1 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.
2 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.
3 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.
Explain the concept of non-proportional odds.
Assess the assumption of proportional odds via the Brant-Wald test.
Contrast the Ordinal Logistic regression models under proportional and non-proportional odds assumptions.
4 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.
5 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 a parametric technique.
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.
Outline the modelling framework of a Cox Proportional Hazards model.
Fit a Cox Proportional Hazards model in R.
Interpret the regression coefficients of a Cox Proportional Hazards model, and identify the model assumptions.
Obtain predicted survival functions from a Cox Proportional Hazards model.
6 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.
7 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.
8 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.