summary.SemiParSampleSel: SemiParSampleSel summary

Description

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

Usage

# S3 method for SemiParSampleSel
summary(object, n.sim=1000, s.meth="svd", prob.lev=0.05, 
                  cm.plot = FALSE, xlim = c(-3, 3), ylab = "Outcome margin",
                  xlab = "Selection margin", ...)

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.

prob.lev

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

cm.plot

If TRUE display contour plot of the model based on average parameter values.

xlim

Maximum and minimum values of the selection margin to be displayed by cm.plot.

ylab

Label of the outcome margin axis.

xlab

Label of the selection margin axis.

...

Other arguments.

Value

tableP1

Table containing parametric estimates, their standard errors, z-values and p-values for equation 1.

tableP2,tableP3,tableP4,tableP5

As above but for equation 2, and equations 3, 4 and 5 if present.

tableNP1

Table 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.

tableNP2,tableNP3,tableNP4,tableNP5

As above but for equation 2 and equations 3, 4 and 5 if present.

Sample size.

n.sel

Number of selected observations.

sigma

Estimated standard deviation for the response of the outcome equation in the case of normal marginal distribution of the outcome.

shape

Estimated shape parameter for the response of the outcome equation in the case of gamma marginal distribution of the outcome.

phi

Estimated dispersion for the response of the outcome equation.

theta

Estimated coefficient linking the two equations.

Estimated coefficient for the response of the outcome equation when the Delaporte and Sichel distributions are employed.

formula1,formula2,formula3,formula4,formula5

Formulas used for equations 1, 2, 3, 4 and 5.

l.sp1,l.sp2,l.sp3,l.sp4,l.sp5

Number of smooth components in equations 1, 2, 3, 4 and 5.

t.edf

Total 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.

CInu

`Confidence' interval for the shape parameter in the case of a discrete distribution of the outcome.

CIth

`Confidence' intervals for \(\theta\).

BivD

Selected copula function.

margins

Margins used in the bivariate copula specification.

n.sel

Number of selected observations.

Details

Using a low level function 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. 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.

Covariate selection can also be achieved using a single penalty shrinkage approach as shown in Marra and Wood (2011).

See Wojtys et al. (in press) for further details.

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.

Wojtys M., Marra G. and Radice R. (in press), Copula Regression Spline Sample Selection Models: The R Package SemiParSampleSel. Journal of Statistical Software.

Examples

Run this code

## see examples for SemiParSampleSel

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