###### Applied Linear Regression I: scatter plot

## install R package "alr3" first
## see also http://users.stat.umn.edu/~sandy/alr3ed/website/R.html
install.packages("alr3", dependencies=TRUE)

# load R package "alr3"
library(alr3)
#alrWeb("primer")

# obtain Scripts of R commands at
# http://users.stat.umn.edu/~sandy/alr3ed/website/Links/Rscripts.zip
#alrWeb(script="chapter1")

# scatter plot of Dheight (Y axis) vs. Mheight (X axis)
with(heights, plot(Mheight, Dheight, xlim=c(55,75), ylim=c(55,75), pch=21, cex=.7))


# simulate random normal vectors
n <- 1000
x <- rnorm(n, mean=62, sd=4)
y <- rnorm(n, mean=63, sd=3)
plot(x,y)
z <- x*0.3 + y*0.7
plot(x,z)


# use "jittering" trick to check if there is any "overplotting" problem
#   That is "many points at exactly the same location".
with(heights, plot(Mheight, Dheight+runif(length(Dheight),-0.5,0.5), xlim=c(55,75), 
ylim=c(55,75), pch=21, cex=.7))

par(mfrow=c(1,2))     # divide the graphical area into 1*2 parts
with(heights, plot(Mheight, Dheight, xlim=c(55,75), ylim=c(55,75), pch=21, cex=.7))
with(heights, plot(Mheight, Dheight+runif(length(Dheight),-0.5,0.5), xlim=c(55,75), 
ylim=c(55,75), pch=21, cex=.7))
par(mfrow=c(1,1))




#### Applied Linear Regression II: missing data
### see also http://www.statmethods.net/input/missingdata.html
###       or http://www.ats.ucla.edu/stat/r/faq/missing.htm         with more examples
###       or http://www.stat.columbia.edu/~gelman/arm/missing.pdf   for more readings

## read data with missing values into R
xy5 <- read.table("xy5.txt", header=T)    # does not work
xy5 <- read.table("xy5.txt", sep="\t", header=T) # separated by TABS
sum(as.vector(is.na(xy5))) # how many "NA" in total
apply(is.na(xy5),1,sum)    # how many "NA" in each row
apply(is.na(xy5),2,sum)    # how many "NA" in each column


## check if there is any missing value
y = c(1,2,3,NA)
is.na(y)
sum(is.na(y))  # number of missing values


# list rows of data that have missing values 
x = runif(5*4,-1,1)      # simulated data set
dim(x) = c(5,4)          # rearrange x into 5 by 4 matrix form
x[2,3]=x[3,4]=NA         # two missing values
x
x[!complete.cases(x),]

## ignore missing values
mean(y)
mean(y, na.rm=T)  # ignore missing values when using "mean"

## create new dataset by removing missing data 
y <- c(3, 5, 2, NA)
y <- na.omit(y)
y

x
x <- na.omit(x)
x

xy5
xy5 <- na.omit(xy5)
xy5


## Some R packages relevant to missing value imputation
# Amelia	   Amelia II: A Program for Missing Data      (Version:	1.5-4, Published:	2011-08-23)
# ForImp	   Imputation of missing values through a forward imputation algorithm (Version:	1.0, Published:	2011-06-15)
# mi           Missing Data Imputation and Model Checking (Version:	0.09-14, Published:	2011-04-25)
# missForest   Nonparametric Missing Value Imputation using Random Forest
# mitools	   Tools for multiple imputation of missing data
# VIM	       Visualization and Imputation of Missing Values
# vmv	       Visualization of Missing Values
# arrayImpute       Missing imputation for microarray data
# arrayMissPattern	Exploratory analysis of Missing patterns for microarray data
# MissingDataGUI  	A GUI for Missing Data Exploration

## Some R packages for analysis with missing values
# cat               Analysis of categorical-variable datasets with missing values
# missMDA           Handling missing values with/in multivariate data analysis (principal component methods)
# mlmmm           	ML estimation under multivariate linear mixed models with missing values
# monomvn           Estimation for multivariate normal and Student-t data with monotone missingness
# mvnmle            ML estimation for multivariate normal data with missing values
# NestedCohort	    Survival Analysis for Cohorts with Missing Covariate Information
# norm              Analysis of multivariate normal datasets with missing values