Maximum-likelihood estimation and influence analysis in multivariate skew-normal reproductive dispersion mixed models for longitudinal data

References

• D Hedeker, RD Gibbons. Longitudinal data analysis. New York: Wiley; 2006.
   Google Scholar
• DA Harville. Maximum likelihood approach to variance component estimation and related problems. J Am Statist Assoc. 1977;72:320–340. doi: 10.1080/01621459.1977.10480998
   Web of Science ®Google Scholar
• R Schall. Estimation in generalized linear model with random effects. Biometrika. 1991;78:719–727. doi: 10.1093/biomet/78.4.719
   Web of Science ®Google Scholar
• Y Lee, JA Nelder. Hierarchical generalized linear models (with discussion). J R Statist Soc Ser B. 1996;58:619–678.
   Google Scholar
• D Bandyopadhyay, VH Lachos, LM Castro, DK Dey. Skew-normal/independent linear mixed models for censored responses with application to HIV viral loads. Biom J. 2012;54:405–425. doi: 10.1002/bimj.201000173
   PubMed Web of Science ®Google Scholar
• B Jorgensen. The theory of dispersion models. London: Chapman and Hall; 1997.
   Google Scholar
• ZW Birnbaum, SC Saunders. A new family of life distributions. J Appl Probab. 1969;6:319–327. doi: 10.2307/3212003
   Web of Science ®Google Scholar
• D Zhang, M Davidian. Linear mixed models with flexible distributions of random effects for longitudinal data. Biometrics. 2001;57:795–802. doi: 10.1111/j.0006-341X.2001.00795.x
   PubMed Web of Science ®Google Scholar
• W Ghidey, E Lesaffre, P Eilers. Smooth random effects distribution in a linear mixed model. Biometrics. 2004;60:945–953. doi: 10.1111/j.0006-341X.2004.00250.x
   PubMed Web of Science ®Google Scholar
• RB Arellano-Valle, H Bolfarine, VH Lachos. Skew-normal linear mixed models. J Data Sci. 2005;3:415–438.
   Google Scholar
• VH Lachos, P Ghosh, RB Arellano-Valle. Likelihood based inference for skew-normal independent linear mixed models. Statist Sinica. 2010;20:303–322.
   Web of Science ®Google Scholar
• D Bandyopadhyay, VH Lachos, CA Abanto-Valle, P Ghosh. Linear mixed models for skew-normal/independent bivariate responses with an application to periodontal disease. Stat Med. 1998;29:2643–2655. doi: 10.1002/sim.4031
   Web of Science ®Google Scholar
• AP Dempster, NM Laird, DB Rubin. Maximum likelihood from incomplete data via the EM algorithm (with discussion). J R Statist Soc Ser B. 1977;39:1–38.
   Google Scholar
• GCG Wei, MA Tanner. A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithm. J Am Statist Assoc. 1990;85:699–704. doi: 10.1080/01621459.1990.10474930
   Web of Science ®Google Scholar
• DR Cook. Detection of influential observations in linear regression. Technometrics. 1977;19:15–18. doi: 10.2307/1268249
   Web of Science ®Google Scholar
• R Christensen, LM Pearson, W Johnson. Case deletion diagnostics for mixed models. Technometrics. 1992;34:38–45. doi: 10.2307/1269550
   Web of Science ®Google Scholar
• BC Wei. Exponential family nonlinear models. Singapore: Springer-Verlag; 1998.
   Google Scholar
• HT Zhu, SY Lee, BC Wei, J Zhou. Case-deletion measures for models with incomplete data. Biometrika. 2001;88:727–737. doi: 10.1093/biomet/88.3.727
   Web of Science ®Google Scholar
• RD Cook. Assessment of local influence (with discussion). J R Statist Soc B. 1986;48:133–169.
   Google Scholar
• E Lesaffre, G Verbeke. Local influence in linear mixed model. Biometrics. 1998;54:570–583. doi: 10.2307/3109764
   PubMed Web of Science ®Google Scholar
• HT Zhu, S-Y Lee. Local influence for incomplete data models. J R Statist Soc Ser B. 2001;63:111–126. doi: 10.1111/1467-9868.00279
   Google Scholar
• W Thomas, RD Cook. Assessing influence on regression coefficients in generalized linear models. Biometrika. 1989;76:741–749. doi: 10.1093/biomet/76.4.741
   Web of Science ®Google Scholar
• SY Lee, NS Tang. Local influence analysis of nonlinear structural equation models. Psychometrika. 2004;69:759–773. doi: 10.1007/BF02289856
   Web of Science ®Google Scholar
• MJ Ouwens, FE Tan, MP Berger. Local influence to detect influential data structures for generalized linear mixed models. Biometrics. 2001;54:1166–1172. doi: 10.1111/j.0006-341X.2001.01166.x
   Web of Science ®Google Scholar
• A Azzalini, A Dalla-Valle. The multivariate skew-normal distribution. Biometrika. 1996;83:715–726. doi: 10.1093/biomet/83.4.715
   Web of Science ®Google Scholar
• NS Tang, BC Wei, WZ Zhang. Influence diagnostics in nonlinear reproductive dispersion mixed models. Statistics. 2006;40:227–246. doi: 10.1080/02331880600688197
   Web of Science ®Google Scholar
• GCG Wei, MA Tanner. A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithm. J Am Statist Assoc. 1990;85:699–704. doi: 10.1080/01621459.1990.10474930
   Web of Science ®Google Scholar
• CH Liu, DB Rubin. The ECME algorithm: a simple extension of EM and ECM with faster monotone convergence. Biometrika. 1994;81:633–648. doi: 10.1093/biomet/81.4.633
   Web of Science ®Google Scholar
• XL Meng, S Schilling. Fitting full-information item factor models and an empirical investigation of bridge sampling. J Am Statist Assoc. 1996;91:1254–1267. doi: 10.1080/01621459.1996.10476995
   Web of Science ®Google Scholar
• TA Louis. Finding the observed information when using the EM algorithm. J R Statist Soc Ser B. 1982;44:226–233.
   Web of Science ®Google Scholar
• HT Zhu, SY Lee. Local influence for incomplete data models. J R Statist Soc Ser B. 2001;63:111–126. doi: 10.1111/1467-9868.00279
   Google Scholar
• WY Poon, YS Poon. Conformal normal curvature and assessment of local influence. J R Statist Soc Ser B. 1999;61:51–61. doi: 10.1111/1467-9868.00162
   Google Scholar
• LC Montenegro, VH Lachos, H Bolfarine. Local influence analysis for skew-normal linear mixed models. Comm Stat Theory Methods. 2009;38:484–496. doi: 10.1080/03610920802238647
   Web of Science ®Google Scholar
• SY Lee, HT Zhu. Maximum likelihood estimation of nonlinear structural equation models. Psychometrika. 2002;67:189–210. doi: 10.1007/BF02294842
   Web of Science ®Google Scholar
• RJA Little, DB Rubin. Statistical analysis with missing data. New York: Wiley; 1987.
   Google Scholar