Linear mixed models based on skew scale mixtures of normal distributions

References

• Akaike, H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19 (6):716–23. doi:10.1109/TAC.1974.1100705.
   Web of Science ®Google Scholar
• Andrews, D. F., and C. L. Mallows. 1974. Scale mixtures of normal distributions. Journal of the Royal Statistical Society: Series B (Methodological) 36 (1):99–102. doi:10.1111/j.2517-6161.1974.tb00989.x.
   Web of Science ®Google Scholar
• Arellano-Valle, R. B., H. Bolfarine, and V. H. Lachos. 2005. Skew-normal linear mixed models. Journal of Data Science 3:415–38.
   Google Scholar
• Arellano-Valle, R. B., C. S. Ferreira, and M. G. Genton. 2018. Scale and shape mixtures of multivariate skew-normal distributions. Journal of Multivariate Analysis 166:98–110. doi:10.1016/j.jmva.2018.02.007.
   Web of Science ®Google Scholar
• Azzalini, A. 1985. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 12:171–78.
   Web of Science ®Google Scholar
• Azzalini, A., T. D. Capello, and S. Kotz. 2003. Log-skew-normal and log-skew-t distributions as models for family income data. Journal of Income Distribution 11:13–21.
   Google Scholar
• Azzalini, A., and A. Capitanio. 1999. Statistical applications of the multivariate skew-normal distribution. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 61 (3):579–602. doi:10.1111/1467-9868.00194.
   Web of Science ®Google Scholar
• Azzalini, A., and A. Dalla-Valle. 1996. The multivariate skew-normal distribution. Biometrika 83 (4):715–26. doi:10.1093/biomet/83.4.715.
   Web of Science ®Google Scholar
• Belsley, D. A. 1991. Conditioning diagnostics: Collinearity and weak data in regression. New York: Wiley.
   Google Scholar
• Berkane, M., Y. Kano, and P. M. Bentler. 1994. Pseudo maximum likelihood estimation in elliptical theory: Effects of misspecification. Computational Statistics & Data Analysis 18 (2):255–67. doi:10.1016/0167-9473(94)90175-9.
   Web of Science ®Google Scholar
• Branco, M. D., and D. K. Dey. 2001. A general class of multivariate skew elliptical distributions. Journal of Multivariate Analysis 79 (1):99–113. doi:10.1006/jmva.2000.1960.
   Web of Science ®Google Scholar
• Cook, R. D. 1986. Assessment of local influence. Journal of the Royal Statistical Society: Series B (Methodological) 48 (2):133–69. doi:10.1111/j.2517-6161.1986.tb01398.x.
   Google Scholar
• Dempster, A., N. Laird, and D. 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.
   Web of Science ®Google Scholar
• Diggle, P. J., K. Y. Liang, and S. L. Zeger. 1996. Analysis of longitudinal data. Oxford: Clarendon Press.
   Google Scholar
• Ferreira, C. S., and R. B. Arellano-Valle. 2018. Estimation and diagnostic analysis in skew-generalized-normal regression models. Journal of Statistical Computation and Simulation 88 (6):1039–59. doi:10.1080/00949655.2017.1419351.
   Web of Science ®Google Scholar
• Ferreira, C. S., H. Bolfarine, and V. H. Lachos. 2011. Skew scale mixtures of normal distributions: Properties and estimation. Statistical Methodology 8 (2):154–71. doi:10.1016/j.stamet.2010.09.001.
   Google Scholar
• Ferreira, C. S., V. H. Lachos, and H. Bolfarine. 2016. Likelihood-based inference for multivariate skew scale mixtures of normal distributions. AStA Advances in Statistical Analysis 100 (4):421–41. doi:10.1007/s10182-016-0266-z.
   Web of Science ®Google Scholar
• Ferreira, C. S., and G. A. Paula. 2017. Estimation and diagnostic for skew-normal partially linear models. Journal of Applied Statistics 44 (16):3033–53. doi:10.1080/02664763.2016.1267124.
   Web of Science ®Google Scholar
• Gómez, H. W., O. Venegas, and H. Bolfarine. 2007. Skew-symmetric distributions generated by the normal distribution function. Environmetrics 18 (4):395–407. doi:10.1002/env.817.
   Web of Science ®Google Scholar
• Henderson, C. R. 1984. Applications of linear models in animal breeding. Guelph: University of Guelph Press.
   Google Scholar
• Johnson, N. L., S. Kotz, and N. Balakrishnan. 1994. Continuous univariate distributions. Vol. 1. New York: Wiley.
   Google Scholar
• Kahrari, F., C. S. Ferreira, and R. B. Arellano-Valle. 2019. Skew-normal-cauchy linear mixed models. Sankhya B 81 (2):185–202. doi:10.1007/s13571-018-0173-2.
   Google Scholar
• Lachos, V. H. 2004. Modelos lineares mistos assimétricos. PhD thesis, Departamento de Estatística, IME-USP.
   Google Scholar
• Lachos, V. H., and H. Bolfarine. 2007. Skew probit error-in-variables models. Statistical Methodology 3:1–12.
   Google Scholar
• Lachos, V. H., H. Bolfarine, R. B. Arellano-Valle, and L. C. Montenegro. 2007. Likelihood based inference for multivariate skew-normal regression models. Communications in Statistics - Theory and Methods 36 (9):1769–86. doi:10.1080/03610920601126241.
   Web of Science ®Google Scholar
• Lachos, V. H., P. Ghosh, and R. B. Arellano-Valle. 2010. Likelihood based inference for skew-normal independent linear mixed models. Statistica Sinica 20:303–22.
   Web of Science ®Google Scholar
• Laird, N. M., and J. H. Ware. 1982. Random effects models for longitudinal data. Biometrics 38 (4):963–74. doi:10.2307/2529876.
   PubMed Web of Science ®Google Scholar
• Lange, K. L., R. Little, and J. Taylor. 1989. Robust statistical modeling using t distribution. Journal of the American Statistical Association 84 (408):881–96. doi:10.2307/2290063.
   Web of Science ®Google Scholar
• Lange, K. L., and J. S. Sinsheimer. 1993. Normal/independent distributions and their applications in robust regression. Journal of Computational and Graphical Statistics 2 (2):175–98. doi:10.2307/1390698.
   Google Scholar
• Lee, S. Y., and L. Xu. 2004. Influence analysis of nonlinear mixed-effects models. Computational Statistics & Data Analysis 45 (2):321–41. doi:10.1016/S0167-9473(02)00303-1.
   Web of Science ®Google Scholar
• Lee, Y., and J. A. Nelder. 2004. Conditional and marginal model: Another view. Statistical Science 19 (2):219–38. doi:10.1214/088342304000000305.
   Web of Science ®Google Scholar
• Lesaffre, E., and G. Verbeke. 1998. Local influence in linear mixed models. Biometrics 54 (2):570–82. doi:10.2307/3109764.
   PubMed Web of Science ®Google Scholar
• Lin, T. I. 2010. Robust mixture modeling using multivariate skew t distributions. Statistics and Computing 20 (3):343–56. doi:10.1007/s11222-009-9128-9.
   Web of Science ®Google Scholar
• Lin, T. I., and J. C. Lee. 2008. Estimation and prediction in linear mixed models with skew-normal random effects for longitudinal data. Statistics in Medicine 27 (9):1490–507. doi:10.1002/sim.3026.
   PubMed Web of Science ®Google Scholar
• Little, R. J. A. 1988. Robust estimation of the mean and covariance matrix from data with missing values. Applied Statistics 37 (1):23–38. doi:10.2307/2347491.
   Web of Science ®Google Scholar
• Lucas, A. 1997. Robustness of the student t based m-estimator. Communications in Statistics - Theory and Methods 26 (5):1165–82. doi:10.1080/03610929708831974.
   Web of Science ®Google Scholar
• Ma, Y., M. G. Genton, and M. Davidian. 2004. Linear mixed effects models with flexible generalized skew-elliptical random effects. In Skew-elliptical distributions and their applications: A journey beyond normality, ed. M. G. Genton, 339–58. Boca Raton: Chapman & Hall.
   Google Scholar
• McLachlan, G. J., and T. Krishnan. 2008. The EM algorithm and extensions. 2nd ed. Hoboken: Wiley.
   Google Scholar
• Schumacher, F. L., L. A. Matos, and V. H. Lachos. 2020. Skewlmm: Scale Mixture of Skew-Normal Linear Mixed Models. R package version 0.2.2. https://CRAN.R-project.org/package=skewlmm.
   Google Scholar
• Yu, B., A. J. O'Malley, and P. Ghosh. 2014. Linear mixed models for multiple outcomes using extended multivariate skew-t distributions. Statistics and Its Interface 7 (1):101–11. doi:10.4310/SII.2014.v7.n1.a11.
   PubMed Web of Science ®Google Scholar
• Zeller, C. B., F. V. Labra, V. H. Lachos, and N. Balakrishnan. 2010. Influence analyses of skew-normal/independent linear mixed models. Computational Statistics & Data Analysis 54 (5):1266–80. doi:10.1016/j.csda.2009.11.008.
   Web of Science ®Google Scholar
• Zeller, C. B., V. H. Lachos, and F. V. Labra. 2011. Local influence analysis for regression models with scale mixtures of skew-normal distributions. Journal of Applied Statistics 38 (2):343–68. doi:10.1080/02664760903406504.
   Web of Science ®Google Scholar
• Zhu, H., and S. Lee. 2001. Local influence for incomplete-data models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63 (1):111–26. doi:10.1111/1467-9868.00279.
   Web of Science ®Google Scholar