Approaches when faced with special conditions in regression, and consequences of ignoring these conditions.

By the end of the course, students are expected to:

- Describe the risk and value of making parametric assumptions in regression.
- Fit model functions that represent probabilistic quantities besides the mean.
- Identify situations where standard linear regression is sub-optimal, and apply alternative regression methods that better address the situation.
- Link the bias-variance tradeoff to the fundamental tradeoff of machine learning.

Check out the About page for a description of the course.

Deliverable | Weight |
---|---|

lab assignment 1 | 15% |

lab assignment 2 | 15% |

quiz 1 | 20% |

lab assignment 3 | 15% |

lab assignment 4 | 15% |

quiz 2 | 20% |

Note: Topics covered are conditional on time available.

Lecture | Date | Topic |
---|---|---|

1 | 2019-02-04 | Model functions in regression |

2 | 2019-02-06 | Regression on restricted scales: GLM and transformations |

3 | 2019-02-11 | Regression beyond the mean Part I: variance, quantiles |

4 | 2019-02-13 | Regression beyond the mean Part II: probabilistic forecasts, robust regression |

5 | 2019-02-25 | Regression on censored response data: survival analysis |

6 | 2019-02-27 | Regression on ordinal response data: proportional odds model |

7 | 2019-03-04 | Regression in many groups: mixed effects models |

8 | 2019-03-06 | Regression when data are missing |

If time remains, here are some topics we could cover:

- Regression in between linear and non-parametric: Generalized Additive Models
- Copula Regression
- Non-identifiability
- Heavy-tailed distributions

- Julian J. Faraway. Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models, Second Edition (Chapman & Hall/CRC Texts in Statistical Science), 2016.
- For survival analysis: David G. Kleinbaum, Mitchel Klein (2012) Survival analysis: a self-learning text, 3rd edition
- Non-technical explanation of survival analysis, with a nice succinct summary along the side of each page.
- Recommends epidemiological background, but we will avoid those parts.

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