Mixed-model analysis of a censored normal distribution with reference to animal breeding.

A mixed-model procedure for analysis of censored data assuming a multivariate normal distribution is described. A Bayesian framework is adopted which allows for estimation of fixed effects and variance components and prediction of random effects when records are left-censored. The procedure can be extended to right- and two-tailed censoring. The model employed is a generalized linear model, and the estimation equations resemble those arising in analysis of multivariate normal or categorical data with threshold models. Estimates of variance components are obtained using expressions similar to those employed in the EM algorithm for restricted maximum likelihood (REML) estimation under normality.

[1]  W. G. Cochran,et al.  Improvement by Means of Selection , 1951 .

[2]  C. R. Henderson.  ESTIMATION OF VARIANCE AND COVARIANCE COMPONENTS , 1953 .

[3]  H. D. Patterson,et al.  Recovery of inter-block information when block sizes are unequal , 1971 .

[4]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[5]  D. Lindley,et al.  Bayes Estimates for the Linear Model , 1972 .

[6]  D. Cox.  Regression Models and Life-Tables , 1972 .

[7]  Takeshi Amemiya,et al.  Regression Analysis when the Dependent Variable is Truncated Normal , 1973 .

[8]  C. R. Henderson.  SIRE EVALUATION AND GENETIC TRENDS , 1973 .

[9]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[10]  D. Harville.  Bayesian inference for variance components using only error contrasts , 1974 .

[11]  D. Harville.  Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems , 1977 .

[12]  James V. Beck,et al.  Parameter Estimation in Engineering and Science , 1977 .

[13]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[14]  G. J. Hahn,et al.  A Simple Method for Regression Analysis With Censored Data , 1979 .

[15]  Murray Aitkin,et al.  A Note on the Regression Analysis of Censored Data , 1981 .

[16]  T. Famula,et al.  Exponential Stayability Model with Censoring and Covariates , 1981 .

[17]  M. Binns,et al.  Stayability of Dairy Cattle: Models with Censoring and Covariates , 1983 .

[18]  D. Gianola,et al.  Sire evaluation for ordered categorical data with a threshold model , 1983, Génétique, sélection, évolution.

[19]  D Gianola,et al.  Scotland summary , 1983 .

[20]  New York Dover,et al.  ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM , 1983 .

[21]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[22]  P. Schmidt,et al.  Limited-Dependent and Qualitative Variables in Econometrics. , 1984 .

[23]  D. Gianola,et al.  Estimation of genetic merit from bivariate « all or none » responses , 1984, Génétique, sélection, évolution.

[24]  J. Ware,et al.  Random-effects models for serial observations with binary response. , 1984, Biometrics.

[25]  R. L. Quaas,et al.  Productive Lifespan of Bull Progeny Groups: Failure Time Analysis , 1984 .

[26]  C. R. Henderson.  Applications of linear models in animal breeding , 1984 .

[27]  Robert W. Mee,et al.  A mixed-model procedure for analyzing ordered categorical data , 1984 .

[28]  A. L. Rae,et al.  The analysis of binomial data by a generalized linear mixed model , 1985 .

[29]  Lyle D. Broemeling,et al.  Bayesian Analysis of Linear Models. , 1986 .

[30]  D. Gianola,et al.  Genetic evaluation for multiple binary responses , 1986, Génétique, sélection, évolution.

[31]  F. R. Allaire,et al.  Analysis of Failure Times Measured on Dairy Cows: Theoretical Considerations in Animal Breeding , 1986 .

[32]  K. Meyer,et al.  Estimation of variance components: What is missing in the EM algorithm? , 1986 .

[33]  Anthony N. Pettitt,et al.  Censored observations, repeated measures and mixed effects models: An approach using the EM algorithm and normal errors , 1986 .

[34]  Daniel Gianola,et al.  Bayesian Methods in Animal Breeding Theory , 1986 .

[35]  D. Gianola,et al.  Prediction of breeding values when variances are not known , 1986, Génétique Sélection Évolution.

[36]  D. Gianola,et al.  Empirical Bayes estimation of parameters for n polygenic binary traits , 1987, Génétique, sélection, évolution.