summary.SemiParSampleSel: SemiParSampleSel summary

Description

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

Usage

## S3 method for class 'SemiParSampleSel':
summary(object,n.sim=1000,s.meth="svd",sig.lev=0.05,...)

Arguments

object

A fitted SemiParSampleSel object as produced by SemiParSampleSel().

n.sim

The number of simulated coefficient vectors from the posterior distribution of the estimated model parameters. This is used to calculate `confidence' intervals for $\theta$ and $\phi$.

s.meth

Matrix decomposition used to determine the matrix root of the covariance matrix. See the documentation of mvtnorm for further details.

sig.lev

Significance level used for intervals obtained via posterior simulation.

...

Other arguments.

Value

tableP1Table containing parametric estimates, their standard errors, z-values and p-values for equation 1.
tableP2As above but for equation 2.
tableNP1Table of nonparametric summaries for each smooth component including estimated 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.
tableNP2As above but for equation 2.
nSample size.
n.selNumber of selected observations.
sigmaEstimated standard deviation for the response of the outcome equation in the case of normal marginal distribution of the outcome.
shapeEstimated shape parameter for the response of the outcome equation in the case of gamma marginal distribution of the outcome.
phiEstimated dispersion for the response of the outcome equation.
thetaEstimated coefficient linking the two equations.
tauEstimated Kendall's tau association coefficient between the two equations.
formula1Formula used for equation1.
formula2Formula used for equation2.
l.sp1Number of smooth components in equation 1.
l.sp2Number of smooth components in equation 2.
t.edfTotal degrees of freedom of the estimated sample selection model.
CIsig`Confidence' interval for $\sigma$ in the case of normal marginal distribution of the outcome.
CIshape`Confidence' interval for the shape parameter in the case of gamma distribution of the outcome.
CIth`Confidence' intervals for $\theta$.
CIkt`Confidence' intervals for $\tau$.
BivDSelected copula function.
marginsMargins used in the bivariate copula specification.
n.selNumber of selected observations.

Details

As in the package 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. Let $\hat{\bf f}$ and ${\bf V}_f$ denote the vector of values of a smooth term evaluated at the original covariate values and the corresponding Bayesian covariance matrix, and let ${\bf V}_f^{r-}$ denote the rank $r$ pseudoinverse of ${\bf V}_f$. The statistic used is $T=\hat{\bf f}^\prime {\bf V}_f^{r-} \hat{\bf f}$. This is compared to a chi-squared distribution with degrees of freedom given by $r$, which is obtained by biased rounding of the estimated degrees of freedom. See Marra (2013) for further details. Note that covariate selection can also be achieved using a single penalty shrinkage approach as shown in Marra and Wood (2011).

References

Marra G. (2013), On P-values for Semiparametric Bivariate Probit Models. Statistical Methodology, 10(1), 23-28. 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.

Examples

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## see examples for SemiParSampleSel

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