Non-linear logistic regression

In chapter 3, you explored the distance commuters traveled and the linear effect this had on the probability of somebody riding the bus. However, what if this relationship is non-linear and non-monotonic?

probitVsLogit

For example, what if people who commute the shortest distances and longest are less likely to ride the bus? You can add non-linear terms to formulas in R using the I(..) function as part of your formula. For example y~I(x^2) allows you to estimate a coefficient for x*x. During this exercise, you will examine the bus data more.

This exercise is part of the course

Generalized Linear Models in R

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Exercise instructions

Add the formula y ~ I(x^2) to the formula option in the second call to geom_smooth().

Hands-on interactive exercise

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

# Plot linear effect of travel distance on probability of taking the bus
gg_jitter <-
	ggplot(data = bus, aes(x = MilesOneWay, y = Bus2)) + 
	geom_jitter(width = 0, height = 0.05) + 
	geom_smooth(method = 'glm', 
                method.args = list(family = 'binomial'))

# Add a non-linear equation to a geom_smooth()
gg_jitter +
	geom_smooth(method = 'glm', 
                method.args = list(family = 'binomial'), 
                formula = ___, 
                color = 'red')

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