Generalized Linear Models and Nonparametric Regression

Generalized Linear Models and Nonparametric Regression

This course is part of Statistical Modeling for Data Science Applications Specialization

Instructor: Brian Zaharatos

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4 modules

Gain insight into a topic and learn the fundamentals.

21 reviews

Intermediate level

Recommended experience

4 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

4 modules

Gain insight into a topic and learn the fundamentals.

21 reviews

Intermediate level

Recommended experience

4 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

What you'll learn

Describe how to generalize the linear model framework to accommodate data that is not suitable for the standard linear regression model.
State some advantages and disadvantages of (generalized) additive models.
Describe how an additive model can be generalized to incorporate non-normal response variables (i.e., define a generalized additive model).

Skills you'll gain

Tools you'll learn

R Programming

Details to know

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Assessments

8 assignments

Taught in English

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This course is part of the Statistical Modeling for Data Science Applications Specialization

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There are 4 modules in this course

In the final course of the statistical modeling for data science program, learners will study a broad set of more advanced statistical modeling tools. Such tools will include generalized linear models (GLMs), which will provide an introduction to classification (through logistic regression); nonparametric modeling, including kernel estimators, smoothing splines; and semi-parametric generalized additive models (GAMs). Emphasis will be placed on a firm conceptual understanding of these tools. Attention will also be given to ethical issues raised by using complicated statistical models.

This course can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) degree offered on the Coursera platform. The MS-DS is an interdisciplinary degree that brings together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the MS-DS is ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://www.coursera.org/degrees/master-of-science-data-science-boulder. Logo adapted from photo by Vincent Ledvina on Unsplash

In this module, we will introduce generalized linear models (GLMs) through the study of binomial data. In particular, we will motivate the need for GLMs; introduce the binomial regression model, including the most common binomial link functions; correctly interpret the binomial regression model; and consider various methods for assessing the fit and predictive power of the binomial regression model.

What's included

7 videos5 readings3 assignments2 programming assignments2 peer reviews1 discussion prompt2 ungraded labs

7 videos Total 75 minutes

From Linear Models to Generalized Linear Models 13 minutes
The Components of a GLM 6 minutes
The Exponential Family of Distributions 15 minutes
Introduction to Binomial Regression 10 minutes
Binomial Regression Parameter Estimation 12 minutes
Interpretation of Binomial Regression 8 minutes
Binomial Regression in R 12 minutes

5 readings Total 41 minutes

Course Updates and Accessibility Support 1 minute
Earn Academic Credit for your Work! 10 minutes
Course Support 10 minutes
Assessment Expectations 10 minutes
FairML Book, Introduction 10 minutes

3 assignments Total 90 minutes

Introduction to Generalized Linear Models 30 minutes
Binomial Regression 30 minutes
Binomial Regression Inference 30 minutes

2 programming assignments Total 300 minutes

Optional Introduction to Jupyter and R 180 minutes
Module 1 Autograded Assignment 120 minutes

2 peer reviews Total 120 minutes

Ethical Issues in Statistics and Data Science (Fair ML Intro) 60 minutes
Module 1 Peer-Review Assignment Submission 60 minutes

1 discussion prompt Total 10 minutes

Introduce Yourself 10 minutes

2 ungraded labs Total 120 minutes

Assessing the fit of the binomial regression model 60 minutes
Module 1 Peer-Review Lab 60 minutes

In this module, we will consider how to model count data. When the response variable is a count of some phenomenon, and when that count is thought to depend on a set of predictors, we can use Poisson regression as a model. We will describe the Poisson regression in some detail and use Poisson regression on real data. Then, we will describe situations in which Poisson regression is not appropriate, and briefly present solutions to those situations.

What's included

7 videos2 assignments1 programming assignment1 peer review3 ungraded labs

7 videos Total 83 minutes

Poisson Regression: A New Model for Count Data 13 minutes
Poisson Regression Parameter Estimation 7 minutes
Interpreting the Poisson Regression Model 7 minutes
Poisson Regression on Real Data in R 22 minutes
Goodness of Fit for Poisson Regression I 17 minutes
Goodness of Fit for Poisson Regression II 5 minutes
Overdispersion 12 minutes

2 assignments Total 60 minutes

Poisson Regression Basics 30 minutes
Poisson Regression Inference and Goodness of Fit 30 minutes

1 programming assignment Total 180 minutes

Module 2 Autograded Assignment 180 minutes

1 peer review Total 60 minutes

Module 2 Peer-Review Lab Submission 60 minutes

3 ungraded labs Total 180 minutes

Poisson regression on real data in R 60 minutes
Poisson regression goodness of fit in R 60 minutes
Module 2 Peer-Review Lab 60 minutes

In this module, we will introduce the concept of a nonparametric regression model. We will contrast this notion with the parametric models that we have studied so far. Then, we’ll study particular nonparametric regression models: kernel estimators and splines. Finally, we will introduce additive models as a blending of parametric and nonparametric methods.

What's included

6 videos1 assignment1 programming assignment1 peer review3 ungraded labs

6 videos Total 66 minutes

Introduction to Nonparametric Regression Models 12 minutes
Motivating Kernel Estimators 6 minutes
Kernel Estimators 14 minutes
Smoothing Splines 13 minutes
Loess: Locally Estimated Scatterplot Smoothing 14 minutes
Kernel Estimation in R 6 minutes

1 assignment Total 30 minutes

Nonparametric Regression: Theory 30 minutes

1 programming assignment Total 180 minutes

Module 3 Autograded Assignment 180 minutes

1 peer review Total 60 minutes

Module 3 Peer-Review Assignment Submission 60 minutes

3 ungraded labs Total 180 minutes

Smoothing Splines in R 60 minutes
The Loess Fit in R 60 minutes
Module 3 Peer-Review Lab 60 minutes

Some models, such as linear regression, are easily interpretable, but inflexible, in that they don't capture many real-world relationships accurately. Other models, such as neural networks, are quite flexible, but very difficult to interpret. Generalized additive models (GAMs) are a nice balance between flexibility and interpretability. In this module, we will further motivate GAMs, learn the basic mathematics of fitting GAMs, and implementing them on simulated and real data in R.

What's included

6 videos1 reading2 assignments1 programming assignment1 peer review3 ungraded labs

6 videos Total 81 minutes

Motivating Generalized Additive Models 18 minutes
Generalized Additive Models in R 16 minutes
Inference with Generalized Additive Models: Effective Degrees of Freedom 12 minutes
Inference with Generalized Additive Models: Tests 5 minutes
Generalized Additive Models in R: Inference and Interpretation 14 minutes
Generalized Additive Models: A Complete Example with Real Data 17 minutes

1 reading Total 10 minutes

Required: Generalized additive models for data science 10 minutes

2 assignments Total 60 minutes

Generalized Additive Models: Basics 30 minutes
Generalized Additive Models: Inference and Data Analysis 30 minutes

1 programming assignment Total 180 minutes

Module 4 Autograded Assignment 180 minutes

1 peer review Total 180 minutes

Module 4 Peer-Review Assignment Submission 180 minutes

3 ungraded labs Total 180 minutes

Generalized Additive Models in R 60 minutes
Generalized Additive Models in R: Inference and Interpretation 60 minutes
Module 4 Peer-Review Lab 60 minutes

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This course is part of the following degree program(s) offered by University of Colorado Boulder. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹

Instructor

Instructor ratings

(9 ratings)

Brian Zaharatos

University of Colorado Boulder

4 Courses 14,831 learners

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University of Colorado Boulder

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Reviewed on Jun 27, 2023

The pace of instruction is excellent and the assignments make it easy to translate theory to practice.

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