Exploration of advanced statistical modeling techniques, focusing on generalized linear models (GLMs), linear mixed models (LMMs), and generalized linear mixed models (GLMMs). Topics include applications to binary, count, and polytomous data, longitudinal analysis, spatial analysis, model selection, and model interpretation. Emphasis is on real-world applications across various diverse disciplines
Athena Title
Advanced Statistical Models
Prerequisite
STAT 8260 and (STAT 4520/6520 or STAT 6820)
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Student learning Outcomes
Students will distinguish between linear, generalized linear, linear-mixed effect, and generalized linear mixed-effect model-based methodology and identify the domains of applications of these model classes.
Students will apply generalized linear models (GLMs) to binary, count, and polytomous response data, including proper estimation, inference, and interpretation
Students will identify applications and longitudinal data, for which mixed-effect models are suitable and apply those models using appropriate methods of estimation and inference.
Students will choose appropriate computational tools such as packages and options to fit the desired model.
Students will apply appropriate methodology for model selection, including goodness-of-fit and information criteria.
Students will understand the special problems such as overdispersion, censoring, missing data, and misspecification of underlying probability models.
Students will communicate inferences and conclusions from real-world applications via well-crafted written reports that integrate statistical reasoning, data visualization, and model interpretations at an appropriate level of technicality to the intended audience.
Topical Outline
Generalized Linear Models (GLMs) – Theory
• Exponential dispersion family of distributions
• Link functions and their interpretation
• Maximum likelihood estimation and inference
• Model diagnostics and selection
GLMs – Binary and (finite) Ordinal Response
• Logistic regression for binary outcomes
• Probit and complementary log-log models
• Overdispersion and quasi-likelihood approaches
• Applications in epidemiology and social sciences
GLMs – Unbounded Counts
• Poisson regression models
• Negative binomial regression for over-dispersed counts
• Zero-inflated and hurdle models
• Generalized additive models
• Applications in biostatistics and econometrics
Review of Linear Mixed Models (LMMs)
• Motivation for mixed-effects modeling
• Fixed vs. random effects
• Estimation methods (REML, ML)
• Inference methods on fixed-effects and variance-covariance parameters.
• Model interpretation and diagnostics
LMMs – Applications to Longitudinal and Spatial Data
• Random effects models in ANOVA with repeated measures
• Modeling subject-specific trajectories with random intercept and slope
• Covariance structures for spatial data
• Applications in, e.g., agricultural and medical sciences
Introduction to Generalized Linear Mixed Models (GLMMs)
• Extending GLMs to include random effects
• Estimation techniques (Laplace approximation, adaptive quadrature, Bayesian MCMC)
• Model selection and interpretation
• Applications in, e.g., healthcare, finance, and social sciences
Special topics
• Missing data and censored data
• Geographically weighted regression
• Model regularization
• Advanced methods chosen at the discretion of the instructor (e.g., multiple imputation, EM algorithm, and Bayesian approaches)
Institutional Competencies Learning Outcomes
Analytical Thinking
The ability to reason, interpret, analyze, and solve problems from a wide array of authentic contexts.
