PML: combining predictors

fit-model-that-combines-predictors.R

library(ISLR)
library(ggplot2)
library(caret)

data(Wage)

# remove logwag as predicting wage, so this would be a pretty good predictor :)
Wage <- subset(Wage, select = -c(logwage))

# cross-validation data
inBuild <- createDataPartition(y = Wage$wage, p = 0.7, list = FALSE)
validation <- Wage[-inBuild, ]

# training / test data
buildData <- Wage[inBuild, ]
inTrain <- createDataPartition(y = buildData$wage, p = 0.7, list = FALSE)
training <- buildData[inTrain, ]; testing <- buildData[-inTrain, ]

# train
mod1 <- train(wage ~., method = "glm", data = training)
mod2 <- train(wage ~., method = "rf", data = training, trControl = trainControl(method = "cv"), number = 3)

# predict
pred1 <- predict(mod1, testing)
pred2 <- predict(mod2, testing)

# plot it: will demonstrate difference between model predictions + highlight how
# accurate / inaccurate the overall prediction was graphically
qplot(pred1, pred2, color = wage, data = testing)

# combine predictors and re-predict
predDF <- data.frame(pred1, pred2, wage = testing$wage)
combModFit <- train(wage ~ ., method = "gam", data = predDF)
combPred <- predict(combModFit, predDF)

# show that sse is less for combined vs singular predictors
sqrt(sum((pred1 - testing$wage)^2))
sqrt(sum((pred2 - testing$wage)^2))
sqrt(sum((combPred - testing$wage)^2))

# cross-validate predictions
pred1V <- predict(mod1, validation); pred2V <- predict(mod2, validation)
predVDF <- data.frame(pred1 = pred1V, pred2 = pred2V)
combPredV <- predict(combModFit, predVDF)

# again show that sse was reduced using the validation data set and the
# combination of the two models
sqrt(sum((pred1V - validation$wage)^2))
sqrt(sum((pred2V - validation$wage)^2))
sqrt(sum((combPredV - validation$wage)^2))

qplot.md