The ANOVA-Type Inference in Linear Mixed Model with Skew-Normal Error
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摘要
Linear mixed effect models with skew-normal errors and distribution-free random effects are considered. The ANOVA-type F-tests are proposed to test the significance of random effects and the hypothesis on fixed effects of interest, respectively. Both tests are proved to be exact F-tests under this model, and the exact confidence interval for fixed effects of interest is derived. Simulation results are given to study the powers of ANOVA-type tests.
Linear mixed effect models with skew-normal errors and distribution-free random effects are considered. The ANOVA-type F-tests are proposed to test the significance of random effects and the hypothesis on fixed effects of interest, respectively. Both tests are proved to be exact F-tests under this model, and the exact confidence interval for fixed effects of interest is derived. Simulation results are given to study the powers of ANOVA-type tests.
Linear mixed effect models with skew-normal errors and distribution-free random effects are considered. The ANOVA-type F-tests are proposed to test the significance of random effects and the hypothesis on fixed effects of interest, respectively. Both tests are proved to be exact F-tests under this model, and the exact confidence interval for fixed effects of interest is derived. Simulation results are given to study the powers of ANOVA-type tests.
引文
[1]Laird N M and Ware J H,Random effects models for longitudinal data,Biometrics,1982,38:963-974.
[2]Khuri A I,Mathew T,and Sinha B K,Statistical Tests for Mixed Linear Models,John Wiley&Sons,New York,1998.
[3]Searle S R,Casella G,and Mc Culloch C E,Variance Components,Wiley,New York,1992.
[4]Wu M X,Introduction to Linear Mixed Models,Science Press,Beijing,2013.
[5]Zhang D and Davidian M,Linear mixed models with flexible distributions of random effects for longitudinal data,Biometrics,2001,57:795-802.
[6]Ma Y and Genton M G,Flexible class of skew-symmetric distributions,Scand.J.Stat.,2004,31:459-468.
[7]Arellano-Valle R B,Bolfarine H,and Lachos V H,Skew-normal linear mixed models,J.Data Science,2005,3:415-438.
[8]Lin T I and Lee J C,Estimation and prediction in linear mixed models with skew-normal random effects for longitudinal data,Stat.Med.,2008,27:149-1507.
[9]Lachos V H,Dey D K,and Cancho V G,Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective,J.Statist.Plann.Infer.,2009,139:4098-4110.
[10]Lachos V H,Ghosh P,and Arellano-Valle R B,Likelihood based inference for skew-normal independent linear mixed models,Stat.Sinica,2010,20:303-322.
[11]Ye R D,Wang T H,and Gupta A K,Tests in variance components models under skew-normal settings,Metrika,2015,78:885-904.
[12]Azzalini A and Dalla Valle A,The multivariate skew-normal distribution,Biometrika,1996,83:715-726.
[13]Arellano-Valle R B and Genton M G,Fundamental skew distributions,J.Multivariate Analy.,2005,96:93-116.
[14]Wang T H,Li B K,and Gupta A K,Distribution of quadratic forms under skew normal settings,J.Multivariate Anal.,2009,100:533-545.
[15]Wang S G and Chow S C,Advanced Linear Models:Theory and Applications,Marcel Dekker,Inc.,New York,1994.
[16]Wu M X and Wang S G,Simultaneous optimal estimates of fixed effects and variance components in the mixed model,Sci.China.Ser.A,2004,47:787-799.
[17]Wu M X,Yu K F,and Liu A Y,Exact inference on contrasts in means of intraclass correlation models with missing responses,J.Multivariate.Anal.,2009,100:301-308.
[2]Khuri A I,Mathew T,and Sinha B K,Statistical Tests for Mixed Linear Models,John Wiley&Sons,New York,1998.
[3]Searle S R,Casella G,and Mc Culloch C E,Variance Components,Wiley,New York,1992.
[4]Wu M X,Introduction to Linear Mixed Models,Science Press,Beijing,2013.
[5]Zhang D and Davidian M,Linear mixed models with flexible distributions of random effects for longitudinal data,Biometrics,2001,57:795-802.
[6]Ma Y and Genton M G,Flexible class of skew-symmetric distributions,Scand.J.Stat.,2004,31:459-468.
[7]Arellano-Valle R B,Bolfarine H,and Lachos V H,Skew-normal linear mixed models,J.Data Science,2005,3:415-438.
[8]Lin T I and Lee J C,Estimation and prediction in linear mixed models with skew-normal random effects for longitudinal data,Stat.Med.,2008,27:149-1507.
[9]Lachos V H,Dey D K,and Cancho V G,Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective,J.Statist.Plann.Infer.,2009,139:4098-4110.
[10]Lachos V H,Ghosh P,and Arellano-Valle R B,Likelihood based inference for skew-normal independent linear mixed models,Stat.Sinica,2010,20:303-322.
[11]Ye R D,Wang T H,and Gupta A K,Tests in variance components models under skew-normal settings,Metrika,2015,78:885-904.
[12]Azzalini A and Dalla Valle A,The multivariate skew-normal distribution,Biometrika,1996,83:715-726.
[13]Arellano-Valle R B and Genton M G,Fundamental skew distributions,J.Multivariate Analy.,2005,96:93-116.
[14]Wang T H,Li B K,and Gupta A K,Distribution of quadratic forms under skew normal settings,J.Multivariate Anal.,2009,100:533-545.
[15]Wang S G and Chow S C,Advanced Linear Models:Theory and Applications,Marcel Dekker,Inc.,New York,1994.
[16]Wu M X and Wang S G,Simultaneous optimal estimates of fixed effects and variance components in the mixed model,Sci.China.Ser.A,2004,47:787-799.
[17]Wu M X,Yu K F,and Liu A Y,Exact inference on contrasts in means of intraclass correlation models with missing responses,J.Multivariate.Anal.,2009,100:301-308.