The paper by Douglas M. Bates and Jose C. Pinheiro discusses the advancements in computational methods for maximum likelihood (ML) and restricted maximum likelihood (REML) estimation in linear mixed-effects models, which have significantly simplified the analysis of data in agricultural settings. The authors highlight the flexibility of software like SAS PROC MIXED and the nlme library for S-PLUS in handling various types of data, including random-effects one-way classifications, blocked designs, hierarchical designs, and longitudinal data. They emphasize the importance of new computational methods that do not require balanced data, making it easier to handle observational studies and missing data. The paper also introduces graphical methods, particularly trellis graphics, for data exploration and model assessment. These methods are illustrated through examples such as ultrasonic travel times in railway rails, growth curves of baby chicks, and blood pressure changes in rabbits. The authors extend the Laird-Ware formulation to nonlinear mixed-effects models, demonstrating how to fit sigmoidal growth curves and other nonlinear patterns. They provide detailed computational methods for ML and REML estimation, including the use of the lme function in the nlme library. Finally, the paper concludes by summarizing the versatility of linear mixed-effects models and their extensions, emphasizing the importance of combining computational methods with graphical analysis for effective data modeling.The paper by Douglas M. Bates and Jose C. Pinheiro discusses the advancements in computational methods for maximum likelihood (ML) and restricted maximum likelihood (REML) estimation in linear mixed-effects models, which have significantly simplified the analysis of data in agricultural settings. The authors highlight the flexibility of software like SAS PROC MIXED and the nlme library for S-PLUS in handling various types of data, including random-effects one-way classifications, blocked designs, hierarchical designs, and longitudinal data. They emphasize the importance of new computational methods that do not require balanced data, making it easier to handle observational studies and missing data. The paper also introduces graphical methods, particularly trellis graphics, for data exploration and model assessment. These methods are illustrated through examples such as ultrasonic travel times in railway rails, growth curves of baby chicks, and blood pressure changes in rabbits. The authors extend the Laird-Ware formulation to nonlinear mixed-effects models, demonstrating how to fit sigmoidal growth curves and other nonlinear patterns. They provide detailed computational methods for ML and REML estimation, including the use of the lme function in the nlme library. Finally, the paper concludes by summarizing the versatility of linear mixed-effects models and their extensions, emphasizing the importance of combining computational methods with graphical analysis for effective data modeling.