SemiParBIVProbit-package: Semiparametric Bivariate Probit Modelling
Description
SemiParBIVProbit provides a function for bivariate probit modelling with semiparametric
predictors, including linear and nonlinear effects. Several bivariate copula distributions and asymmetric link
functions are also supported.Details
SemiParBIVProbit provides a function for flexible bivariate probit modelling, in the presence of
correlated error equations, endogeneity, non-random sample selection or partial observability. The underlying representation and
estimation of the model is based on a penalized regression spline approach, with automatic smoothness selection. Several
bivariate copula distributions and asymmetric links are also available. The
numerical routine carries out function minimization using a trust region Newton algorithm from the package trust in combination with
an adaptation of a low level smoothness estimation fitting procedure from the package mgcv.
SemiParBIVProbit supports the use of many smoothers as extracted from mgcv. Estimation is by penalized
maximum likelihood with automatic smoothness estimation achieved
by using the approximate Un-Biased Risk Estimator (UBRE) which can also be viewed as an approximate AIC.
Confidence intervals for smooth components are derived using a Bayesian approach. Approximate p-values for testing
individual smooth terms for equality to the zero function are also provided. Functions plot.SemiParBIVProbit and
summary.SemiParBIVProbit extract such information from a fitted SemiParBIVProbitObject. Model/variable
selection is also possible via the use of shrinakge smoothers or information criteria.
Tools for testing the hypothesis of uncorrelated error equations/absence of unobserved
confounding/absence of endogeneity/absence of non-random sample selection are also available.References
Marra G. (2013), On P-values for Semiparametric Bivariate Probit Models. Statistical Methodology, 10(1), 23-28.
Marra G. and Radice R. (2011), Estimation of a Semiparametric Recursive Bivariate Probit in the Presence of Endogeneity. Canadian Journal of Statistics, 39(2), 259-279.
Marra G. and Radice R. (2013), A Penalized Likelihood Estimation Approach to Semiparametric Sample Selection Binary Response Modeling. Electronic Journal of Statistics, 7, 1432-1455.
Marra G. and Radice R. (submitted), Flexible Bivariate Binary Models for Estimating the Efficacy of Phototherapy for Newborns with Jaundice.
Marra G., Radice R. and Missiroli S. (2014), Testing the Hypothesis of Absence of Unobserved Confounding in Semiparametric Bivariate Probit Models. Computational Statistics, 29(3-4), 715-741.
Marra G., Radice R. and Filippou P. (submitted), Regression Spline Bivariate Probit Models: A Practical Approach to Testing for Exogeneity.
McGovern M.E., Barnighausen T., Marra G. and Radice R. (forthcoming), On the Assumption of Joint Normality in Selection Models: A Copula Based Approach Applied to Estimating HIV Prevalence. Epidemiology.
Radice R., Marra G. and M. Wojtys (submitted), Copula Regression Spline Models for Binary Outcomes.