log linear model in ggplot? - r

Question

The data is from: http://www.principlesofeconometrics.com/poe5/poe5rdata.html, in the file: collegetown.csv
A log linear model is of the form: ln(y) = b1 + b2x
library(ggthemes)
library(ggplot2)
theUrl <- "../poedata/collegetown.csv"
collegetown <- read.csv(theUrl)
g1 <- ggplot(data = collegetown, aes(x = sqft, y = price))+
geom_point(col = "blue")
plot(g1)
logLinearModel <- lm(log(price)~sqft, data = collegetown)
g1 + geom_smooth(method = "lm", formula = y ~ exp(x), se = F, col = "green")+
theme_economist()
summary(logLinearModel)
This gives me the weird plot below:
How do I plot the proper curve? Do I need to store the predicted values explicitly in the data frame?
PS: I want the axis to stay untransformed i.e. in their original scales.

Answer 1

The model y~exp(x) is not the same as the model log(y)~x, so you're not getting the smoother you expect. You can specify that the smoother is a generalised linear model with a log-link function using the code:
g1 <- ggplot(data = collegetown, aes(x = sqft, y = price))+
geom_point(col = "blue")
g1 + geom_smooth(method = "glm", formula = y ~ x, se = F, col = "green",
method.args = list(family=gaussian(link="log"))) +
theme_economist()
which gives what you're wanting. If that doesn't seem intuitive, you can fit the lm outside the plotting with:
logLinearModel <- lm(log(price)~sqft, data = collegetown)
collegetown$pred <- exp(predict(logLinearModel))
ggplot(data = collegetown, aes(x = sqft, y = price))+
geom_point(col = "blue") +
geom_line(aes(y=pred), col = "green")+
theme_economist()
Warning - the two versions aren't the same if you want the standard errors; the first approach gives symmetric errors, the standard errors that you might get from the lm prediction are symmetric on a log scale. See here.

Answer 2

I think a relatively simpler method to build the curve is using stat_function() method.
# LOG LINEAR MODEL
logLinearModel <- lm(log(price)~sqft, data = collegetown)
smodloglinear <- summary(logLinearModel)
logLinearModel
names(logLinearModel)
yn <- exp(logLinearModel$fitted.values)
rgloglinear <- cor(yn, collegetown$price)
rgloglinear^2
b1 <- coef(smod)[[1]]
b2 <- coef(smod)[[2]]
sighat2 <- smod$sigma^2
g2 <- ggplot(data = collegetown,aes(x = sqft, y = price))+
geom_point(col = "white") +
stat_function(fun = function(x){exp(b1+b2*x)}, aes(color = "red"))+
stat_function(fun = function(x){exp(b1+b2*x+sighat2/2)} , aes(color = "green"))+
dark_theme_bw()+
scale_color_identity(name = "Model fit",
breaks = c("red", "green"),
labels = c("yn", "yc"),
guide = "legend")
g2
which gives: