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Original Articles

Joint modeling for longitudinal set-inflated continuous and count responses

, &
Pages 1134-1160 | Received 11 Jul 2018, Accepted 18 Jul 2019, Published online: 01 Aug 2019

References

  • Alfo, M., and A. Maruotti. 2010. Two-part regression models for longitudinal zero-inflated count data. Canadian Journal of Statistics 38 (2):197–216. doi:10.1002/cjs.10056.
  • Arminger, G., and U. Küsters. 1998. Latent trait models with indicators of mixed measurement level. In Latent trait and latent class models leds, ed. R. Langeheine and J. Rost, 51–73. New York: Plenum.
  • Bahrami Samani, E. 2014. Sensitivity analysis for the identifiability with application to latent random effect model for the mixed data. Journal of Applied Statistics 41 (12):2761–76. doi:10.1080/02664763.2014.929641.
  • Bahrami Samani, E., M. Ganjali, and Y. Amirian. 2012. Likelihood estimation for longitudinal zero-inated power series regression models. Journal of Applied Statistics 39 (9):1965–74. doi:10.1080/02664763.2012.699951.
  • Behboodian, J. 1970. On the modes of a mixture of two normal distributions. Technometrics 12 (1):131–9. doi:10.1080/00401706.1970.10488640.
  • Binder, D. A. 1978. Bayesian cluster analysis. Biometrika 65 (1):31–8. doi:10.1093/biomet/65.1.31.
  • Deb, P., and A. M. Holmes. 2000. Estimates of use and costs of behavioural health care: A comparison of standard and finite mixture models. Health Economics 9 (6):475–89. doi:10.1002/1099-1050(200009)9:6<475::AID-HEC544>3.0.CO;2-H.
  • Dempster, A. P., N. M. Laird, and D. B. Rubin. 1977. Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society: Series B (Methodological) 39 (1):1–38. doi:10.1111/j.2517-6161.1977.tb01600.x.
  • Dietz, E. 1968. Limits for qualitative detection and quantitative determination. Application to radiochemistry. Analytical Chemistry 40 (3):586–93.
  • Dietz, E., and D. Bohning. 1996. Statistical inference based on a general model of unobserved heterogeneity. In Advances in GLIM and statistical modeling. Lecture notes in statistics, ed. R Gilchrist, G. Tutz, L. Fahrmeir, and F. Francis, 75–82. Berlin. Springer.
  • Duan, N., W. G. Manning, C. N. Morris, and J. P. Newhouse. 1983. A comparison of alternative models for the demand for medical care. Journal of Business & Economic Statistics 1:115–26. doi:10.2307/1391852.
  • Eisenberger, I. 1964. Genesis of bimodal distributions. Technometrics 6 (4):357–63. doi:10.1080/00401706.1964.10490199.
  • Fahrmeir, L., and G. Tutz. 2001. Multivariate statistical modelling based on generalized linear models. Berlin: Springer.
  • Fletcher, R. 2000. Practical methods of optimization. New York: John Wiley and Sons.
  • French, M. T., E. C. Norton, H. Fang, and J. C. Maclean. 2010. Alcohol consumption and body weight. Health Economics 19 (7):814–32. doi:10.1002/hec.1521.
  • Frühwirth-Schnatter, S. 2006. Finite mixture and markov switching models. Springer Series in Statistics. New York: Springer.
  • Galvis, D. M., D. Bandyopadhyay, and V. H. Lachos. 2014. Augmented mixed beta regression models for periodontal proportion data. Statistics in Medicine 33 (21):3759–71. doi:10.1002/sim.6179.
  • Hall, D. 2000. Zero-inflated Poisson and binomial regression with random effects: A case study. Biometrics 56 (4):1030–9. doi:10.1111/j.0006-341X.2000.01030.x.
  • Harris, H., and C. A. B. Smith. 1949. The sib-sib age of onset correlation among individuals suffering from the same hereditary syndrome produced by more than one gene. Annals of Eugenics 14 (1):309–18. doi:10.1111/j.1469-1809.1947.tb02409.x.
  • Hartigan, J. A. 1985. A failure of likelihood asymptotics for normal mixtures, Proceedings of the Berkeley Conference in Honor of Jerzy Neyman, California, Vol. 2, 807–10.
  • Lam, K. F., H. Xue, and Y. B. Cheung. 2006. Semiparametric analysis of zero-inflated count data. Biometrics 62 (4):996–1003. doi:10.1111/j.1541-0420.2006.00575.x.
  • Lambert, D. 1992. Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics 34 (1):1–14. doi:10.2307/1269547.
  • Lee, A. H., K. Wang, J. A. Scott, K. K. W. Yau, and G. J. McLachlan. 2006. Multi-level Zero-inflated Pisson regression modelin of correlated count data with excess zeros. Statistical Methods in Medical Research 15 (1):47–61. doi:10.1191/0962280206sm429oa.
  • Liu, Q., and D. A. Pierce. 1994. A note on Gaussian-Hermite quadrature. Biometrika 81:624–9. doi:10.2307/2337136.
  • Manning, W. G., C. N. Morris, and J. P. Newhouse. 1981. A two-part model of the demand for medical care: Preliminary results from the health insurance experiment. In Health, economics, and health economics, ed. J. van der Gaag and M. Perlman, 103–24. Amsterdam: North Holland Publishing Co.
  • McLachlan, G. J. 1987. On bootsrapping the likelihood ratio test statistic for the number of components in a normal mixture. Applied Statistics 36 (3):318–24. doi:10.2307/2347790.
  • McLachlan, G. J., and K. E. Basford. 1988. Mixture models. Inference and applications to clustering. NewYork: Marcel Dekker.
  • McLachlan, G. J., and N. Khan. 2004. On a resampling approach for tests on the number of clusters with mixture model-based clustering of tissue samples. Journal of Multivariate Analysis 90 (1):90–105. doi:10.1016/j.jmva.2004.02.002.
  • McLachlan, G. J., and D. Peel. 2000. Finite mixture models. NewYork: Wiley.
  • Min, Y., and A. Agresti. 2002. Modeling nonnegative data with clumping at zero: A survey. Journal of the Iranian Statistical Society 1 (1):7–33.
  • Min, Y., and A. Agresti. 2005. Random effects models for repeated measures of zero-inflated count data. Statistical Modelling: An International Journal 5 (1):1–19. doi:10.1191/1471082X05st084oa.
  • Mirkamali, S. J., and M. Ganjali. 2016. A general location model with zero-inflated counts and skew normal outcomes. Journal of Applied Statistics 44 (15):2716–28. doi:10.1080/02664763.2016.1261813.
  • Mullahy, J. 1986. Specification and testing of some modified count data models. Journal of Econometrics 33 (3):341–65. doi:10.1016/0304-4076(86)90002-3.
  • Muthén, B. 2004. Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data. In The Sage handbook of quantitative methodology for the social sciences, ed. D. Kaplan, 345–68. Newbury Park, CA: Sage Publications.
  • Neelon, B., and A. J. O’Malley. 2017. Two-part models for zero-modified count and semicontinuous data. In Methods in health services research. Health Services Research, ed. B. Sobolev and C. Gatsonis, 1–17. New York, NY: Springer Science+Business Media LLC.
  • Olsen, M. K., and J. L. Schafer. 2001. A two-part random-effects model for semicontinuous longitudinal data. Journal of the American Statistical Association 96 (454):730–45. doi:10.1198/016214501753168389.
  • Pearson, K. 1984. Contributions to the mathematical theory of evolution. Philosophical Transactions of the Royal Society of London A 185:71–110. doi:10.1098/rsta.1894.0003.
  • Pinheiro, J. C., and D. M. Bates. 1995. Approximations to the loglikelihood function in the nonlinear mixed effects model. Journal of Computational and Graphical Statistics 4:12–35. doi:10.2307/1390625.
  • Pinheiro, J. C., and D. M. Bates. 1996. Unconstrained parameterizations for variance-covariance matrices. Statistics and Computing 6 (3):289–96. doi:10.1007/BF00140873.
  • Quandt, R. E., and J. B. Ramsey. 1978. Estimating mixtures of normal distributions and switching regressions. Journal of the American Statistical Association 73 (364):730–8. doi:10.1080/01621459.1978.10480085.
  • Razie, F., E. Bahrami Samani, and M. Ganjali. 2013. Analysis of mixed correlated bivaariate negative binomial and continuous responses. Applications and Applied Mathematics: An International Journal (AAM) 8 (2):404–15.
  • Razie, F., E. Bahrami Samani, and M. Ganjali. 2016. A latent variable model for analyzing mixed longitudinal (k,l)-inflated count and ordinal responses. Journal of Applied Statistics 43 (12):2203–24. doi:10.1080/02664763.2015.1134448.
  • Robertson, C. A., and J. G. Fryer. 1969. Some descriptive properties of normal mixtures. Scandinavian Actuarial Journal 52:137–46. doi:10.1080/03461238.1969.10404590.
  • Samuel, M., L. Ryan, and J. M. Legler. 1997. Latent variable models for mixed discreteand continuous outcomes. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 59:667–78. doi:10.1111/1467-9868.00090.
  • Self, S. G., and K. Y. Liang. 1987. Asymptotic properties of maximum likelihood estimators and likelihood ratio test under nonstandard conditions. Journal of the American Statistical Association 82 (398):605–10. doi:10.1080/01621459.1987.10478472.
  • Teixeira-Pinto, A., and S. L. T. Normand. 2009. Correlate continuous and binary outcomes: Issues and applications. Statistics in Medicine 28 (13):1753–73. doi:10.1002/sim.3588.
  • Titterington, D. M., A. F. M. Smith, and U. E. Markove. 1985. Statistical analysis of finite mixture distributions. New York: Wiley.
  • Verbeke, G., and E. Lesaffre. 1996. A linear mixed-effects model with heterogeneity in the random-effects population. Journal of the American Statistical Association. Journal of the American Statistical Association 91 (433):217–21. doi:10.1080/01621459.1996.10476679.
  • Wolfe, J. H. 1971. A Monte Carlo study of the sampling distribution of the likelihood ratio for mixtures of multinormal distributions. Technical report STB 72-2, U.S. Naval Personnel and Training Research Laboratory, San Diego.
  • 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:10.1002/sim.2776.

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