During the spring of 2016, I had the opportunity to design and teach a topics course that is new to Macalester: Advanced Statistical Modeling. Students in this course were primarily seniors with either majors in Applied Math and Statistics or a minor in Statistics. All students had taken several statistics classes, including Probability and Mathematical Statistics.
We began the semester with model diagnostics for linear models. We then discussed model selection criteria (such as AIC and BIC) and formal tests to compare models (such as the ANOVA F-test, Wald tests, and likelihood ratio tests). Students learned to use forward selection and backward elimination with various selection criteria. We then reviewed the likelihood function and likelihood-based inference. The majority of the semester was spent creating, interpreting, and testing generalized linear models, linear mixed models, and generalized linear mixed models. Students also discussed random effect structure (crossed and nested) for mixed models and learned to identify the structure based on a study’s description.
The students in Advanced Statistical Modeling applied their new statistical tools in individual projects. They developed research questions on a topic of their choosing, gathered the necessary data, produced the appropriate models to answer their research questions, wrote reports to explain and conclude their work, and verbally presented their results to their classmates. The students also swapped papers to critically assess others’ work, provide constructive feedback, and suggest potential statistical analyses.