summary.SemiParBIVProbit: SemiParBIVProbit summary

Description

It takes a fitted SemiParBIVProbit object produced by SemiParBIVProbit() and produces some summaries from it.

Usage

## S3 method for class 'SemiParBIVProbit':
summary(object, n.sim = 100, prob.lev = 0.05, cm.plot = FALSE, 
        xlim = c(-3, 3), ylim = c(-3, 3), 
        ylab = "Margin 2", xlab = "Margin 1", gm = FALSE, ...)

Arguments

object

A fitted SemiParBIVProbit object as produced by SemiParBIVProbit().

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

prob.lev

Probability of the left and right tails of the posterior distribution used for interval calculations.

cm.plot

If TRUE then a filled bivariate contour meta plot corresponding to the assumed bivariate model errors with estimated association parameter (and dispersion parameter if present) is produced.

xlim, ylim

Limits of the bivariate contour meta plot.

ylab, xlab

Labels for the bivariate contour meta plot.

If TRUE then intervals for the gamma measure and odds ratio are calculated.

...

Other graphics parameters to pass on to plotting commands. These are used only when cm.plot=TRUE.

Value

tableP1Table 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.
tableNP1Table 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.
nSample size.
thetaEstimated 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.edfTotal degrees of freedom of the estimated bivariate model.
CIthetaInterval(s) for $\theta$.
n.selNumber of selected observations in the sample selection case.
OR, CIorOdds 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, CIgmGamma 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.

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. The bivariate contour meta plot has been introduced to provide the user with a pictorial representation of the latent distribution of the model errors.

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.

Examples

Run this code

## see examples for SemiParBIVProbit

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