Generalized Linear Mixed Models with Applications in Agriculture and Biology

This open access book offers an introduction to mixed generalized linear models with applications to the biological sciences, basically approached from an applications perspective, without neglecting the rigor of the theory. For this reason, the theory that supports each of the studied methods is addressed and later - through examples - its application is illustrated. In addition, some of the assumptions and shortcomings of linear statistical models in general are also discussed.

An alternative to analyse non-normal distributed response variables is the use of generalized linear models (GLM) to describe the response data with an exponential family distribution that perfectly fits the real response. Extending this idea to models with random effects allows the use of Generalized Linear Mixed Models (GLMMs). The use of these complex models was not computationally feasible until the recent past, when computational advances and improvements to statistical analysis programs allowed users to easily, quickly, and accurately apply GLMM to data sets. GLMMs have attracted considerable attention in recent years. The word "Generalized" refers to non-normal distributions for the response variable and the word "Mixed" refers to random effects, in addition to the fixed effects typical of analysis of variance (or regression). With the development of modern statistical packages such as Statistical Analysis System (SAS), R, ASReml, among others, a wide variety of statistical analyzes are available to a wider audience. However, to be able to handle and master more sophisticated models requires proper training and great responsibility on the part of the practitioner to understand how these advanced tools work. GMLM is an analysis methodology used in agriculture and biology that can accommodate complex correlation structures and types of response variables. 

Josafhat Salinas Ruiz holds BS in Agroindustrial Engeniering from Universidad Autónoma Chapingo, Mexico, Masters in Statistics from Colegio de Postgraduados of México and PhD in Biometry from the University of Nebraska-Lincoln, USA. Josafhat Salinas-Ruíz is currently a Professor of Statistics, Multivariate statistics, and Experimental Designs at Colegio de Postgraduados campus Córdoba, Mexico. His areas of interest include the advanced statistical modeling in plant sciences, agriculture and agronomy, generalized linear mixed models, multivariate analysis and experimental designs. 

Osval Antonio Montesinos López holds a BS in Agroindustrial Engineering from Universidad Autónoma Chapingo of México, Masters in Statistics from Colegio de Postgraduados of México and PhD in Statistics and Biometry from the University of Nebraska-Lincoln. Osval A. Montesinos-López is currently a Professor of Statistics, Probability and Statistical Learning at University of Colima, México. His areas of interest include the development of novel genomic prediction models for plant breeding, high-dimensional data analysis, generalized linear mixed models and Bayesian analysis, multivariate analysis and experimental designs. He has contributed univariate and multivariate genomic prediction models for predicting breeding values in plants with normal, binary, count and ordinal phenotypes. He also has taught courses on genomic prediction, statistical and machine learning in Mexico, the United States of America, Brazil, Peru, Nigeria, France and India. 

Gabriela Hernández Ramírez holds a BS in Chemical Engineering from Tecnológico de Orizaba Veracruz, México, Masters and PhD in Entomology and Acarology from Colegio de Postgraduados of México. Gabriela Hernández-Ramírez is currently a Professor of Experimental Designs, Introduction to statistics at Instituto Superior de Tierra Blanca, Mexico. Her areas of interest include the development of alternatives for sustainable agriculture and the application of fungi and bacteria as a biological control agent to contribute to the production of food with a tendency towards sustainable production, improving the physical, chemical and biological properties of the soils where these crops are established. 

José Crossa holds a BS in Agriculture from Republic University of Uruguay and a PhD in Statistics and Quantitative Genetics from the University of Nebraska-Lincoln. He has helped define key methodologies for conserving and using the center's maize genetic resources, covering proper regeneration procedures and strategies for forming core subsets of large germplasm collections. Crossa’s became Head of the Biometrics and Statistics Unit of CIMMYT and developed theoretical and practical work on genetic resources conservation that made him to be selected the best scientist of the CGIAR Centers in 2008. His substantive body of research and publications has addressed many other areas of breeding and agronomyresearch, including developing new statistical models for genotype x environment, and QTL x environment interactions, general breeding and experimental design, hybrids and heterotic patterns, and association mapping, to name a few important subjects, and enjoys international acclaim and application. Crossa was given the Distinguish Scientist recognition in CIMMYT and is a Fellow of the Agronomy Society of America and of the Crop Science Society of America, Member of the Mexican Academy of Science, Member of the National Research System of the National Council of Research and Technology (CONACYT) of Mexico, invited professor at Universities in Mexico and Uruguay, and Adjunct Professor at the University of Nebraska. Recently, Crossa and colleges impacted plant breeding by being one of the first researchers in showing genomic-enabled predictions models with high accuracy using pedigree and markers information applied in massive maize and wheat field data.