R Notes

Basics

=R= objects have attributes which can be observed by attributes() functions.

=<-= is the assignment operator

=:= is used to create integer sequences. 1:4 = 1 2 3 4

=c= function can be used to create vectors from different kinds of objects. (concatenate) c(TRUE, FALSE) creates a logical vector, c(1+3i, 4+8i, 3-5i) creates a complex vector. Coercion happens if different kinds of objects are mixed.

=as.*= functions can be used to coerce different kinds of data. as.numeric(TRUE) returns 1.

=matrix(ncol = 3, nrow = 4)= creates a matrix.

=cbind= and rbind are other options to create a matrix from vectors by binding them to columns or rows.

=factor=s are categorized data, like male///female. They are created using factor function. table and unclass functions can also be used to get information and change the factor into a numeric table.

=levels= parameter to factor function can be used to determined the factor <-> number correspondence.

=is.nan= and is.na functions are used to check whether vector values are NaN or NA.

=data.frame=s are used to store tabular data like matrices. but unlike matrices, they can store different types of data in each column. first column can be numeric, second row can be factor, third can be logical etc.

=data.frame=s are created usually by read.table and read.csv functions. each row has a name which can be accessed by row.names It can be converted to matrix with data.matrix.

=nrow= and ncol functions can be used to get row and columns sizes of data.table.

=str= and summary functions can be used to get a concise information about a structure.

Use getwd to report the working directory, and use setwd to change it:

The ls function displays the names of objects in your workspace:

> x <- 10
> y <- 50
> z <- c("three", "blind", "mice")
26 | Chapter 2: Some Basics
> f <- function(n,p) sqrt(p*(1-p)/n)
> ls()
[1] "f" "x" "y" "z"

=rm= function removes, permanently, one or more objects from the workspace:

source("myScript.R")

$ R CMD BATCH /home/jim/psych/adoldrug/partyuse1.R

Statistical Functions for Discrete Distributions

=library(distrEx)= has functions E, var and sd that calculates mean, variance and standard deviation.

Uniform random events can be emulated with sample function. It has three parameters. The first determines the range of values to select randomly, the second (size) determines the number of events and the third (replace) sets whether we replace the balls we have drawn.

1000 dice: sample(6, size=1000, replace=TRUE)

50 random numbers from 1000 to 2000: sample(1000:2000, size=50, replace=TRUE)

Flip a fair coin 100 times: sample(c("H", "T"), size=100, replace=TRUE)

Reading and Writing Data

=read.table= and read.csv reads tabular data from text files.

=readLines= reads lines of text.

=source= and dget reads R code files.

=load= and unserialize is used to read binary objects.

=dump= and dput are inverse of source and dget. They include the metadata of object in the output.

=file= is used to open files. gzfile opens gzipped, bzfile opens bzip2 files. url command is used to open a connection to a web page.

Plotting

=plot(x, y)= plots the values in x with the corresponding values in y.

Additional parameters to the plot can be used to configure the visual settings.

Use the density function to approximate the sample density; then use lines to draw the approximation:

hist(x, prob=T)
lines(density(x))

Installing R packages

$ R CMD INSTALL mypkg -l /my/own/R-packages/

> install.packages("mypkg", lib="/my/own/R-packages/")

> library("mypkg", lib.loc="/my/own/R-packages/")

density

Use the density function to approximate the sample density; then use lines to draw the approximation:

> hist(x, prob=T)
> lines(density(x))

Creating Data Frame

> points <- data.frame(label=c("Low", "Mid", "High"),
                       lbound=c(0, 0.67, 1.64),
                       ubound=c(0.674, 1.64, 2.33))

The print function

lets you vary the number of printed digits using the digits parameter:

> print(pi, digits=4)

The cat function does not give you direct control over formatting.

Instead, use the format function to format your numbers before calling cat:

> cat(pi, "\n")

The list.files function shows the contents of your working directory:

> list.files()

The write.csv function can write a CSV file:

> write.csv(x, file="filename", row.names=FALSE)

~ notation for relations between variables

R has a special notation for describing relationships between variables. Suppose that you are assuming a linear model for a variable y, predicted from the variables x₁, x₂, ..., x_n. (Statisticians usually refer to y as the dependent variable, and x₁, x₂, ..., x_n as the independent variables.) In equation form, this implies a relationship like: In R, you would write the relationship as y ~ x1 + x2 + ... + xn, which is a formula object.

Factor analysis

Factor analysis is available in R through the function factanal in the stats package:

factanal(x, factors, data = NULL, covmat = NULL, n.obs = NA,
          subset, na.action, start = NULL,
          scores = c("none", "regression", "Bartlett"),
          rotation = "varimax", control = NULL, ...)

PCA

Principal components analysis breaks a set of (possibly correlated) variables into a set of un- correlated variables. In R, principal components analysis is available through the function prcomp in the stats package:

distributions in R

Binomial binom n = number of trials; p = probability of success for one trial Geometric geom p = probability of success for one trial Hypergeometric hyper m = number of white balls in urn; n = number of black balls in urn; k = number of balls drawn from urn 177 Discrete distribution R name Parameters Negative binomial (NegBinomial) nbinom size = number of successful trials; either prob = probability of successful trial or mu = mean Poisson pois lambda = mean Table 8-2. Continuous distributions Continuous distribution R name Parameters Beta beta shape1; shape2 Cauchy cauchy location; scale Chi-squared (Chisquare) chisq df = degrees of freedom Exponential exp rate F f df1 and df2 = degrees of freedom Gamma gamma rate; either rate or scale Log-normal (Lognormal) lnorm meanlog = mean on logarithmic scale; sdlog = standard deviation on logarithmic scale Logistic logis location; scale Normal norm mean; sd = standard deviation Student’s t (TDist) t df = degrees of freedom Uniform unif min = lower limit; max = upper limit Weibull weibull shape; scale Wilcoxon wilcox m = number of observations in first sample; n = number of observations in second sample

combination calculation

A common problem in computing probabilities of discrete variables is counting combinations: the number of distinct subsets of size k that can be created from n items. The number is given by $\frac{n!}{r!(n − r)!}, but it’s much more convenient to use the choose function—especially as n and k grow larger:

> choose(5,3) # How many ways can we select 3 items from 5 items?
[1] 10
> choose(50,3) # How many ways can we select 3 items from 50 items?
[1] 19600
> choose(50,30) # How many ways can we select 30 items from 50 items?
[1] 4.712921e+13

These numbers are also known as binomial coefficients.

generating combinations

When you want to generate all combinations of n items taken k at a time. Use the combn function:

> combn(items, k)

selecting n items from a vector

The sample function will randomly select n items from a vector:

> sample(vec, n)

dotplot() of lattice

The dotplot() function in library(lattice) is useful for displaying labeled quantitative values

measuring intelligence

The classic examples come from the social sciences. Suppose that you wanted to measure intelligence. It’s not possible to directly measure an abstract concept like intelligence, but it is possible to measure performance on different tests. You could use factor analysis to analyze a set of test scores (the observed values) to try to determine intelligence (the hidden value).

correlation

Correlation measures range between −1 and 1; 1 means that one variable is a (positive) linear function of the other, 0 means the two variables aren’t correlated at all, and −1 means that one variable is a negative linear function of the other (the two move in completely opposite directions;

bootstrapping

Would we get a similar result if we were to omit a few points? What are the range of values for the statistic? It is possible to answer this question for an arbitrary statistic using a technique called bootstrapping. Formally, bootstrap resampling is a technique for estimating the bias of an estimator. An estimator is a statistic calculated from a data sample that provides an estimate of a true underlying value, often a mean, standard deviation, or a hidden parameter. Bootstrapping works by repeatedly selecting random observations from a data sam- ple (with replacement) and recalculating the statistic. In R, you can use bootstrap resampling through the boot function in the boot package:

paste

The paste function allows you to concatenate multiple character vectors into a single vector.

chi-squared distribution

The chi-squared distribution allows for statistical tests of categorical data. Among these tests are those for goodness of fit and independence.

chi-square test

The chi-square test for homogeneity does a similar analysis as the chi-square test for independence. For each cell it computes an expected amount and then uses this to compare to the frequency.

plotting the regression line

To plot the regression line You make a plot of the data, and then add a line with the abline command

> plot(x,y)
> abline(lm.result)

coefficients of regression

To access the coefficients The coef function will return a vector of coefficients.

> coef(lm.result)
(Intercept)            x
210.0484584 -0.7977266

anova

For example, to test if there is a difference between control and treatment groups. The method called analysis of variance (ANOVA) allows one to compare means for more than 2 independent samples.

regression analysis

Regression analysis is used for explaining or modeling the relationship between a single variable y, called the response, output or dependent variable; and one or more predictor, input, independent or explanatory variables, x₁, ..., X_p. When p = 1, it is called simple regression but when p > 1 it is called multiple regression or sometimes multivariate regression. When there is more than one y, then it is called multivariate multiple regression

i.i.d

independent and identically distributed (i.i.d.)

linear models

Linear models seem rather restrictive, but because the predictors can be transformed and combined in any way, they are actually very flexible. The term linear is often used in everyday speech as almost a synonym for simplicity. This gives the casual observer the impression that linear models can only handle small simple datasets. This is far from the truth—linear models can easily be expanded and modified to handle complex datasets. Linear is also used to refer to straight lines, but linear models can be curved.

nonlinear models

Truly nonlinear models are rarely absolutely necessary and most often arise from a theory about the relationships between the variables, rather than an empirical investigation.

failing to reject the null hypothesis

A failure to reject the null hypothesis is not the end of the game—you must still investigate the possibility of nonlinear transformations of the variables and of outliers which may obscure the relationship. Even then, you may just have insufficient data to demonstrate a real effect, which is why we must be careful to say “fail to reject” the null rather than “accept” the null. It would be a mistake to conclude that no real relationship exists.

lurking variable Z that affects two seemingly related variables

The first objection is that there may be some lurking variable Z that is the real driving force behind y that also happens to be associated with x1. Once Z is accounted for, there may be no relationship between x1 and y. Unfortunately, we can usually never be certain that such a Z does not exist.

Statistical inference is based on the assumption that

none of the expected counts is smaller than 1 and most (80%) are bigger than 5. As well, the data must be independent and identically distributed – that is multinomial with some specified probability distribution. If these assumptions are satisfied, then the χ2 statistic is approximately χ2 distributed with n − 1 degrees of freedom

using null hypothesis for independence testing

The same statistic can also be used to study if two rows in a contingency table are “independent”. That is, the null hypothesis is that the rows are independent and the alternative hypothesis is that they are not independent.