GJRM-package: Generalised Joint Regression Modelling
In KironmoyDas/KD-STAT0035-GMupdate: Generalised Joint Regression Modelling
Description
Details
Author(s)
References
See Also
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 (Cass Business School, City, University of London)
with contributions from Panagiota Filippou (specifically on the trivariate binary models), Francesco Donat (on the bivariate models with ordinal and
continuous margins), Matteo Fasiolo (for the implementation of the pdf and cdf, and related
derivatives, of the Tweedie distribution), and Alessia Eletti (on survival models with mixed censoring and excess hazards).
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 giampiero.marra@ucl.ac.uk
Part funded by EPSRC: EP/J006742/1
References
Key methodological references:
Dettoni R., Marra G., Radice R. (in press), Generalized Link-Based Additive Survival Models with Informative Censoring. Journal of Computational and Graphical Statistics.
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.
Filippou P., Marra G., Radice R. (2017), Penalized Likelihood Estimation of a Trivariate Additive Probit Model. Biostatistics, 18(3), 569-585.
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.
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.
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. (2017), Bivariate Copula Additive Models for Location, Scale and Shape. Computational Statistics and Data Analysis, 112, 99-113.
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.
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., Radice R., Zimmer D. (in press), Estimating the Binary Endogenous Effect of Insurance on Doctor Visits by Copula-Based Regression Additive Models. Journal of the Royal Statistical Society Series C.
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.
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.
For applied case studies see https://www.homepages.ucl.ac.uk/~ucakgm0/pubs.htm.
See Also
KironmoyDas/KD-STAT0035-GMupdate documentation built on Feb. 15, 2021, 12:17 a.m.
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Description Details Author(s) References See Also
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 (Cass Business School, City, University of London)
with contributions from Panagiota Filippou (specifically on the trivariate binary models), Francesco Donat (on the bivariate models with ordinal and continuous margins), Matteo Fasiolo (for the implementation of the pdf and cdf, and related derivatives, of the Tweedie distribution), and Alessia Eletti (on survival models with mixed censoring and excess hazards).
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 giampiero.marra@ucl.ac.uk
Part funded by EPSRC: EP/J006742/1
References
Key methodological references:
Dettoni R., Marra G., Radice R. (in press), Generalized Link-Based Additive Survival Models with Informative Censoring. Journal of Computational and Graphical Statistics.
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.
Filippou P., Marra G., Radice R. (2017), Penalized Likelihood Estimation of a Trivariate Additive Probit Model. Biostatistics, 18(3), 569-585.
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.
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.
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. (2017), Bivariate Copula Additive Models for Location, Scale and Shape. Computational Statistics and Data Analysis, 112, 99-113.
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.
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., Radice R., Zimmer D. (in press), Estimating the Binary Endogenous Effect of Insurance on Doctor Visits by Copula-Based Regression Additive Models. Journal of the Royal Statistical Society Series C.
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.
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.
For applied case studies see https://www.homepages.ucl.ac.uk/~ucakgm0/pubs.htm.
See Also
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