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101b_finalproj.Rmd
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101b_finalproj.Rmd
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---
title: "101b_final_proj"
output: html_document
---
```{r}
library(randomForest)
library(FrF2)
library(AlgDesign)
library(corrplot)
```
```{r}
# dataset = diabetes
# x's: tuning parameters of random forest
# y: cross-validation accuracy
# max number of runs = 35
diabetes <- load("diabetes.Rdata")
source("CrossValidation_RF.R")
```
# Part 1: Design of the Experiment
## Question 1
```{r}
# 7 factors
# Fractional Factorial Design
fr.design.cod <- FrF2(nruns = 32, nfactors = 7, randomize = F)
fr.design.mat <- desnum(fr.design.cod)
convert_design <- function(coded_design){
ntree <- ifelse(coded_design[,1] == 1, 1000, 100)
replace <- ifelse(coded_design[,2] == 1, 1, 0)
mtry <- ifelse(coded_design[,3] == 1, 6, 2)
nodesize <- ifelse(coded_design[,4] == 1, 11, 1)
maxnodes <- ifelse(coded_design[,5] == 1, 1000, 10)
classwt <- ifelse(coded_design[,6] == 1, 0.9, 0.5)
cutoff <- ifelse(coded_design[,7] == 1, 0.8, 0.2)
design <- data.frame(ntree, replace, mtry, nodesize, maxnodes, classwt, cutoff)
design
}
fr.design <- convert_design(fr.design.mat)
cv.fr.design <- cv.rf(fr.design, y, X) # diabetes dataset used in cv function
cv.fr.design
```
```{r}
# D-Optimal Design
candidate.set <- gen.factorial(levels = 2, nVars = 7, varNames = c("A", "B", "C", "D", "E", "F", "G"))
alt.design <- optFederov(~(A + B + C + D + E + F + G)^2, candidate.set, nTrials = 35, nRepeats = 100) # includes all linear terms and two-factor interactions
d.optimal.design <- alt.design$design
d.design <- convert_design(d.optimal.design)
cv.d.design <- cv.rf(d.design, y, X)
cv.d.design
```
We propose a fractional factorial design with 7 factors and 32 runs (resolution 4, 7-2), and a d-optimal design with 35 runs.
## Question 2
```{r}
# VIF and multicollinearity plots
# Model matrix for fractional design
X <- model.matrix(~(A + B + C + D + E + F + G)^2-1, data.frame(fr.design.mat))
# Create color map on pairwise correlations.
contrast.vectors.correlations.two <- cor(X)
corrplot(contrast.vectors.correlations.two, type = "full",
tl.col = "black", tl.srt = 90, method = "color",
addgrid.col = "gray", title = "Hi")
```
```{r}
X_new <- X[,-c(9, 12, 21)]
var.eff.one <- diag(solve(t(X_new)%*%X_new))
vif <- nrow(X)*var.eff.one
vif
```
```{r}
# Model matrix for d-optimal design
X.alt <- model.matrix(~(A + B + C + D + E + F + G)^2-1, data.frame(d.optimal.design))
# Create color map on pairwise correlations for d-optimal design
contrast.vectors.correlations.alt <- cor(X.alt)
corrplot(contrast.vectors.correlations.alt, type = "full", addgrid.col = "gray",
tl.col = "black", tl.srt = 90, method = "color", tl.cex=0.8)
```
```{r}
var.eff.one <- diag(solve(t(X.alt)%*%X.alt))
vif <- nrow(X.alt)*var.eff.one
vif
```
## Question 3
## Question 4
```{r}
prof.design <- data.frame("Run" = 1:22, "ntree" = c(100, 550, 1000, 1000, 1000, 100, 1000, 100, 100, 100, 100, 1000, 100, 550, 100, 1000, 1000, 1000, 100, 1000, 550, 550), "replace" = c(1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1), "mtry" = c(2, 2, 4, 6, 6, 2, 2, 2, 6, 6, 4, 2, 6, 4, 6, 6, 2, 6, 2, 2, 4, 6), "nodesize" = c(11, 1, 1, 1, 1, 1, 6, 11, 1, 1, 11, 11, 6, 6, 11, 11, 11, 11, 1, 1, 6, 11), "maxnodes" = c(10, 10, 10, 1000, 1000, 1000, 10, 10, 10, 10, 1000, 1000, 1000, 505, 505, 10, 1000, 10, 1000, 505, 505, 1000), "classwt" = c(0.5, 0.5, 0.5, 0.5, 0.9, 0.5, 0.9, 0.9, 0.7, 0.9, 0.9, 0.5, 0.5, 0.7, 0.5, 0.5, 0.7, 0.9, 0.9, 0.9, 0.7, 0.9), "cutoff" = c(0.8, 0.2, 0.2, 0.8, 0.2, 0.8, 0.8, 0.2, 0.8, 0.5, 0.8, 0.5, 0.2, 0.5, 0.2, 0.8, 0.2, 0.2, 0.2, 0.8, 0.5, 0.8))
# Model matrix for d-optimal design
X.prof <- model.matrix(~(ntree + replace + mtry + nodesize + maxnodes + classwt + cutoff)^2-1, data.frame(prof.design))
# Create color map on pairwise correlations for d-optimal design
contrast.vectors.correlations.alt <- cor(X.prof)
corrplot(contrast.vectors.correlations.alt, type = "full", addgrid.col = "gray",
tl.col = "black", tl.srt = 90, method = "color", tl.cex=0.8)
```
# Part 2
## Question 5
```{r}
print.data.frame(cv.fr.design)
```
## Question 6
```{r}
# A = ntree, B = replace, C = mtry, D = nodesize, E = maxnodes, F = classwt, G = cutoff
# model with all factors
f.model <- lm(CV ~ (ntree + replace + mtry + nodesize + maxnodes + classwt + cutoff + ntree:replace + ntree:nodesize + ntree:maxnodes + ntree:cutoff + replace:mtry + replace:nodesize + replace:maxnodes + replace:classwt + replace:cutoff + mtry:nodesize + mtry:maxnodes + mtry:cutoff + nodesize:maxnodes + nodesize:classwt + nodesize:cutoff + maxnodes:classwt + maxnodes:cutoff + classwt:cutoff), data = cv.fr.design)
DanielPlot(f.model)
```
```{r}
# significant factors
rev.cv.fr.design <- cv.fr.design[-c(26, 27),]
revised.1.f.model <- lm(CV ~ nodesize + classwt + cutoff + maxnodes + maxnodes:cutoff + classwt:cutoff + maxnodes:classwt, data = cv.fr.design)
# high leverage = 2*7/32 = 0.4375 therefore no high leverage
par(mfrow = c(2, 2))
plot(revised.1.f.model)
#summary(revised.1.f.model)
# independence? plot(cv.fr.design$replace, revised.1.f.model$residuals)
```
```{r}
re.revised.1.f.model <- lm(CV ~ nodesize + classwt + cutoff + maxnodes + maxnodes:cutoff + classwt:cutoff + maxnodes:classwt, data = rev.cv.fr.design)
# high leverage = 2*7/32 = 0.4375 therefore no high leverage
plot(re.revised.1.f.model)
```
```{r}
# "confirmation experiment"
abs(re.revised.1.f.model$fitted.values - rev.cv.fr.design$CV)
```
```{r}
summary(re.revised.1.f.model)
```
```{r}
rstandard(revised.1.f.model)
```