Write a GLM
For any exponential family of distributions, write a GLM in the random/link/systematic component framework.
Identify the canonical link
Determine the canonical link for any distribution in the exponential family.
Fit GLM using software
Fit (using frequentist and Bayesian methods) and choose an appropriate generalized linear model for binary, ordered categorical, unordered categorical, and count response variables using R, SAS, and WinBUGS/OpenBUGS/JAGS.
Mathematically solve and compute the MLE's for coefficients of any basic GLM
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.
Evaluate a fitted GLM
Evaluate the validity/appropriateness of the chosen model using model diagnostics such as residual plots and deviance.
Identify model weaknesses and strengths
Identify weaknesses and strengths in the chosen model for a given data set.
Predict and provide confidence intervals
Make predictions and determine confidence intervals using the fitted model.
Identify and account for overdispersion
Identify when overdispersion is present in a given data set and ways to account for overdispersion in the model.
Fit and interpret output from a non-standard GLM
Fit using R and/or SAS and interpret the output from a generalized linear mixed model, zero-inflated model, gamma regression model, and GLM's for dependent data.