Teasing apart multi-scale interactions

In the previous exercise, you fit the following model:

tensor_mod <- gam(cadmium ~ te(x, y, elev), 
                  data = meuse, method = "REML")

In this exercise, you will fit a model with smooths and tensor interactions to separate out the independent and interacting effects of variables.

This exercise is part of the course

Nonlinear Modeling with Generalized Additive Models (GAMs) in R

Exercise instructions

Convert the above model such that x and y interact on the same scale, the effect elev is a separate smooth, and the interaction of all three on different scales is a separate term.
Summarize and plot the model.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Fit the model
tensor_mod2 <- ___


# Summarize and plot
___
___(___, pages = 1)

Edit and Run Code

This exercise is part of the course

Nonlinear Modeling with Generalized Additive Models (GAMs) in R

IntermediateSkill Level

4.8+

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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.

Exercise 1: Introduction Exercise 2: Motorcycle crash data: linear approach Exercise 3: Motorcycle crash data: non-linear approach Exercise 4: Parts of non-linear function Exercise 5: Basis functions and smoothing Exercise 6: Setting complexity of the motorcycle model Exercise 7: Using smoothing parameters to avoid overfitting Exercise 8: Complexity and smoothing together Exercise 9: Multivariate GAMs Exercise 10: Multivariate GAMs of auto performance Exercise 11: Adding categorical to the auto performance model Exercise 12: Category-level smooths for different auto types

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.

Exercise 1: Interpreting GAM outputs Exercise 2: Significance and linearity (I)Exercise 3: Significance and linearity (II)Exercise 4: Visualizing GAMs Exercise 5: Plotting the motorcycle crash model and data Exercise 6: Plotting multiple auto performance variables Exercise 7: Visualizing auto performance uncertainty Exercise 8: Model checking with gam.check()Exercise 9: Reading model diagnostics Exercise 10: Fixing problems with model diagnostics Exercise 11: Checking concurvity Exercise 12: Examining overall concurvity in auto data Exercise 13: Examining concurvity between auto variables

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.

Exercise 1: Two-dimensional smooths and spatial data Exercise 2: Modeling soil pollution in the Netherlands Exercise 3: Adding more variables to predict soil pollution Exercise 4: Plotting and interpreting GAM interactions Exercise 5: Plotting the model surface Exercise 6: Customizing 3D plots Exercise 7: Extrapolation in surface plots Exercise 8: Visualizing categorical-continuous interactions Exercise 9: Soil pollution in different land uses Exercise 10: Plotting pollution in different land uses Exercise 11: Interactions with different scales: Tensors Exercise 12: Pollution models with multi-scale interactions Exercise 13: Teasing apart multi-scale interactions

Current Exercise

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.

Exercise 1: Types of model outcomes Exercise 2: Classifying purchasing behavior Exercise 3: Purchase behavior with multiple smooths Exercise 4: Visualizing logistic GAMs Exercise 5: Visualizing influences on purchase probability Exercise 6: Interpreting purchase effect plots (I)Exercise 7: Interpreting purchase effect plots (II)Exercise 8: Interpreting purchase effect plots (III)Exercise 9: Making predictions Exercise 10: Predicting purchase behavior and uncertainty Exercise 11: Explaining individual behaviors Exercise 12: Doing more with GAMs