Working with models

Andrew Irwin, a.irwin@dal.ca

2024-02-13

Models and visualizations

• Adding regression and smoothing lines to ggplot visualizations

• Describing, fitting, and using models

  • Linear regression

  • Other regression

  • Generalized additive models

  • LOESS smooths

Examples

• Linear regression

• Polynomial model

• Quantile regression (fitting line to medians or other quantiles)

• Generalized additive model (piecewise splines)

• LOESS (local linear and quadratic regression)

• Putting multiple smooths on one plot

• Smooths on facetted plots

Start with a basic graph

mpg |> mutate(city_l100km = 235.214583 / cty) |>
   ggplot(aes(x =displ, y= city_l100km)) + geom_point() +
   labs(x = "Engine displacement (L)",
        y = "Fuel economy, city (L/100km)") + my_theme

Add a regression line

p + geom_smooth(method = "lm", formula = y ~ x)

Add a regression line for each group

p + geom_smooth(aes(color = factor(cyl)), method = "lm", formula = y ~ x)

Polynomial regression

p + geom_smooth(method = "lm", formula = y ~ poly(x,2))

Quantile regression

p + geom_quantile(method = "rqss", formula = y ~ x,
                  quantiles = c(0.1, 0.5, 0.9))

Generalized additive model

p + geom_smooth(method = "lm", 
                formula = y ~ splines::bs(x, df = 5))

Generalized additive model

p + geom_smooth(method = "gam", 
                formula = y ~ s(x, bs="cs"))

LOESS

p + geom_smooth(method = "loess", 
                formula = y ~ x) 

LOESS

p + geom_smooth(method = "loess", formula = y ~ x,
                span = 0.3) 

Putting multiple smooths on one plot

p + geom_smooth(aes(color = "Linear"), method = "lm", se=FALSE) +
    geom_smooth(aes(color = "GAM"), method = "gam", se=FALSE) +
    geom_smooth(aes(color = "LOESS"), method = "loess", formula = y ~ x, se=FALSE) +
    labs(color = "Type")

Smooths on facetted plots

p + geom_smooth(method = "lm", se=FALSE, formula = y ~ x) +
  facet_wrap( ~ class)

Other customizations

p + geom_smooth(method = "lm", se=TRUE, 
                fullrange = TRUE, level = 0.50) + xlim(1,8)

Modelling x as a function of y

p + geom_smooth(method = "loess", formula = y ~ x, orientation = "y")

Modelling x as a function of y

p + geom_smooth(method = "lm", formula = y ~ x, orientation = "y") +
  geom_smooth(method = "lm", formula = y ~ x, color = "red")

Summary

• Regression lines (based on a model) and “smooths” (no simple model) can be used to draw attention to patterns in data

• We are using smooths for their visual effect

• Logical reasoning for the lines you draw is important (next lessons)

Further reading

• Course notes

• Healy Chapter 6. Work with models.