SemiParBIVProbit-package: Semiparametric Bivariate Probit Modelling
Description
SemiParBIVProbit provides a function for fitting bivariate probit models with semiparametric
predictors, including linear and nonlinear effects. Several bivariate copula distributions are supported. The dependence parameter of
the bivariate distribution employed can be specified as a function of a semiparametric predictor as well. Smoothness selection is
achieved automatically and interval calculations are based on a Bayesian approach.Details
SemiParBIVProbit provides a function for fitting flexible bivariate probit models, 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 likelihood-based regression spline approach, with automatic smoothness selection. Several
bivariate copula distributions are available. The
numerical routine carries out function minimization using a trust region 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 and nonlinear functions of the model
parameters 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 SemiParBIVProbit object. 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 available (see gt.bpm
and LM.bpm).
For recursive bivariate and sample selection models AT and est.prev calculate
the average effect of an endogenous covariate and corrected prevalence. mb provides the
nonparametric (worst-case) Manski's bound which is useful to check whether the average effect from a recursive model
is included within the possibilites of the bound.
Models with asymmetric link functions are also implemented. However, in our experience, this approach
is not likely to lead to significant improvements as compared to using probit links.
If it makes sense then the dependence parameter of the bivariate distribution employed can be specified as a function of covariates.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. (2015), Flexible Bivariate Binary Models for Estimating the Efficacy of Phototherapy for Newborns with Jaundice. International Journal of Statistics and Probability.
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. (2015), On the Assumption of Joint Normality in Selection Models: A Copula Approach Applied to Estimating HIV Prevalence. Epidemiology, 26(2), 229-237.
Radice R., Marra G. and M. Wojtys (submitted), Copula Regression Spline Models for Binary Outcomes.