# summary.SemiParSampleSel: SemiParSampleSel summary In SemiParSampleSel: Semi-Parametric Sample Selection Modelling with Continuous or Discrete Response

## Description

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

## Usage

 1 2 3 4 ## S3 method for class '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 θ and φ. 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.

## 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 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 V_f^{r-} denote the rank r pseudoinverse of 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.

## 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. n 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. nu 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 σ 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 θ. BivD Selected copula function. margins Margins used in the bivariate copula specification. n.sel Number of selected observations.

## Author(s)

Maintainer: Giampiero Marra [email protected]

## 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.

SemiParSampleSelObject, plot.SemiParSampleSel, predict.SemiParSampleSel
 1 ## see examples for SemiParSampleSel