Lecture Learning Objectives

Lecture 1 - Generalized Linear Models: Link Functions and Count Regression

• Explain the Data Science workflow in Regression Analysis.

• Recall the basics of Ordinary Least-squares (OLS) regression.

• Identify cases where OLS regression is not suitable.

• Distinguish what makes a regression model “linear.”

• Explain the concept of generalized linear models (GLMs).

• Explore the concept of the link function.

• Outline the modelling framework of count regression.

• Fit and interpret count regression.

• Use count regression for prediction.

• Explain and test overdispersion on count-type data.

Lecture 2 - Generalized Linear Models: Model Selection and Multinomial Logistic Regression

• Perform likelihood-based model selection through analysis of deviance, Akaike Information Criterion, and Bayesian Information Criterion.

• Extend the link function concept of the generalized linear models (GLMs) to other discrete categorical responses.

• Outline the modelling framework of the Multinomial Logistic regression.

• Fit and interpret the Multinomial Logistic regression.

• Use the Multinomial Logistic regression for prediction.

Lecture 3 - Generalized Linear Models: Ordinal Logistic Regression

• Outline the modelling framework of the Ordinal Logistic regression.

• Explain the concept of proportional odds.

• Fit and interpret Ordinal Logistic regression.

• Use the Ordinal Logistic regression for prediction.

Lecture 4 - Linear Mixed-Effects Models

• Identify the model assumptions in a linear Mixed-Effects model.

• Associate a term (or combination of terms) in a Mixed-Effects model with the following quantities:

  • Fixed effect estimates.

  • Variances of the random effects.

  • Regression coefficients for each group and population.

  • Predictions on existing groups and a new group.

• Fit a linear Mixed-Effects model in R, and extract estimates of the above quantities.

• Identify the consequences of fitting a fixed-effects linear regression model when there are groups, whether a slope parameter is pooled or fit separately per group.

• Explain the difference between the distributional assumption on the random effects and the fixed effects estimates’ sampling distribution.

Lecture 5 - Survival Analysis

• Identify when data is censored.

• Understand the consequence of subsetting to uncensored data or ignoring the censored property instead of using Survival Analysis methods.

• Obtain univariate estimates for the mean, median, and survival function in R with the Kaplan-Meier technique.

• Identify when the Kaplan-Meier survival function estimate cannot produce mean and high quantile estimates.

• Interpret the regression coefficients of a Cox Proportional Hazards model, and identify the model assumptions.

• Obtain predictions from a Cox Proportional Hazards model.

Lecture 6 - Local Regression

• Define the concept of local regression.

• Model and perform piecewise constant, linear, and continuous linear local regressions.

• Extend the concept of \(k\)-NN classification to a regression framework.

• Define and apply locally weighted scatterplot smoother regression.

Lecture 7 - Quantile Regression

• Review what a quantile is.

• Compare the error functions of Ordinary Least-Squares (OLS) regression versus Quantile regression.

• Recognize the impacts of parametric and distributional assumptions in Quantile regression.

• Perform non-parametric Quantile regression.

• Perform parametric Quantile regression.

Lecture 8 - Missing Data

• Identify and explain the three common types of missing data mechanisms.

• Identify a potential consequence of removing missing data on downstream analyses.

• Identify a potential consequence of a mean imputation method on downstream analyses.

• Identify the four steps involved with a multiple imputation method for handling missing data.

• Use the mice package in R to fit multiple imputed models.