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Course

Nonlinear Modeling with Generalized Additive Models (GAMs) in R

IntermediateSkill Level

4.7+

Updated 09/2024

GAMs model relationships in data as nonlinear functions that are highly adaptable to different types of data science problems.

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Course Description

Generalized Additive Models are a powerful tool for both prediction and inference. More flexible than linear models, and more understandable than black-box methods, GAMs model relationships in data as nonlinear functions that are highly adaptable to different types of data and data science problems. In this course, you'll learn how GAMs work and how to construct them with the popular mgcv package. You'll learn how to interpret, explain and visualize your model results, and how to diagnose and fix model problems. You'll work with data sets that will show you how to apply GAMs to a variety of situations: automobile performance data for building mixed linear and nonlinear models, soil pollution data for building geospatial models, and consumer purchasing data for classification and prediction. By the end of this course, you'll have a toolbox for solving many data science problems.

Prerequisites

Introduction to Regression in R

1

Introduction to Generalized Additive Models

In this chapter, you will learn how Generalized additive models work and how to use flexible, nonlinear functions to model data without over-fitting. You will learn to use the gam() function in the mgcv package, and how to build multivariate models that mix nonlinear, linear, and categorical effects to data.

Introduction

Motorcycle crash data: linear approach

Motorcycle crash data: non-linear approach

Parts of non-linear function

Basis functions and smoothing

Setting complexity of the motorcycle model

Using smoothing parameters to avoid overfitting

Complexity and smoothing together

Multivariate GAMs

Multivariate GAMs of auto performance

Adding categorical to the auto performance model

Category-level smooths for different auto types

2

Interpreting and Visualizing GAMs

In this chapter, you will take a closer look at the models you fit in chapter 1 and learn how to interpret and explain them. You will learn how to make plots that show how different variables affect model outcomes. Then you will diagnose problems in models arising from under-fitting the data or hidden relationships between variables, and how to iteratively fix those problems and get better results.

Interpreting GAM outputs

Significance and linearity (I)

Significance and linearity (II)

Visualizing GAMs

Plotting the motorcycle crash model and data

Plotting multiple auto performance variables

Visualizing auto performance uncertainty

Model checking with gam.check()

Reading model diagnostics

Fixing problems with model diagnostics

Checking concurvity

Examining overall concurvity in auto data

Examining concurvity between auto variables

3

Spatial GAMs and Interactions

In this chapter, you will extend the types of models you can fit to those with interactions of multiple variables. You will fit models of geospatial data by using these interactions to model complex surfaces, and visualize those surfaces in 3D. Then you will learn about interactions between smooth and categorical variables, and how to model interactions between very different variables like space and time.

Two-dimensional smooths and spatial data

Modeling soil pollution in the Netherlands

Adding more variables to predict soil pollution

Plotting and interpreting GAM interactions

Plotting the model surface

Customizing 3D plots

Extrapolation in surface plots

Visualizing categorical-continuous interactions

Soil pollution in different land uses

Plotting pollution in different land uses

Interactions with different scales: Tensors

Pollution models with multi-scale interactions

Teasing apart multi-scale interactions

4

Logistic GAMs for Classification

In the first three chapters, you used GAMs for regression of continuous outcomes. In this chapter, you will use GAMs for classification. You will build logistic GAMs to predict binary outcomes like customer purchasing behavior, learn to visualize this new type of model, make predictions, and learn how to explain the variables that influence each prediction.

Types of model outcomes

Classifying purchasing behavior

Purchase behavior with multiple smooths

Visualizing logistic GAMs

Visualizing influences on purchase probability

Interpreting purchase effect plots (I)

Interpreting purchase effect plots (II)

Interpreting purchase effect plots (III)

Making predictions

Predicting purchase behavior and uncertainty

Explaining individual behaviors

Doing more with GAMs

Nonlinear Modeling with Generalized Additive Models (GAMs) in R

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FAQs

What prior knowledge do I need before taking this GAMs course?

You should be comfortable with linear regression, ggplot2, dplyr, and intermediate R. The course builds on regression concepts and introduces nonlinear extensions using the mgcv package.

What real-world datasets are used in this course?

You work with automobile performance data for mixed models, soil pollution data for geospatial modeling, and consumer purchasing data for classification tasks.

Will I learn how to diagnose and fix problems in GAM models?

Yes. Chapter 2 covers how to detect underfitting and hidden variable relationships, then walks you through iteratively improving your models for better results.

How are GAMs different from linear regression and black-box models?

GAMs offer more flexibility than linear models by fitting nonlinear smooth functions, while remaining more interpretable than black-box methods like neural networks or random forests.

Does this course cover classification problems using GAMs?

Yes. The final chapter teaches logistic GAMs for binary classification, including how to visualize predictions and explain which variables influence each outcome.

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