In boxizhang/boxridge: A linear regression package in R

knitr::opts_chunk$set(comment = NA)

library(mlbench)
library(caret)
library(leaps)
library(ggplot2)
library(lattice)
data("BostonHousing")

Divide the BostonHousing data (or your own API data) into a test and training dataset using the caret package.

Dividing the BostonHousing data into 70% training and 30% test data

data("BostonHousing")
names(BostonHousing)
train_data <- caret::createDataPartition(BostonHousing$age, p = .7,
                                         list = FALSE,
                                         times= 1)
Trainingdata <- BostonHousing[train_data, ]
Testdata <- BostonHousing[-train_data, ]


nrow(Trainingdata)
nrow(Testdata)

#For the 20-fold cross-validation
ctr <- caret::trainControl(method = "repeatedcv",
  number = 20, # k=20
  repeats = 20) # repeat 10 times

1. Fit a linear regression model on the Trainingdata dataset.

The first two arguments of the train function are predictor and outcome data objects.Traincontrol object in train allows us to specify the resampling method.The resampling method used here is cv-cross validation. For our analysis we have taken crim variable . R-squared and RMSE(Root Mean Square Error)is used measure model performance. RSME values is low .

lm <- caret::train(indus~.,
                      data = Trainingdata,
                      method='lm',
                      trControl = trainControl(method = "cv")
)

print(lm)

2. Fit a linear regression model and with a linear regression model with forward selection of covariates. Fitting a linear model with method = leapForward on the Trainingdata dataset.

lflmGrid <- expand.grid(nvmax=1:(ncol(Trainingdata)-1))
lflm <- caret::train(indus~.,
                      data = Trainingdata,
                      method='leapForward',
                      tuneGrid = lflmGrid,
                      trControl = trainControl(method = "cv")
)
print(lflm)

3. Evaluate the performance of this model on the Trainingdata dataset.

since we have got a low RMSE,we think that our model has good perfomance with 8(number of predictors).

p_data <- as.data.frame(cbind(predict(lflm), scale(resid(lflm))))

plot <- ggplot(p_data, aes(x = p_data[,1], y = p_data[,2])) + geom_point() +
          geom_smooth(method = "loess", color = "red") + xlab("Fitted") +
          ylab("Residuals") + ggtitle("Resid vs Fitted with 9 factors") +
          theme(plot.title = element_text(hjust = 0.5))

plot(plot)

4~5. Fit a ridge regression model using ridgereg() function in boxridge package and finding a best parameter lambda using 10-fold cross-validation on the Trainingdata set.

#To use rigdereg() function
ridge <- list(type=c("Classification", "Regression"),
            library="boxridge",
            loop=NULL,
            prob=NULL)

#Parameter setting
ridge$label<-"Ridge regression"

ridge$parameters <- data.frame(parameter = "lambda",
                  class = "numeric",
                  label = "lambda")

ridge$fit <- function(x, y, lambda, param, lev, last, classProbs, ...) { 
  dat <- as.data.frame(x)

  respvector <- NULL
  respname <- NULL
  respnum <- NULL

  for(i in 1:ncol(x)){
    if(identical(y,dat[,i])){
    respvector <- dat[,i]
    respname <- names(x)[i]
    respnum <- i
    }
  }

  formula <- paste(respname,"~", sep="")

  if(ncol(x) > 1){
    for(i in 1:ncol(x)-1){
            formula <- paste(formula, "+", names(dat)[i], sep="")
    }
  }

  formula <- as.formula(formula)

  ridgereg$new(formula = formula, data=dat,lambda= param$lambda)
 }

  ridge$predict <- function(modelFit, newdata, preProc=NULL, submodels = NULL){
  if (!is.data.frame(newdata)) 
    newdata <- as.data.frame(newdata)
  modelFit$predict(newdata)
}

ridge$sort  <- function(x) x[order(-x$lambda),]


ridge$grid <- function(x, y, len=NULL, search="grid"){
  data.frame(lambda=seq(from=0, to=10, by=1))
}

set.seed(12345)
ridge_fit <- caret::train(x = Trainingdata,
                  y = Trainingdata$indus,
                  method = ridge,
                  trControl = ctr)

ridge_fit

6. Evaluate the performance of all three models

#Linear regression
lm$results[,]

#Regression with forward selection
lflm$results[7,]

#Ridge regression
ridge_fit$results[1,]

boxizhang/boxridge documentation built on May 28, 2019, 7:12 p.m.