Introduction to S-PLUS (Win2000/NT)

1
Introduction to S-PLUS
(Win2000/NT)

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2
Preliminaries

• History of S-Plus
• Open Source, Public Domain version of the S
  language
• Example of using R in a teaching context
• Useful resources

3
The History of S-Plus

• The S Language is developed by ATT Bell Labs
  1980s
• The commercial value-added version marketed by
  Stat-Sci Inc.
• MathSoft acquires Statsci in 1992 (markets
  MathCad software)
• S-Plus 4.0 released in 1997
• S-Plus 4.5 released in 1998 (WIN95/NT)
• S-Plus 2000 released in 2000 (marketed by
  Insightful Corp http//www.insightful.com)
• S-Plus 6.0 released in fall 2001

4
Open Source Version of the S language

• R is an open source version of the S language
  (http//www.cran.r-project.org)
• Implemented for Linux, Windows, Macintosh
• No GUI, only command interface
• Has many libraries available covering almost all
  areas of modern statistics

5
An Example of Using R through a Web Application
Server

• http//www.unt.edu/benchmarks/october01/rss.htm
• Programs can be submitted through a web browser
  interface
• Programs can be modified and resubmitted to get
  new results
• Useful as a teaching aid

6
Useful Resources

• http//www.insightful.com/
• The Basics of S and S-PLUS (second
  edition)Andreas Krause and Melvin
  OlsonSpringer-Verlag, New York (2000)
• An introduction to S-PLUS and the Hmisc and
  Design libraries C.F. Alzola and F.E. Harrell,
  Freely available document
• Regression Modeling Strategies with Applications
  to Linear Models, Logistic Regression, and
  Survival Analysis F.E. Harrell, Springer (2001)

7
Use Resources (cont.)

• Modern Applied Biostatistical Methods Using
  S-PLUSS. Selvin, Oxford University Press
  (1998)ISBN 0-19-512025-6
• Introduction to Robust Estimation and Hypothesis
  TestingRand Wilcox, Academic Press (1997)ISBN
  0-12-751545-3
• WebLinks (S-news listserve, and Software archive)
• http//lib.stat.cmu.edu/s-news/
• http//lib.stat.cmu.edu/S/

8
Features of S-Plus

• S-Plus is an objected oriented programming
  language
• Version 2000 has a GUI which is extensible
• S-Plus has over 3,000 functions which allow total
  control of data and graphics
• S-Plus 2000 accommodates data analysts from
  novice to expert
• There is a very active S-Plus user group (S-news)

9
Getting Help in S-Plus

• Help for general tasks, S-Plus functions, etc.
• Can use the Help index from GUI interface
• Alternatively can use help function in the
  Command Window
• Example In the command window at the gt prompt
  type,
• gt help(help) help on help
• gt help(scan) help on scan()
  function
• General Help Help Menu from GUI
• Function index, keyword search, on-line manuals
  (user manual, programmer manual, statistics
  manual, visual demo

10
How to stop computations or quit an S-Plus session

• To cancel an ongoing computation, press ESC
• Cancels long outputs
• Aborts long computations
• To quit from S-Plus
• From GUI use File-Exit
• From Command Window use
• gt q ( )

11
Getting Data into S-Plus

• Dialog box starts up as a default
• Select existing data or import data from a file
• For existing data, enter the name of an S-Plus
  object in the Name box

12
Data Import Options

• Select the Options tab for import options
• By default, ASCII files are assumed to have
• column labels on row 1 (blank rows ignored)
• data from row 2 on
• columns are seperated by whitespace or comma
• Can change defaults with import options
• First data line, separators, column
  specifications
• Note .dat files are assumed to be GAUSS files

13
Data Objects

• When data are imported, the data are displayed in
  a data window and a new object is created
• The name of the data object is chosen from the
  file name, or can be specified in the import
  dialog

14
Data Window

• The data appears in a spreadsheet
• This includes row names and column names
• Can click on a column name to select a column
• Use shift-click to select a block of columns
• Use ctrl-click to select non-adjacent columns

15
Data Window (cont.)

• The order of selection is important (selected
  columns will be used in graphs and analyses)

16
Object Browser

• S-Plus is object oriented
• All data, functions, results from analyses,
  plots, etc., are objects
• The object browser organizes all the objects you
  create
• Left half - object type Right half - list of
  objects

17
Command Window

• Every menu and toolbar generates the S-Plus
  command language
• S-Plus is a complete programming language
• This language has loops, functions, expressions,
  and is object oriented
• Most of the functionality and flexibility of
  S-Plus is accessed through the language

18
Creating Graphs

• Open GRAPH - 2D Plot, or GRAPH - 3D Plot
  menu option
• Select column(s) for plotting from the Data
  Window
• ctrl-click the column for the x-axis
• ctrl-click the column for the y-axis

19
Creating Graphs (cont.)

• ctrl-click the column for the z-axis if needed
• click on the palette button for the desired plot

20
Creating Trellis Graphics

• Any plot can be conditioned by the value of any
  other variable in the data
• First create a plot, then select the conditioning
  column in the data window
• Drag the column (grabbing a cell) to the title
  area of plot

21
Creating Trellis Graphics (cont.)

• The cursor will change to a when ready to
  drop
• The plot is redrawn with panels for subranges of
  the conditioning variable

22
The S-Plus Language

• Expressions are entered at the prompt gt
• S-Plus prints out the result

• gt 33
• 1 6
• gt sin(pi)
• 1 1.224606e-016
• gt sqrt(100)
• 1 10

23
Additional prompt

• An incomplete expression leads to a second
  prompt
• Can continue at the second prompt

• gt sqrt(
• 100)
• 1 10

24
Getting stuck at prompt

• If the prompt continues after hitting return,
  then enter many ) to get the gt prompt
• Then start your expression again

• gt sqrt(
• )))))
• Error in parse(text txt) Syntax error No
  opening parenthesis, before ")" at this point
• sqrt(
• ))
• Dumped
• gt sqrt(100)

25
Scalars and Assignments

• Read this as weight gets 190
• This assigns the value 190 to the scalar named
  weight
• The assignment operator is the sequence of
  characters lt-

• gt weightlt-190
• gt weight
• 1 190

26
Character Assignments

• Character values are inserted in quotes
• If the quotes are omitted, S-Plus will look for a
  data object called, Jim , to assign to person
• The result is not printed until you enter the
  object name

• gt personlt-"Jim"
• gt person
• 1 "Jim"

27
Vectors

• gt rnorm(10)
• 1 0.3037020
• 2 -0.5248669
• 3 1.4674553
• 4 0.4536315
• 5 0.4077797
• 6 0.5362221
• 7 0.0759569
• 8 0.3239556
• 9 -1.3531665
• 10 -2.4226150

• The function rnorm( ), returns a vector of
  random deviates from the normal distribution
• The n on the left shows where the row starts

28
Vectors (cont.)

• A single number is a vector of length 1
• We can make vectors using the concatenation
  function c( )
• We assign the integers 1,2,3 to the vector x

• gt mean(rnorm(10))
• 1 0.5807564
• gt xlt-c(1,2,3)
• gt x
• 1 1 2 3

29
Vectors (cont.)

• We can create a vector of names
• We can create a vector of sequential integers
  using the function ab , where a is the
  starting integer and b is the ending integer

• gt peoplelt-c("Jim", "Sue", "Dave")
• gt people
• 1 "Jim" "Sue" "Dave"
• gt 510
• 1 5 6 7 8 9 10

30
Object Names

• Object names may contain,
• Letters abcDEF
• Numbers 0123456789
• Dot .

• Examples of valid names
• height
• weight
• x.var
• .yvar
• x.y.var
• x110

31
Object names (cont.)

• Objects names cannot use an underscore, a hyphen,
  begin with a number, or use reserved symbols

• Examples of invalid object names
• _xvar
• y_var
• x-yvar
• 120xvar
• T
• F
• NA

32
Handling Objects

• We can list out all of the objects
• gt objects()
• 1 ".Last.value" ".Random.seed" "Cars"
  "last.dump"
• 5 "last.warning" "people" "person"
  "weight"
• 9 "weights" "x"
• Objects remain until removed, even if one quits
  S-Plus
• gt rm(x)
• gt x
• Error Object "x" not found
• Dumped
• Equivalently, you can use the object browser

33
Objects as variables

• Objects can be used in expressions

• gt xlt-110
• gt mean(x)
• 1 5.5
• gt ylt-c(x,10)
• gt length(y)
• 1 11
• gt 2y
• 1 2 4 6 8 10 12 14 16 18 20 20

34
Vector Arithmetic

• Scalar Functions work on elementwise basis
• Can perform scalar and vector arithmetic

• gt xlt-15
• gt x2
• 1 1 4 9 16 25
• gt 2x
• 1 2 4 6 8 10
• gt 2xsqrt(x)
• 1 3.000000 5.414214
• 3 7.732051 10.000000
• 5 12.236068

35
Logical Vectors

• Expressions with relational operators return
  logical vectors
• T is True, F is False

• gt xlt-rnorm(5)
• gt x
• 1 1.2698616 -1.1080517
• 3 0.5627334 0.2454234
• 5 0.2919052
• gt xlt0
• 1 F T F F F

36
Missing values

• A missing value is represented by NA
• Operations on NA return NA
• The function is.na( ) checks for missing values

• gt xlt-c(1, NA, 3)
• gt x
• 1 1 NA 3
• gt x1
• 1 2 NA 4
• gt sum(x)
• 1 NA
• gt is.na(x)
• 1 F T F

37
Vector indexing

• Use brackets, to select elements of a vector
• Negative indices remove elements

• gt xlt-c(2,4,6,8,10)
• gt x
• 1 2 4 6 8 10
• gt x1
• 1 2
• gt x35
• 1 6 8 10
• gt xc(1,3,5)
• 1 2 6 10
• gt x-(13)
• 1 8 10

38
Logical Indices

• gt xlt-rnorm(5)
• gt x
• 1 -2.4592950 0.9074605
• 3 0.5088648 -1.1184415
• 5 0.5137160
• gt xxlt0
• 1 -2.459295 -1.118441
• gt log.xlt-log(x)
• Warning messages
• NAs generated in log(x)
• gt xis.na(log.x)
• 1 -2.459295 -1.118441
• gt log.x!is.na(log.x)
• 1 -0.09710521 -0.67557299
• 3 -0.66608473

• A logical index selects elements
• Symbols for logical operators
• lt Less than
• gt Greater than
• lt Less than or equal to
• gt Greater than or equal to
• Equal to
• ! Negation operator
• ! Not equal to

39
Replacement

• You can use on the left hand side of an
  assignment, lt-

• gt xlt-sample(18)
• gt x
• 1 2 6 8 3 1 5 7 4
• gt x6lt-NA
• gt x
• 1 2 6 8 3 1 NA 7 4
• gt xis.na(x)lt-0
• gt x
• 1 2 6 8 3 1 0 7 4

40
Functions

• Functions are called like this
• function.name(argument, argument, .)
• Functions always return a value
• NULL represents no value
• Example
• seq(from1, toend, by1, lengthinferred,
  alongNULL)

• gt seq(1,5)
• 1 1 2 3 4 5
• gt seq(10, 20, length6)
• 1 10 12 14 16 18 20
• gt seq(to100, by15, length7)
• 1 10 25 40 55 70 85 100
• gt seq(length10)
• 1 1 2 3 4 5 6 7 8
• 9 9 10

41
Functions (cont.)

• Function arguments have
• position(first, second, .)
• function name
• default values for function options (sometimes)
• Examples
• rnorm(n, mean0, sd1)
• rep(x, timesinferrred, length.outinferred)

gt rep(13,2) 1 1 2 3 1 2 3 gt rep(13,
length8) 1 1 2 3 1 2 3 1 2 gt rep(13,
c(3,2,1)) 1 1 1 1 2 2 3 gt rep() Error in rep
Argument "x" is missing, with no default rep()
Dumped gt rep(13, c(3,2,1), 5) 1 1 2 3 1 2
42
Matrices

• matrix(dataNA, nrowinferred,
  ncolinferred, byrowF, dimnamesNULL)
• The function matrix( ) reads data into a matrix
• The number of columns is specified by using the
  argument ncol
• And/Or the number of rows can be specified by the
  argument, nrow

• gt xlt-matrix(110, nrow2)
• gt x
• ,1 ,2 ,3 ,4 ,5
• 1, 1 3 5 7 9
• 2, 2 4 6 8 10
• gt dim(x)
• 1 2 5
• gt x.matrixlt-matrix(c(20,10,3,1,7,4), ncol2)
• gt x.matrix
• ,1 ,2
• 1, 20 1
• 2, 10 7
• 3, 3 4

43
Matrices (cont.)

• We can attach names to columns with the dimnames
  option
• gt xlt-matrix(c(120), ncol4, byrowT,
  dimnameslist(NULL, c("col1", "col2", "col3",
  "col4")))
• gt x
• col1 col2 col3 col4
• 1, 1 2 3 4
• 2, 5 6 7 8
• 3, 9 10 11 12
• 4, 13 14 15 16
• 5, 17 18 19 20

44
Matrices (cont.)

• Specifying byrowT forces S-Plus to read the data
  in row by row
• When the argument is not specified, or specified
  as byrowF , S-Plus assumes the data is
  written in column by column

• gt x.matrixlt-matrix(c(20,10,3,1,7,4), ncol2,
  byrowT)
• gt x.matrix
• ,1 ,2
• 1, 20 10
• 2, 3 1
• 3, 7 4

45
Matrices (cont.) - Indexing

• gt xlt-matrix(115, nrow3, byrowT)
• gt x
• ,1 ,2 ,3 ,4 ,5
• 1, 1 2 3 4 5
• 2, 6 7 8 9 10
• 3, 11 12 13 14 15
• gt x2,3
• 1 8
• gt x23, 35
• ,1 ,2 ,3
• 1, 8 9 10
• 2, 13 14 15
• gt x,1
• 1 1 6 11
• gt x1,
• 1 1 2 3 4 5

• To extract a value from a matrix, use two
  elements in the subscript
• The first element applies to rows
• The second element applies to columns
• If one dimension is not specified, all elements
  for that dimension are extracted

46
Constructing Matrices from vectors

• Matrices can be constructed from row vectors and
  column vectors using cbind and rbind
• Binding together vectors of different attributes
  (character and numeric for example), is not
  allowed - vectors will be coerced to a similar
  attribute
• Numeric and character vectors will be coerced to
  character

• gt x lt- c(3,4,5)
• gt y lt- c(6,7,8)
• gt x.ylt-cbind(x,y)
• gt x.y
• x y
• 1, 3 6
• 2, 4 7
• 3, 5 8
• gt x lt- c(3,4,5)
• gt x lt- c(6,7,8)
• gt x.ylt-rbind(x,y)
• gt x.y
• ,1 ,2 ,3
• x 3 4 5
• y 6 7 8

47
Constructing Matrices from vectors (cont.)

• Example binding together a character vector and
  a numeric vector coerces to a character matrix
• What is need is a data object called a data frame
  (similar to SPSS or SAS datasets)

• gt x lt- c(3,4,5)
• gt y lt- c("Three","Four","Five")
• gt x.ylt-rbind(x,y)
• gt x.y
• ,1 ,2 ,3
• x "3" "4" "5"
• y "Three" "Four" "Five"

48
Converting Matrices to Data Frames

• Data Frames are a data object that allows one to
  bind data vectors of different types together,
  such that the data can be accessed like a matrix
• Most of the dialog boxes in the GUI operate on
  Data Frames

• gt x lt- c(3,4,5)
• gt y lt- c("Three","Four","Five")
• gt x.ylt-data.frame(x, y)
• gt x.y
• x y
• 1 3 Three
• 2 4 Four
• 3 5 Five

49
Arrays

• gt xlt-array(124, c(3, 4, 2))
• gt x
• , , 1
• ,1 ,2 ,3 ,4
• 1, 1 4 7 10
• 2, 2 5 8 11
• 3, 3 6 9 12
• , , 2
• ,1 ,2 ,3 ,4
• 1, 13 16 19 22
• 2, 14 17 20 23
• 3, 15 18 21 24
• gt x,2,
• ,1 ,2
• 1, 4 16
• 2, 5 17

• An array is a data construct that can be thought
  of as a multi-dimensional (up to eight
  dimensions)
• An array is defined as
• array(data, dim)
• If we fix second index at 2 we get a 3x2 matrix

50
The apply( ) function

• gt xlt-matrix(c(110), ncol2, byrowT)
• gt x
• ,1 ,2
• 1, 1 2
• 2, 3 4
• 3, 5 6
• 4, 7 8
• 5, 9 10
• gt x.loglt-apply(x, 2, log)
• gt x.log
• ,1 ,2
• 1, 0.000000 0.6931472
• 2, 1.098612 1.3862944
• 3, 1.609438 1.7917595
• 4, 1.945910 2.0794415
• 5, 2.197225 2.3025851

• The apply function successively applies a
  function of your choice to each row, each column,
  and each level of a higher dimension of a matrix
  or array
• apply(data, dim, function)

51
Lists

• gt xlistlt-list(dat15, name"John", yc(32, 45))
• gt xlist
• dat
• 1 1 2 3 4 5
• name
• 1 "John"
• y
• 1 32 45
• gt xlistdat
• 1 1 2 3 4 5
• gt xlistname
• 1 "John"
• gt xlisty
• 1 32 45
• gt xlist3
• 1 32 45

• A List is an ordered collection of arbitrary
  objects
• A list can be indexed like a matrix or array
• Index an element of a list by using
• listnameelementname listnameindex
  listnameelementnameindex

52
lapply( ) function

• gt Llt-list(vec110, matmatrix(9988, 3,4))
• gt L
• vec
• 1 1 2 3 4 5 6 7 8 9 10
• mat
• ,1 ,2 ,3 ,4
• 1, 99 96 93 90
• 2, 98 95 92 89
• 3, 97 94 91 88
• gt lapply(L, mean)
• vec
• 1 5.5
• mat
• 1 93.5

• The tool lapply ( ) is designed for working on
  all elements of a list using the same function
• Example Calculate the mean of every list
  element

53
lapply () function (cont.)

• Can use the lapply to apply an arbitrary function
  to the corresponding elements of two lists
• Example Take the mean of elements in first list
  position, and add the mean of elements in the
  first position of a second list

• gt list1 lt- list(c(2,4,6,8), c(10,12,14,16))
• gt list2 lt- list(c(18,20,22,24), c(26,28,30,32))
  
• gt lapply(12, function(i, x, y) mean(xi)
  mean(yi), x list1, y list2)
• 1
• 1 26
• 2
• 1 42

54
unlist() function

• Simplifies the recursive structure of a list
• Usage
• unlist(data, recursiveT, use.namesT)
• Example Create a vector from a list with two
  elements

• gt x.listlt-list(c(2,4,6,8), c(10,12,14,16),
  c(18,20,22,24))
• gt x.list
• 1
• 1 2 4 6 8
• 2
• 1 10 12 14 16
• 3
• 1 18 20 22 24
• gt unlist(x.list)
• 1 2 4 6 8 10 12 14 16 18 20 22 24

55
Creating Functions

• Functions allow modular programming
• Functions can call other functions
• Functions have calling parameters enclosed in
  parenthesis with the main body inclosed in braces

• gt x.powerlt-function(x, power)
• xlt-xpower
• x
• gt xlt-c(2,4,6,8)
• gt x.power(x, 2)
• 1 4 16 36 64
• gt x.power(x, 3)
• 1 8 64 216 512

56
Looping

• Looping can allow iteration over indices of a
  scalar, vector, matrix, or list
• Looping is slow in S-Plus vector operations
  are encouraged

• gt templt-0
• gt for (i in 14)
• templt-itemp
• gt temp
• 1 10

57
ifelse() function

• Compares the elements of two objects according to
  some boolean statement
• Can return scalar or vector values for a true
  condition, and a different set of values for a
  false condition

• gt xlt-c(1,3,5)
• gt ylt-c(6,4,2)
• gt zlt-ifelse(xlty, 1, 0)
• gt z
• 1 1 1 0

58
Matrix Algebra

• Transpose t( )

Matrix Multiply gt t(x)x ,1 ,2
1, 5 15 2, 15 55 gt
gt xlt-cbind(rep(1,5), 15) gt x ,1 ,2
1, 1 1 2, 1 2 3, 1
3 4, 1 4 5, 1 5 gt t(x) ,1
,2 ,3 ,4 ,5 1, 1 1 1 1
1 2, 1 2 3 4 5 gt
59
Matrix Algebra (cont.)

• Matrix Inverse solve ()
• gt solve(t(x)x)
• ,1 ,2
• 1, 1.1 -0.3
• 2, -0.3 0.1
• gt

• Matrix Decompositions
• Eigenvector eigen ( )
• Singular Value svd ( )
• Cholesky chol ( )

gt eigen(solve(t(x)x)) values 1 1.18309519
0.01690481 vectors ,1 ,2
1, 0.9637149 0.2669336 2, -0.2669336
0.9637149
60
Exercises (a)

• Create the following matrix called marks and put
  in the appropriate label names

• gt marks
• Test1 Test2 Test3 Final
• 1, 20 23 18 48
• 2, 16 15 18 40
• 3, 25 20 22 40
• 4, 14 19 18 42

61
Solutions (a)

• gt markslt-matrix(c(20,23,18,48,16,15,18,40,25,20,22
  ,40,14,19,18,42),byrowT,
• nrow4,dimnameslist(NULL,c("Test1","Test2","Tes
  t3","Final")))

62
Exercises (b)

• Add the following row to the bottom of the
  matrix
• 10 15 14 30

63
Solutions (b)

• gt markslt-rbind(marks,c(10,15,14,30))
• gt marks
• Test1 Test2 Test3 Final
• 1, 20 23 18 48
• 2, 16 15 18 40
• 3, 25 20 22 40
• 4, 14 19 18 42
• 5, 10 15 14 30

64
Exercises (c)

• Change the fifth mark for test 2 from a 15 to a
  17

65
Solutions (c)

• gt marks5,2lt-17
• gt marks
• Test1 Test2 Test3 Final
• 1, 20 23 18 48
• 2, 16 15 18 40
• 3, 25 20 22 40
• 4, 14 19 18 42
• 5, 10 17 14 30

66
Exercises (d)

• Print all the marks for test 3

67
Solutions (d)

• gt marks, 3
• 1 18 18 22 18 14

68
Exercises (e)

• Print the final marks for those people with marks
  greater than 16 on test 1

69
Solutions (e)
gt marksmarks,1gt16,1 1 20 25
70
Exercises (f)

• Print the marks matrix without the column for
  test 3

71
Solutions (f)

• gt marks,-3
• Test1 Test2 Final
• 1, 20 23 48
• 2, 16 15 40
• 3, 25 20 40
• 4, 14 19 42
• 5, 10 17 30

72
Exercises (g)

• Print the number of rows in the matrix

73
Solutions (g)

• gt nrow(marks)
• 1 5

74
Additional Exercises

• Create a vector INTS containing the integers from
  1 to 50
• Create a vector X which is 2 to the power of INTS
  
• Create a vector Y which is INTS raised to the
  second power
• Create a T/F vector which contains a T when
  elements of x and y are equal and an F when they
  are not equal

75
Solutions to additonal exercises

• gt Xlt-2INTS
• gt Ylt-INTS2
• gt X
• 1 2.000000e000 4.000000e000 8.000000e000
  1.600000e001 3.200000e001 6.400000e001
  1.280000e002
• 8 2.560000e002 5.120000e002 1.024000e003
  2.048000e003 4.096000e003 8.192000e003
  1.638400e004
• 15 3.276800e004 6.553600e004 1.310720e005
  2.621440e005 5.242880e005 1.048576e006
  2.097152e006
• 22 4.194304e006 8.388608e006 1.677722e007
  3.355443e007 6.710886e007 1.342177e008
  2.684355e008
• 29 5.368709e008 1.073742e009 2.147484e009
  4.294967e009 8.589935e009 1.717987e010
  3.435974e010
• 36 6.871948e010 1.374390e011 2.748779e011
  5.497558e011 1.099512e012 2.199023e012
  4.398047e012
• 43 8.796093e012 1.759219e013 3.518437e013
  7.036874e013 1.407375e014 2.814750e014
  5.629500e014
• 50 1.125900e015
• gt Y
• 1 1 4 9 16 25 36 49 64 81
  100 121 144 169 196 225 256 289 324 361
  400 441
• 22 484 529 576 625 676 729 784 841 900
  961 1024 1089 1156 1225 1296 1369 1444 1521 1600
  1681 1764
• 43 1849 1936 2025 2116 2209 2304 2401 2500
• gt equallt-(XY)
• gt equal
• 1 F T F T F F F F F F F F F F F F F F F F F F
  F F F F F F F F F F F F F F F F F F F F F F F F F
  F F F