Generalized Linear Models
Generalized linear models framework, binary data, polytomous data, log-linear models.
STAT
637
 Hours3.0 Credit, 3.0 Lecture, 0.0 Lab
 PrerequisitesSTAT 535 & STAT 642
 TaughtWinter
Course Outcomes: 


Fit and Choose

Select and fit appropriate frequentist and Bayesian generalized linear models for binary, ordered categorical, unordered categorical, and count response variables using R and SAS.

STAT 537

By the end of the semester, students should be able to:

Evaluate Validity

Evaluate the validity/appropriateness of the chosen model using diagnostics such as residual plots and deviance.

Identify Weaknesses

Identify weaknesses in the chosen model for a given data set.

Fit and Choose

Fit and choose an appropriate generalized linear model for binary, ordered categorical, unordered categorical, and count response variables using R and SAS.

Make Predictions

Make predictions and determine confidence intervals using the fitted model.

Evaluate Validity

Evaluate the validity/appropriateness of the chosen model using model diagnostics such as residual plots and deviance.

Demonstrate Understanding

Demonstrate understanding of the connection between Normal linear model theory and generalized linear model theory by expressing the Normal linear model as a generalized linear model.

Identify Weaknesses

Identify weaknesses in the chosen model for a given data set.

Identify Overdispersion

Identify when overdispersion is present in a given data set and ways to account for overdispersion in the model.

Determine

Determine the canonical link for any distribution in the exponential family.

Make Predictions

Make predictions and determine confidence intervals using the fitted model.

Reproduce Score Equations

Reproduce (for any distribution in the exponential family) score equations, Fisher information, and write out the form of the iterative reweighted least squares algorithm for finding maximum likelihood estimates of the coefficients.

Implement a Simple Model

Implement a simple multi-level model using R and SAS and a Bayesian logistic regression model using R.

Demonstrate Understanding

Demonstrate understanding of the connection between Normal linear model theory and generalized linear model theory by expressing the Normal linear model as a generalized linear model.

Determine

Determine the canonical link ofr any distribution in the exponential family.

Reproduce Score Equations

Reproduce (for any distribution in the exponential family) score equations, Fisher information, and write out the form of the iterative reweighted least squares algorithm for finding maximum likelihood estimates of the coefficients.

Implement a Simple Model

Time permitting, implement a simple multi-level model using R and SAS and a Bayesian logistic regression model using R.