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Summer Institute for Statistics and Genetics: Mixed Models for Quantitative Genetics

By Madi Gamble

The University of Washington hosts short courses on a range of subjects each year through its Summer Institutes program. The course I attended, “Mixed Models for Quantitative Genetics,” is part of the Summer Institute for Statistics and Genetics. The course was two and a half days long and covered a staggering amount of material in that time. The course was taught by Bruce Walsh (University of Arizona), one of the authors of a classic textbook on quantitative genetics, and Guilherme Rosa (University of Wisconsin), who specializes in the biostatistics behind plant and animal breeding.

We began with a review of vectors and matrices and how to use them to store multi-dimensional information. We then reviewed matrix algebra, discussed eigenvalues and eigenvectors as characteristics of matrix geometry and dimensionality, how to express systems of equations in matrix form, and then on to general linear models, generalized linear models, and finally the uses of fixed and random effects in linear mixed models.

Throughout, the course was fast paced but welcoming of questions and discussion. I really appreciated that the instructors encouraged us to ask questions and never expressed surprise or disappointment at more basic questions (that said, one instructor did refer to the second edition of his book as “the new testament” – whether he was referring to its length or its perceived impact on the world was unclear).

While I learned a lot about the mathematics behind linear models, I wish that we had spent less time on the math and more on the applications of those models. For example, I would have liked more concrete examples relative to biology when discussing the use of certain models, and more practice using the models to analyze data with tangible variables.

Perhaps the best part of the course was the people I met, who I will certainly remain in touch with as I use mixed effect models in my research. The participants in the course ranged from mathematicians, to statisticians, to biologists working with humans, livestock, crops, and other plants and animals. The diverse perspectives of the students in the course helped to make the material more accessible to everyone. I would highly recommend this course and others that are part of the Summer Institutes at UW to other students!