Skew-normal factor analysis models with incomplete data

References

• H. Akaike, Information theory and an extension of the maximum likelihood principle, in 2nd Int. Symp. on Information Theory, B. N. Petrov and F. Csaki, eds., Akademiai Kiado, Budapest, 1973, pp. 267–281.
   Google Scholar
• T.W. Anderson, Maximum likelihood estimates for a multivariate normal distribution when some observations are missing, J. Amer. Statist. Assoc. 52 (1957), pp. 200–203. doi: 10.1080/01621459.1957.10501379
   Web of Science ®Google Scholar
• R. Arellano-Valle and A. Azzalini, On the unification of families of skew-normal distributions, Scand. J. Statist. 33 (2006), pp. 561–574. doi: 10.1111/j.1467-9469.2006.00503.x
   Web of Science ®Google Scholar
• R. Arellano-Valle and M. Genton, On fundamental skew distributions, J. Multivariate Anal. 96 (2005), pp. 93–116. doi: 10.1016/j.jmva.2004.10.002
   Web of Science ®Google Scholar
• A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171–178.
   Web of Science ®Google Scholar
• A. Azzalini, Further results on a class of distributions which includes the normal ones, Statistica 46 (1986), pp. 199–208.
   Google Scholar
• A. Azzalini, The skew-normal distribution and related multivariate families, Scand. J. Statist. 32 (2005), pp. 159–188. doi: 10.1111/j.1467-9469.2005.00426.x
   Web of Science ®Google Scholar
• A. Azzalini and A. Capitanio, Statistical applications of the multivariate skew normal distribution, J. R. Stat. Soc. Ser. B 61 (1999), pp. 579–602. doi: 10.1111/1467-9868.00194
   Google Scholar
• A. Azzalini and A. Capitanio, Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution, J. R. Stat. Soc. Ser. B 65 (2003), pp. 367–389. doi: 10.1111/1467-9868.00391
   Google Scholar
• A. Azzalini and A. Dalla Valle, The multivariate skew-normal distribution, Biometrika 83 (1996), pp. 715–726. doi: 10.1093/biomet/83.4.715
   Web of Science ®Google Scholar
• M. Basto and J.M. Pereira, An SPSS R-menu for ordinal factor analysis, J. Statist. Softw. 46 (2012), pp. 1–29.
   PubMed Web of Science ®Google Scholar
• H. Bolfarine, L.C. Montenegro, and V.H. Lachos, Influence diagnostics for skew-normal linear mixed models, Sankhyā 69 (2007), pp. 648–670.
   Google Scholar
• G.E.P. Box and D.R. Cox, An analysis of transformation, J. Roy. Statist. Soc. Ser. A 26 (1964), pp. 211–252.
   Google Scholar
• M. Branco and D. Dey, A general class of multivariate skew-elliptical distribution, J. Multivariate Anal. 79 (2001), pp. 93–113. doi: 10.1006/jmva.2000.1960
   Web of Science ®Google Scholar
• R.D. Cook and S. Weisberg, An Introduction to Regression Graphics, Wiley, New York, 1994.
   Google Scholar
• A.P. Dempster, N.M. Laird, and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm (with discussion), J. Roy. Statist. Soc. B 39 (1977), pp. 1–38.
   Google Scholar
• C. Finkbeiner, Estimation for the multiple factor model when data are missing, Psychometrika 44 (1979), pp. 409–420. doi: 10.1007/BF02296204
   Web of Science ®Google Scholar
• E. Fokoué and D.M. Titterington, Mixtures of factor analyzers. Bayesian estimation and inference by stochastic simulation, Mach. Learn. 50 (2003), pp. 73–94. doi: 10.1023/A:1020297828025
   Web of Science ®Google Scholar
• A. Frank and A. Asuncion, UCI Machine Learning Repository, University of California, School of Information and Computer Science, Irvine, CA, 2010. Available at http://archive.ics.uci.edu/ml.
   Google Scholar
• A.K. Gupta, G. González-Farías, and J. A. Domínguez-Monila, A multivariate skew normal distribution, J. Multivariate Anal. 89 (2004), pp. 181–90. doi: 10.1016/S0047-259X(03)00131-3
   Web of Science ®Google Scholar
• W.K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika 57 (1970), pp. 97–109. doi: 10.1093/biomet/57.1.97
   Web of Science ®Google Scholar
• R.R. Hocking and Wm.B. Smith, Estimation of parameters in the multivariate normal distribution with missing observations, J. Amer. Statist. Assoc. 63 (1968), pp. 159–173.
   Web of Science ®Google Scholar
• M. Jamshidian, An EM algorithm for ML factor analysis with missing data, in Latent Variable Modeling and Applications to Causality, M. Berkane, ed., Springer Verlag, New York, 1997, pp. 247–258.
   Google Scholar
• M. Jamshidian and P.M. Bentler, ML estimation of mean and covariance structures with missing data using complete data routines, J. Edu. Behav. Stat. 24 (1999), pp. 21–41. doi: 10.3102/10769986024001021
   Web of Science ®Google Scholar
• K.G. Jöreskog and I. Moustaki, Factor analysis of ordinal variables: A comparison of three approaches, Multivariate Behav. Res. 36 (2001), pp. 347–387. doi: 10.1207/S15327906347-387
   PubMed Web of Science ®Google Scholar
• V.H. Lachos, P. Ghosh, and R.B. Arellano-Valle, Likelihood based inference for skew-normal/independent linear mixed model, Statist. Sinica 20 (2010), pp. 303–322.
   Web of Science ®Google Scholar
• S.Y. Lee, Estimation for structural equation models with missing data, Psychometrika 51 (1986), pp. 93–99. doi: 10.1007/BF02294002
   Web of Science ®Google Scholar
• S. Lee and G.J. McLachlan, Finite mixtures of multivariate skew t-distributions: Some recent and new results, Statist. Comput. 24 (2014), pp. 181–202. doi: 10.1007/s11222-012-9362-4
   Web of Science ®Google Scholar
• S. Lee and G.J. McLachlan, On mixtures of skew normal and skew t-distributions, Adv. Data Anal. Classif. 7 (2013), pp. 241–266. doi: 10.1007/s11634-013-0132-8
   Web of Science ®Google Scholar
• T.I. Lin, H.J. Ho, and C.L. Chen, Analysis of multivariate skew normal models with incomplete data, J. Multivariate Anal. 100 (2009), pp. 2337–2351. doi: 10.1016/j.jmva.2009.07.005
   Web of Science ®Google Scholar
• T.I. Lin, H.J. Ho, and C.R. Lee, Flexible mixture modelling using the multivariate skew-t-normal distribution, Statist. Comput. 24 (2014), pp. 531–546. doi: 10.1007/s11222-013-9386-4
   Web of Science ®Google Scholar
• T.I. Lin, G.J. McLachlan, and S.X. Lee, Extending mixtures of factor models using the restricted multivariate skew-normal distribution, preprint (2013). Available at arXiv:1307.1748.
   Google Scholar
• R.J.A. Little and D.B. Rubin, Statistical Analysis with Missing Data, 2nd ed.,Wiley, New York, 2002.
   Google Scholar
• C. Liu, Efficient ML estimation of the multivariate normal distribution from incomplete data, J. Multivariate Anal. 69 (1999), pp. 206–217. doi: 10.1006/jmva.1998.1793
   Web of Science ®Google Scholar
• C.H. Liu, D.B. Rubin, and Y.N. Wu, Parameter expansion to accelerate EM: The PX-EM algorithm, Biometrika 85 (1998), pp. 755–770. doi: 10.1093/biomet/85.4.755
   Web of Science ®Google Scholar
• H.F. Lopes and M. West, Bayesian model assessment in factor analysis, Statist. Sinica 4 (2004), pp. 41–67.
   Google Scholar
• X.L. Meng and D.B. Rubin, Maximum likelihood estimation via the ECM algorithm: A general framework, Biometrika 80 (1993), pp. 267–278. doi: 10.1093/biomet/80.2.267
   Web of Science ®Google Scholar
• A. Montanari and C. Viroli, A skew-normal factor model for the analysis of student satisfaction towards university courses, J. Appl. Statist. 37 (2010), pp. 473–487. doi: 10.1080/02664760902736737
   Web of Science ®Google Scholar
• P.M. Murray, R. Browne, and P.D. McNicholas, Mixtures of common skew-t factor analyzers, Statistics 3 (2014), pp. 68–82. doi: 10.1002/sta4.43
   Google Scholar
• P.M. Murray, P.D. McNicholas, and R. Browne, Mixtures of skew-t factor analyzers, Comput. Statist. Data Anal. 77 (2014), pp. 326–335. doi: 10.1016/j.csda.2014.03.012
   Web of Science ®Google Scholar
• S. Pyne, X. Hu, K. Wang, E. Rossin, T.I. Lin, L.M. Maier, C. Baecher-Allan, G.J. McLachlan, P. Tamayo, D.A. Hafler, P.L. De Jager, and J.P. Mesirov, Automated high- dimensional flow cytometric data analysis, Proc. Natl. Acad. Sci (PNAS) USA 106 (2009), pp. 8519–8524. doi: 10.1073/pnas.0903028106
   PubMed Web of Science ®Google Scholar
• D.B. Rubin, Characterizing the estimation of parameters in incomplete-data problems, J. Amer. Statist. Assoc. 69 (1974), pp. 474–476.
   Google Scholar
• D.B. Rubin, Inference and missing data, Biometrika 63 (1976), pp. 581–592. doi: 10.1093/biomet/63.3.581
   Web of Science ®Google Scholar
• D.B. Rubin, Multiple Imputation for Nonresponse in Surveys, John Wiley and Sons, New York, 1987.
   Google Scholar
• S.K. Sahu, D.K. Dey, and M.D. Branco, A new class of multivariate skew distributions with application to Bayesian regression models, Can. J. Statist. 31 (2003), pp. 129–150. doi: 10.2307/3316064
   Web of Science ®Google Scholar
• G. Schwarz, Estimating the dimension of a model, Ann. Statist. 6 (1978), pp. 461–464. doi: 10.1214/aos/1176344136
   Web of Science ®Google Scholar
• M.A. Tanner and W.H. Wong, The calculation of posterior distributions by data augmentation (with discussion), J. Amer. Statist. Assoc. 82 (1987), pp. 528–550. doi: 10.1080/01621459.1987.10478458
   Web of Science ®Google Scholar
• M.M. Wall, J. Guo, and Y. Amemiya, Mixture factor analysis for approximating a non-normally distributed continuous latent factor with continuous and dichotomous observed variables, Multivar. Behav. Res. 47 (2012), pp. 276–313. doi: 10.1080/00273171.2012.658339
   PubMed Web of Science ®Google Scholar
• K. Wang, A. Ng, and G.J. McLachlan, EMMIXskew: EM algorithm for mixture of multivariate skew normal/t distributions, R package version 1.0.1, 2014.
   Google Scholar
• S. Zacks, The Theory of Statistical Inference, John Wiley, New York, 1971.
   Google Scholar