additive Model Components. Scandinavian Journal of Statistics, 39(1), 53-74.

Tajar M., Denuit M. and Lambert P. (2001), Copula-Type Representation for Random Couples with Bernoulli Margins. Discussion Papaer 0118, Universite Catholique De Louvain.

See Also

ATE, prev

GJRM documentation built on Oct. 25, 2024, 5:07 p.m.