GJRM-package {GJRM}

Generalised Joint Regression Modelling

Description

This package provides a function for fitting various generalised joint regression models with several types of covariate effects and distributions. Many modelling options are supported and all parameters of the joint distribution can be specified as flexible functions of covariates.

The orginal name of this package was SemiParBIVProbit which was designed to fit flexible bivariate binary response models. However, since then the package has expanded so much that its orginal name no longer gave a clue about all modelling options available. The new name should more closely reflect past, current and future developments.

The main fitting functions are listed below.

gjrm() which fits bivariate regression models with binary responses (useful for fitting bivariate binary models in the presence of (i) non-random sample selection or (ii) associated responses/endogeneity or (iii) partial observability), bivariate models with binary/discrete/continuous/survival margins in the presence of associated responses/endogeneity, bivariate sample selection models with continuous/discrete response, trivariate binary models (with and without double sample selection). This function essentially merges all previously available fitting functions, namely SemiParBIV(), SemiParTRIV(), copulaReg() and copulaSampleSel().

gamlss() fits flexible univariate regression models where the response can be binary (only the extreme value distribution is allowed for), continuous, discrete and survival. The purpose of this function was only to provide, in some cases, starting values for the above functions, but it has now been made available in the form of a proper function should the user wish to fit univariate models using the general estimation approach of this package.

We are currently working on several multivariate extensions.

Details

GJRM provides functions for fitting general joint models in various situations. The estimation approach is based on a very generic penalized maximum likelihood based framework, where any (parametric) distribution can in principle be employed, and the smoothers (representing several types of covariate effects) are set up using penalised regression splines. Several marginal and copula distributions are available and the numerical routine carries out function minimization using a trust region algorithm in combination with an adaptation of an automatic multiple smoothing parameter estimation procedure for GAMs (see mgcv for more details on this last point). The smoothers supported by this package are those available in mgcv.

Confidence intervals for smooth components and nonlinear functions of the model parameters are derived using a Bayesian approach. P-values for testing individual smooth terms for equality to the zero function are also provided and based on the approach implemented in mgcv. The usual plotting and summary functions are also available. Model/variable selection is also possible via the use of shrinakge smoothers and/or information criteria.

Author(s)

Giampiero Marra (University College London, Department of Statistical Science) and Rosalba Radice (Bayes Business School, Faculty of Actuarial Science and Insurance, City, University of London)

with help and contributions from Panagiota Filippou (trivariate binary models), Francesco Donat (bivariate models with ordinal and continuous margins, and ordinal margins), Matteo Fasiolo (pdf and cdf, and related derivatives, of the Tweedie distribution), Alessia Eletti (survival models with mixed censoring and excess hazards), Kiron Das (Galambos copula), Eva Cantoni and William Aeberhard (robust gamlss), Alessia Eletti and Danilo Petti (copula survival model with general censoring scheme).

Thanks to Bear Braumoeller for suggesting the implementation of bivariate models with partial observability, and Carmen Cadarso for suggesting the inclusion of various modelling extensions.

Maintainer: Giampiero Marra [e-mail]

Part funded by EPSRC: EP/J006742/1 and EP/T033061/1

References

Key methodological references (ordered by year of publication):

Marra G., Radice R., Zimmer D. (2024), A Unifying Switching Regime Regression Framework with Applications in Health Economics. Econometric Reviews, 43(1), 52-70.

Marra G., Fasiolo M., Radice R., Winkelmann R. (2023), A Flexible Copula Regression Model with Bernoulli and Tweedie Margins for Estimating the Effect of Spending on Mental Health. Health Economics, 32(6), 1305-1322.

Eletti A., Marra G., Quaresma M., Radice R., Rubio F.J. (2022), A Unifying Framework for Flexible Excess Hazard Modeling with Applications in Cancer Epidemiology. Journal of the Royal Statistical Society Series C, 71(4), 1044-1062.

Petti D., Eletti A., Marra G., Radice R. (2022), Copula Link-Based Additive Models for Bivariate Time-to-Event Outcomes with General Censoring Scheme. Computational Statistics and Data Analysis, 107550.

Ranjbar S., Cantoni E., Chavez-Demoulin V., Marra G., Radice R., Jaton-Ogay K. (2022), Modelling the Extremes of Seasonal Viruses and Hospital Congestion: The Example of Flu in a Swiss Hospital. Journal of the Royal Statistical Society Series C, 71(4), 884-905.

Aeberhard W.H., Cantoni E., Marra G., Radice R. (2021), Robust Fitting for Generalized Additive Models for Location, Scale and Shape. Statistics and Computing, 31(11), 1-16.

Marra G., Farcomeni A., Radice R. (2021), Link-Based Survival Additive Models under Mixed Censoring to Assess Risks of Hospital-Acquired Infections. Computational Statistics and Data Analysis, 155, 107092.

Hohberg M., Donat F., Marra G., Kneib T. (2021), Beyond Unidimensional Poverty Analysis Using Distributional Copula Models for Mixed Ordered-Continuous Outcomes. Journal of the Royal Statistical Society Series C, 70(5), 1365-1390.

Marra G., Radice R., Zimmer D. (2020), Estimating the Binary Endogenous Effect of Insurance on Doctor Visits by Copula-Based Regression Additive Models. Journal of the Royal Statistical Society Series C, 69(4), 953-971.

Dettoni R., Marra G., Radice R. (2020), Generalized Link-Based Additive Survival Models with Informative Censoring. Journal of Computational and Graphical Statistics, 29(3), 503-512.

Marra G., Radice R. (2020), Copula Link-Based Additive Models for Right-Censored Event Time Data. Journal of the American Statistical Association, 115(530), 886-895.

Filippou P., Kneib T., Marra G., Radice R. (2019), A Trivariate Additive Regression Model with Arbitrary Link Functions and Varying Correlation Matrix. Journal of Statistical Planning and Inference, 199, 236-248.

Gomes M., Radice R., Camarena-Brenes J., Marra G. (2019), Copula Selection Models for Non-Gaussian Outcomes that Are Missing Not at Random. Statistics in Medicine, 38(3), 480-496.

Klein N., Kneib T., Marra G., Radice R., Rokicki S., McGovern M.E. (2019), Mixed Binary-Continuous Copula Regression Models with Application to Adverse Birth Outcomes. Statistics in Medicine, 38(3), 413-436.

Wojtys M., Marra G., Radice R. (2018), Copula Based Generalized Additive Models for Location, Scale and Shape with Non-Random Sample Selection. Computational Statistics and Data Analysis, 127, 1-14.

Filippou P., Marra G., Radice R. (2017), Penalized Likelihood Estimation of a Trivariate Additive Probit Model. Biostatistics, 18(3), 569-585.

Marra G., Radice R. (2017), Bivariate Copula Additive Models for Location, Scale and Shape. Computational Statistics and Data Analysis, 112, 99-113.

Marra G., Radice R., Barnighausen T., Wood S.N., McGovern M.E. (2017), A Simultaneous Equation Approach to Estimating HIV Prevalence with Non-Ignorable Missing Responses. Journal of the American Statistical Association, 112(518), 484-496.

Marra G., Radice R., Filippou P. (2017), Testing the Hypothesis of Exogeneity in Regression Spline Bivariate Probit Models. Communications in Statistics - Simulation and Computation, 46(3), 2283-2298.

Marra G., Wyszynski K. (2016), Semi-Parametric Copula Sample Selection Models for Count Responses. Computational Statistics and Data Analysis, 104, 110-129.

Radice R., Marra G., Wojtys M. (2016), Copula Regression Spline Models for Binary Outcomes. Statistics and Computing, 26(5), 981-995.

Marra G., 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. (2013), Estimation of a Regression Spline Sample Selection Model. Computational Statistics and Data Analysis, 61, 158-173.

Marra G., Radice R. (2011), Estimation of a Semiparametric Recursive Bivariate Probit in the Presence of Endogeneity. Canadian Journal of Statistics, 39(2), 259-279.

For applied case studies see https://www.homepages.ucl.ac.uk/~ucakgm0/pubs.htm.

See Also

gjrm, gamlss