USEFUL R COMMANDS FOR ASSIGNMENT 1

Written 2010-100-08.  There may be updates later.


HELP ON COMMANDS

To get some help on the command called "foo", use 
  
   help(foo)

This may be useful in finding out some details that I don't mention
here.


READING THE DATA

In all the data files for this assignment, the first line is a
"header" with the names of the variables.  You should therefore read
it using read.table with the "head=TRUE" option.  For example:

   d <- read.table("ass1-patients.txt",head=TRUE)

Some of the data files also have names for the observations, which get
printed when you display the data.

For the read.table command above to work, you have to set the working
directory to the one containing the ass1-patients.txt file (where ever
you downloaded it).  You can do this with the setwd command, or with a
menu option if you're using MS Windows or a Mac.

The result of read.table is a "data frame".  You can access the
individual variables in a data frame with, for instance, d$recur to
get the "recur" variable from the data frame above.

Note that the webpage provides different versions of the data files
for Windows and for Unix/Linux/Mac.  The Windows ones start with "w-",
so unless you've changed that, the file name in the example above
would be "w-ass1-patients.txt".


LOOKING AT DATA

Just typing the name of the variable you saved the data in (from
read.table) will display the values of all the variables for all the
observations.  For some of the data files, this is a lot of numbers.
So you you may want to look at subsets...


SUBSETS OF DATA

You can look at just a subset of the data by selecting certain rows or
columns of a data frame or matrix.

For instance, if d is a data frame with 10 variables and 20
observations, you can look at the following:

   d[1:10,]             first 10 cases, all variables
   d[c(-8,-12),]        18 cases, dropping 8th and 12th, all variables
   d[,c(-1,-10)]        8 variables (dropping the first and last), all 20 cases
   d[c(1,15),1:5]       just cases 1 and 15, and just the first 5 variables
   d[,c("MAL","BIR")]   just the "MAL" and "BIR" variables, all cases

If the name of the 4th variable is "xyz", it can be extracted using
either d[,4] or d$xyz. 


DATA FRAMES VERSUS MATRICES

The R "data frame" and "matrix" data types are similar - each can hold
a set of observations (rows) with values for variables (columns).  The
read.table function gets you a data frame.  If you want a matrix
(sometimes necessary when using "lm"), you can say m <- as.matrix(d).
If you have a matrix (say from "prcomp") and want a data frame (eg,
for "plot"), use d <- as.data.frame(m).  Note that d$xxx can be used
to access variable "xxx" in a data frame, but not in a matrix (though
d[,"xxx"] works for both).


ARITHMETIC ON VECTORS, MATRICES, AND DATA FRAMES

You can do arithmetic operations on whole vectors, matrices, or data
frames.  For example, if "m" is a matrix, log(m) will produce a matrix
with elements that are the logs of the corresponding elements of m.


SCATTERPLOTS

You can make a scatterplot of two variables with a command like

   plot (d$KIL, d$CLO)

To make pairwise scatterplots of all variables in a data frame, d, use

   plot (d)

Of course, this isn't a good idea for the gene expression data with
1644 variables.

If there are a lot of variables, the plots will be small, and will
look better if the points are dots rather than circles.  This can be
done with the pch option:

   plot (d, pch=".")

or for somewhat bigger dots:

   plot (d, pch=20)

You can change colours of points with the "col" option, which should
get a vector of colours, one for each observations that is plotted.
For instance, 

   plot (d[,1], d[,2], col=c("green","red")[recur+1])

plots observations in green if recur is 0 and in red if recur is 1.


HISTOGRAMS

The make a histogram of a variable, use a command like

   hist(d$MAL)

or to set how many bins there are in the histogram,

   hist(d$MAL,nclass=30)


QQ PLOTS

To produce a QQ plot of variable "x" in data frame "d", versus
standard normal quantiles, use

   qqnorm(d$x)


SAVING AND PRINTING PLOTS

You can view plots on the screen without doing anything special.  But
if you want to save them or print them, putting the plots in files is
convenient.  You can put a plot in PDF format in a file with

   pdf("myplot.pdf")      # Make plots go to the file myplot.pdf
   plot(... whatever ...) # Create a plot
   dev.off()              # Finish off.  After, plots again go to the screen

You can then print myplot.pdf using the Acrobat Reader program (freely
downloadable), usually called acroread on Unix systems.  Just visiting
the file in your browser may also work.

If you'd like smaller characters (allowing more plot to fit), you can use

   pdf("myplot.pdf",pointsize=9)

To put more than one plot on a page, follow up the "pdf" command with
a command such as

   par(mfrow=c(3,2))

which puts six plots on a page, arranged in 3 rows of 2.


SAMPLE COVARIANCE AND CORRELATION

You can find the covariance of two variables a command like

   cov (d$ROS, d$KIL)

and similar for correlation (using "cor" instead of "cov").

The expression 

   cov (d, d$KIL)

will compute the covariances of all variables in d with the KIL
variable. The expression

   cov (d)

produces the whole covariance matrix of variables in d.

It may be useful to round these before printing them, so they fit on
the page or screen.  Eg,

   round(cov(d),2)

Note that to get things printed in a script, you need to use "print":

   print(round(cov(d),2))


SAMPLE MEANS / MEDIANS

You can find the sample mean of each variable in a data frame or
matrix (say d) with

   colMeans(d)

Similarly, you can find the means of all variables for each
observation using

   rowMeans(d)


PRINCIPAL COMPONENT ANALYSIS

PCA can be done using the buit-in prcomp function.  It takes a matrix
or data frame as its argument, and returns a list in which the element
"rotation" has all the principal components (ie, the eigenvectors) as
columns of a matrix, and "sdev" has the standard deviations in those
directions (ie, the square roots of the eigenvalues).  The "x" field
has the projections of the observations on the principal components.

For example,

  pc = prcomp(X)
  e1 = pc$rotation[,1] 
  e2 = pc$rotation[,2]
  lambda1 = pc$sdev[1]^2
  lambda2 = pc$sdev[2]^2
  plot(pc$x[,1],pc$x[,2])

The last command produces a scatterplot of the observations reduced to
just the first two principal components.

Note that prcomp centres the data by default (ie, looks at the data
after subtracting the sample means, as is standard).  By default,
prcomp does not scale the data to have variance one, but it can be
made to do so with the scale=T option (this has the effect of looking
at the sample correlation matrix rather than the sample covariance
matrix).


LINEAR REGRESSION

Ordinary least-squares linear regression can be done in R using the lm
function.  

Example:

  fit = lm (y ~ X + v)

This fits a regression model for values in the vector y in terms of
variables in X and v.  If the response vector y has length 100, then
we might use a matrix X with 100 rows and 4 columns, each column being
a covariate, and a vector v of length 100 as another covariate.  Of
course, we could also just say lm(y~X) or lm(y~v) to use just the
covariates in X or the covariate in v.  Note that this doesn't work if
X is a data frame (but you can convert the data frame to a matrix).

The summary function can be used to look at the estimated
coefficients, the Adjusted R-Squared value, and other things of
interest:

  summary(fit)

Note that in a script you will need to write print(summary(fit)) to
see the results.

You can get the vector of regression coefficients (starting with the
intercept) with coef(fit).