An advanced companion to Applied Linear Models, explores the material with greater rigor and depth. Problems, background material, and mathematical justifications of the techniques of estimation, diagnostics, variable selection, regularized regression, mixed-effect models and generalized linear models will be covered, emphasizing both conceptual understanding and practical implementation.
Athena Title
Advanced Applied Linear Models
Pre or Corequisite
STAT6420 or permission of department
Semester Course Offered
Offered fall
Grading System
A - F (Traditional)
Student learning Outcomes
Students will describe the relationship and domains of application of estimation methods for linear, linear mixed-effect, and generalized linear models, including least squares, penalized least-squares, weighted/generalized least squares, maximum likelihood, and restricted maximum likelihood estimation.
Students will explain the relationship between t tests, F tests, likelihood ratio, and Wald tests and the corresponding methods of interval construction in the context of linear, linear mixed-effect, and generalized linear models. Students will also understand when such tests are exact versus approximate, and the basis of the relevant approximations.
Students will understand the mathematical underpinnings of splines and the methods of estimation and inference associated with additive models.
Students will explain the concepts of overparameterization and multicollinearity and how these features of a model affect estimation and inference both mathematically and in practical terms.
Students will explain the challenges to causal inference in traditional regression models for observational data and identify and implement some strategies for strengthening causal conclusions.
Topical Outline
Through this course and its corequisite, STAT6420, students will develop the ability to apply least squares estimation and matrix-based linear modeling techniques to analyze relationships in real-world datasets. They will gain a solid understanding of fixed and random effects in linear mixed models, as well as generalized linear models (GLMs) for non-Gaussian response variables. In addition to applied skills, students will deepen their theoretical understanding of the techniques used in least squares estimation, model diagnostics, variable selection, high-dimensional regularization, mixed models, and GLMs. This course also provides strong preparation for the applied linear models component of the departmental Ph.D.-level qualifying examinations.
Introduction to linear models and least squares estimation, statistical inference, hypothesis testing, Gauss-Markov theorem
Model diagnostics and validation
Variable selection
High-dimensional estimation with regularization
Introduction to mixed effects models
Introduction to generalized linear models
Splines and additive models
Handling missing data
Institutional Competencies Learning Outcomes
Analytical Thinking
The ability to reason, interpret, analyze, and solve problems from a wide array of authentic contexts.
