Artículos de revistas
Influence Diagnostics For Skew-normal Linear Mixed Models
Registro en:
Sankhya: The Indian Journal Of Statistics. , v. 69, n. 4, p. 648 - 670, 2007.
9727671
2-s2.0-58149478139
Autor
Bolfarine H.
Montenegro L.C.
Lachos V.H.
Institución
Resumen
Normality (symmetry) of the random effects is a routine assumption in linear mixed models but it may, sometimes, be unrealistic, obscuring important features of among-subjects variation. We relax this assumption by assuming that the random effects density is skew-normal, considered as an extension of the univariate version proposed by Sahu, Dey and Branco (CJS, 2003). Following Zhu and Lee (JRSSB, 2001), we implement an EM-type algorithm to parameter estimation and then using the related conditional expectation of the complete-data log-likelihood function, develop diagnostic measures for implementing the local influence approach under four model perturbation schemes. Results obtained from simulated and real data sets are reported illustrating the usefulness of the approach. © 2007, Indian Statistical Institute. 69 4 648 670 ARELLANO-VALLE, R.B., GENTON, M.G., Fundamental skew distributions (2005) J. Multivariate Anal, 96, pp. 93-116 ARELLANO-VALLE, R.B., BOLFARINE, H., LACHOS, V.H., Skew-normal linear mixed models (2005) J. Data Science, 3, pp. 415-438 AZZALINI, A., DALLA-VALLE, A., The multivariate skew-normal distribution (1996) Biometrika, 83, pp. 715-726 COOK, R.D. (1977). Detection of influential observation in linear regression. Technometrics, 19, 5-18COOK, R.D. (1986). Assessment of local influence (with discussion). J. Roy. Statist. Soc. Ser. B, 48, 133-169DEMPSTER, A.P., LAIRD, N.M., RUBIN, D.B., Maximum likelihood from incomplete data via the EM-algorithm (1977) J. Roy. Statist. Soc. Ser. B, 39, pp. 1-22 FUNG, W.K., ZHU, Z.Y., WEY, B.C., HE, X., Inference diagnostics and outlier tests for semiparametric mixed models (2002) J. Roy. Statist. Soc. Ser. B, 64, pp. 565-579 GALEA, M., PAULA, G.A., BOLFARINE, H., Local influence in elliptical linear regression models (1997) The Statistician, 46, pp. 71-79 LEE, S., XU, L., Influence analysis of nonlinear mixed-effects models (2004) Comput. Statist. Data Anal, 45, pp. 321-341 LESSAFFRE, E., VERBEKE, G., Local influence in linear mixed models (1998) Biometrics, 54, pp. 570-582 LU, B., Song, X.Y., Local influence of multivariate probit latent variable models (2006) J. Multivariate Anal, 97, pp. 1783-1798 MA, Y., GENTON, M.G., DAVIDIAN, M., Linear mixed effects models with flexible generalized skew-elliptical random effects (2004) Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality, pp. 339-358. , Genton, M.G, ed, Chapman & Hall/CRC, Boca Raton, FL MAGDER, L.S., ZEGER, S.L., A smooth nonparametric estimate of a mixing distribution using mixtures of Gaussians (1996) J. Amer. Statist. Assoc, 91, pp. 1141-1151 MAGNUS, J.R., NEUDECKER, H., (1988) Matrix Differential Calculus with Applications in Statistics and Econometrics, , Wiley, New York MENG, X., RUBIN, D.B., Maximum likelihood estimation via ECM algorithm: A general framework (1993) Biometrika, 80, pp. 267-278 PINHEIRO, J.C., BATES, D.M., (2000) Mixed-Effects Models in S and S-plus, , Springer-Verlag, New York POON, W.Y., POON, Y.S., Conformal normal curvature and assessment of local influence (1999) J. Roy. Statist. Soc. Ser. B, 61, pp. 51-61 SAHU, S.K., DEY, D.K., BRANCO, M.D., A new class of multivariate skew distributions with applications to Bayesian regression models (2003) Canad. J. Statist, 31, pp. 129-150 TAO, H., PALTA, M., YANDELL, B.S., NEWTON, M.A., An estimation method for the semi-parametric mixed effects model (1999) Biometrics, 55, pp. 102-110 VERBEKE, G., LESSAFRE, E., A linear mixed-effects model with heterogeneity in the random-effects population (1996) J. Amer. Statist. Assoc, 91, pp. 217-221 VERBEKE, G., MOLENBERGHS, G., (2000) Linear Mixed Models for Longitudinal Data, , Springer, New York ZHANG, D., DAVIDIAN, M., Linear mixed models with flexible distributions of random effects for longitudinal data (2001) Biometrics, 57, pp. 795-802 ZHU, H., LEE, S., Local influence for incomplete-data models (2001) J. Roy. S Soc. Ser. B, 63, pp. 111-126 ZHU, H., LEE, S., Local influence for generalized linear mixed models (2003) Canad. J. Statist, 31, pp. 293-309