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 effect...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.展开更多
Four “cuajada” type fresh cheeses were evaluated by two trained panels in different regions from Oaxaca in Mexico (Instituto Tecnológico de Comitancillo (ITC) and Universidad del Mar (UMAR)). Each panel was int...Four “cuajada” type fresh cheeses were evaluated by two trained panels in different regions from Oaxaca in Mexico (Instituto Tecnológico de Comitancillo (ITC) and Universidad del Mar (UMAR)). Each panel was integrated by six judges. Analysis of variance (ANOVA) in conjunction with principal component analysis (PCA) and the Rv coefficient were used to identify similarities and consensus among trained judges and panels. The ANOVA results revealed that the judges from ITC performed significantly better (P < 0.05) in discrimination and repetitivity, while both panels showed a similar effect in discrimination. The PCA determined some similarities in the position of cheeses in the sensory space, while Rv revealed that judges and panels were consensual. In conclusion, statistical resources determined that both panels were discriminating and that similarities in the positioning of cheeses in the sensory space were found.展开更多
Linear mixed effects models with general skew normal-symmetric （SNS） error are considered and several properties of the SNS distributions are obtained. Under the SNS settings, ANOVA-type estimates of variance compon...Linear mixed effects models with general skew normal-symmetric （SNS） error are considered and several properties of the SNS distributions are obtained. Under the SNS settings, ANOVA-type estimates of variance components in the model are unbiased, the ANOVA-type F-tests are exact F-tests in SNS setting, and the exact confidence intervals for fixed effects are constructed. Also the power of ANOVA-type F-tests for components are free of the skewing function if the random effects normally distributed. For illustration of the main results, simulation studies on the robustness of the models are given by comparisons of multivariate skew-normal, multivariate skew normal-Laplace, multivariate skew normal-uniform, multivariate skew normal-symmetric, and multivariate normal distributed errors. A real example is provided for the illustration of the proposed method.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11171011 and 11471036the Natural Science Foundation of Beijing under Grant No.1132007Beijing Municipal Science and Technology Project under Grant No.km201410005011
文摘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.
文摘Four “cuajada” type fresh cheeses were evaluated by two trained panels in different regions from Oaxaca in Mexico (Instituto Tecnológico de Comitancillo (ITC) and Universidad del Mar (UMAR)). Each panel was integrated by six judges. Analysis of variance (ANOVA) in conjunction with principal component analysis (PCA) and the Rv coefficient were used to identify similarities and consensus among trained judges and panels. The ANOVA results revealed that the judges from ITC performed significantly better (P < 0.05) in discrimination and repetitivity, while both panels showed a similar effect in discrimination. The PCA determined some similarities in the position of cheeses in the sensory space, while Rv revealed that judges and panels were consensual. In conclusion, statistical resources determined that both panels were discriminating and that similarities in the positioning of cheeses in the sensory space were found.
基金The authors are grateful to the referees for their valuable suggestions which considerably improved the paper. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11171011, 11471036）, the Natural Science Foundation of Beijing （Grant No. 1132007）, and Beijing Municipal Science and Technology Project （Grant No. km201410005011）. Research of A. Liu was supported by the Intramural Research Program of the Eunice Kennedy Shriver National Institute of Child Health and Human Development （NICHD） and the National Institutes of Health （NIH）.
文摘Linear mixed effects models with general skew normal-symmetric （SNS） error are considered and several properties of the SNS distributions are obtained. Under the SNS settings, ANOVA-type estimates of variance components in the model are unbiased, the ANOVA-type F-tests are exact F-tests in SNS setting, and the exact confidence intervals for fixed effects are constructed. Also the power of ANOVA-type F-tests for components are free of the skewing function if the random effects normally distributed. For illustration of the main results, simulation studies on the robustness of the models are given by comparisons of multivariate skew-normal, multivariate skew normal-Laplace, multivariate skew normal-uniform, multivariate skew normal-symmetric, and multivariate normal distributed errors. A real example is provided for the illustration of the proposed method.
