References
- Bahrami Samani, E., M. Ganjali, and A. Khodaddadi. 2008. A latent variable model for mixed continuous and ordinal responses. Journal of Statistical Theory and Applications 7 (3):337–49.
- Catalano, P. J., and L. M. Ryan. 1992. Bivariate latent variable models for clustered discrete and continuous outcomes. Journal of the American Statistical Association 87 (419):651–58. doi: https://doi.org/10.1080/01621459.1992.10475264.
- Cook, R. D. 1986. Assessment of local influence. Journal of the Royal Statistical Society: Series B (Methodological) 48 (2):133–69. doi: https://doi.org/10.1111/j.2517-6161.1986.tb01398.x.
- Cox, D. R., and N. Wermuth. 1992. Response models for mixed binary and quantitative variables. Biometrika 79 (3):441–61. doi: https://doi.org/10.1093/biomet/79.3.441.
- de Leon, A. R., and K. Carriègre. 2007. General mixed-data model: Extension of general location and grouped continuous models. Canadian Journal of Statistics 35 (4):533–48. doi: https://doi.org/10.1002/cjs.5550350405.
- de Leon, A. R., and B. Wu. 2011. Copula-based regression models for a bivariate mixed discrete and continuous outcome. Statistics in Medicine 30 (2):175–85. doi: https://doi.org/10.1002/sim.4087.
- Embrechts, P., F. Lindskog, and A. McNeil. 2001. Modelling dependence with copulas. Rapport technique, Département de mathématiques, Institut Fédéral de Technologie de Zurich, Zurich.
- Fletcher, R. 1987. Practical methods of optimization New York: John Wiley & Sons.
- Frey, R., A. J. McNeil, and M. Nyfeler. 2001. Copulas and credit models. Risk 10 (1):111–14.
- Gueorguieva, R., and G. Sanacora. 2006. Joint analysis of repeatedly observed continuous and ordinal measures of disease severity. Statistics in Medicine 25 (8):1307–22. doi: https://doi.org/10.1002/sim.2270.
- Gueorguieva, R. V., and A. Agresti. 2001. A correlated probit model for joint modeling of clustered binary and continuous responses. Journal of the American Statistical Association 96 (455):1102–12. doi: https://doi.org/10.1198/016214501753208762.
- Gunawan, D., M. A. Khaled, and R. Kohn. 2020. Mixed marginal copula modeling. Journal of Business & Economic Statistics 38 (1):137–147. doi: https://doi.org/10.1080/07350015.2018.1469998.
- He, J., H. Li, A. C. Edmondson, D. J. Rader, and M. Li. 2012. A gaussian copula approach for the analysis of secondary phenotypes in case–control genetic association studies. Biostatistics 13 (3):497–508. doi: https://doi.org/10.1093/biostatistics/kxr025.
- Heckman, J. J. 1977. Dummy endogenous variables in a simultaneous equation system. Econometrica 46 (4):931–60.
- Jafari, N., E. Tabrizi, and E. B. Samani. 2015. Gaussian copula mixed models with non-ignorable missing outcomes. Applications & Applied Mathematics 10 (1):39–56.
- Jiryaie, F., N. Withanage, B. Wu, and A. De Leon. 2016. Gaussian copula distributions for mixed data, with application in discrimination. Journal of Statistical Computation and Simulation 86 (9):1643–59. doi: https://doi.org/10.1080/00949655.2015.1077386.
- Lee, H. E. 2014. Copula analysis of correlated counts. In Bayesian model comparison, 325–48. UK: Emerald Group Publishing Limited.
- McCulloch, C. 2008. Joint modelling of mixed outcome types using latent variables. Statistical Methods in Medical Research 17 (1):53–73. doi: https://doi.org/10.1177/0962280207081240.
- Nelsen, R. B. 2007. An introduction to copulas. New York: Springer Science & Business Media.
- Olkin, I., and R. F. Tate. 1961. Multivariate correlation models with mixed discrete and continuous variables. The Annals of Mathematical Statistics 32 (2):448–65. doi: https://doi.org/10.1214/aoms/1177705052.
- Poon, W.-Y., and S.-Y. Lee. 1987. Maximum likelihood estimation of multivariate polyserial and polychoric correlation coefficients. Psychometrika 52 (3):409–30. doi: https://doi.org/10.1007/BF02294364.
- Samani, E., and Z. Tahmasebinejad. 2011. Joint modelling of mixed correlated nominal, ordinal and continuous responses. Journal of Statistical Research 45 (1):37–47.
- Sammel, M. D., L. M. Ryan, and J. M. Legler. 1997. Latent variable models for mixed discrete and continuous outcomes. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 59 (3):667–78. doi: https://doi.org/10.1111/1467-9868.00090.
- Shemyakin, A., and H. Youn. 2006. Copula models of joint last survivor analysis. Applied Stochastic Models in Business and Industry 22 (2):211–24. doi: https://doi.org/10.1002/asmb.629.
- Sklar, M. 1959. Fonctions de repartition an dimensions et leurs marges. Publications de l’Institut de Statistique de L’Université de Paris 8:229–31.
- Song, P. X.-K., M. Li, and Y. Yuan. 2009. Joint regression analysis of correlated data using gaussian copulas. Biometrics 65 (1):60–68. doi: https://doi.org/10.1111/j.1541-0420.2008.01058.x.
- Tang, X.-S., D.-Q. Li, G. Rong, K.-K. Phoon, and C.-B. Zhou. 2013. Impact of copula selection on geotechnical reliability under incomplete probability information. Computers and Geotechnics 49:264–78. doi: https://doi.org/10.1016/j.compgeo.2012.12.002.
- Tang, X.-S., D.-Q. Li, C.-B. Zhou, and K.-K. Phoon. 2015. Copula-based approaches for evaluating slope reliability under incomplete probability information. Structural Safety 52:90–99. doi: https://doi.org/10.1016/j.strusafe.2014.09.007.
- Tang, X.-S., D.-Q. Li, C.-B. Zhou, K.-K. Phoon, and L.-M. Zhang. 2013. Impact of copulas for modeling bivariate distributions on system reliability. Structural Safety 44:80–90. doi: https://doi.org/10.1016/j.strusafe.2013.06.004.
- Tate, R. F. 1954. Correlation between a discrete and a continuous variable. point-biserial correlation. The Annals of Mathematical Statistics 25 (3):603–7. doi: https://doi.org/10.1214/aoms/1177728730.
- Tate, R. F. 1955a. Applications of correlation models for biserial data. Journal of the American Statistical Association 50 (272):1078–95. doi: https://doi.org/10.1080/01621459.1955.10501293.
- Tate, R. F. 1955b. The theory of correlation between two continuous variables when one is dichotomized. Biometrika 42 (1-2):205–16. doi: https://doi.org/10.2307/2333437.
- Teixeira-Pinto, A., and S.-L T. Normand. 2009. Correlated bivariate continuous and binary outcomes: Issues and applications. Statistics in Medicine 28 (13):1753–73. doi: https://doi.org/10.1002/sim.3588.
- Tutz, G. 2005. Modelling of repeated ordered measurements by isotonic sequential regression. Statistical Modelling: An International Journal 5 (4):269–87. doi: https://doi.org/10.1191/1471082X05st101oa.
- Verbeke, G. 1997. Linear mixed models for longitudinal data. In Linear mixed models in practice, ed. G. Verbeke and G. Molenberghs, 63–153. New York: Springer.
- Wu, B., and A. R. de Leon. 2014. Gaussian copula mixed models for clustered mixed outcomes, with application in developmental toxicology. Journal of Agricultural, Biological, and Environmental Statistics 19 (1):39–56. doi: https://doi.org/10.1007/s13253-013-0155-9.
- Yang, Y., J. Kang, K. Mao, and J. Zhang. 2007. Regression models for mixed poisson and continuous longitudinal data. Statistics in Medicine 26 (20):3782–800. doi: https://doi.org/10.1002/sim.2776.