SemiParBIVProbit-package: Semiparametric Bivariate Regression Models
Description
SemiParBIVProbit provides a function for fitting bivariate binary 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.
SemiParBIVProbit has been originally designed to deal with binary responses only. However, the use of
bivariate equation systems in which one response is binary and the other is continuous is allowed for. Other models
will be incorporated from time to time on a case-study basis.Details
SemiParBIVProbit provides a function for fitting flexible bivariate binary models, in the presence of
associated 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 and based on the approach
implemented in mgcv. 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 prev calculate
the average effect of an endogenous covariate and prevalence, respectively. mb provides the
nonparametric (worst-case) Manski's bound which is useful to check whether the average effect from a recursive model or prevalence from
a sample selection model is included within the possibilites of the bound.
If it makes sense then the dependence parameter of the copula distribution can be specified as a function of covariates or a grouping factor.
SemiParBIVProbit has been originally designed to deal with bivariate binary responses in the contexts of associated
error equations, endogeneity, non-random sample selection and partial observability. However, the use of
bivariate equation systems in which one response is binary and the other is continuous is allowed for. This case
is relevant for estimating, for instance, the effect that a binary endogenous variable has on a continuous response.
There are many continuous distributions which can be employed within this context and we plan to include several
options on a case-study basis. Other bivariate models will be implemented from time to time, depending on the case study at hand.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., 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. (in press), Regression Spline Bivariate Probit Models: A Practical Approach to Testing for Exogeneity. Communications in Statistics - Simulation and Computation.
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 (in press), Copula Regression Spline Models for Binary Outcomes. Statistics and Computing.