Spatial Statistics and Spatial Knowledge Discovery First law of geography [Tobler]: Everything is related to everything, but nearby things are more related than distant things. Drowning in Data yet Starving for Knowledge [Naisbitt -Rogers]

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Spatial Statistics and Spatial KnowledgeDiscovery
First law of geography Tobler Everything is
related to everything, but nearby things are more
related than distant things. Drowning in Data
yet Starving for Knowledge Naisbitt -Rogers

• Lecture 1 Introduction to R
• Pat Browne

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Introduction to programming in R

• R is a computer language and environment that
  allows users to program algorithms and use
  pre-written packages. R is a free software
  environment for statistical computing and
  graphics (including mapping).
• There are special R-packages for handling and
  analyzing spatial data. For example, The sp
  package provides classes and methods for points,
  lines, polygons, and grids.
• R can extract spatial data from PostgreSQL. Also,
  R can be combined with SQL using PL/R.

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Installing R

• R for Windows can be downloaded from
• http//ftp.heanet.ie/mirrors/cran.r-project.org/bi
  n/windows/base/R-2.14.1-win.exe
• See Lab1.doc for installation details.

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Starting R

• We will look at the main features of R, see
  lab1.doc for more details. This lecture also
  presents an introduction to programming.
• The basic components of current languages are
• Data types e.g. Integers, String, Polygon.
• Variables to refer to data types e.g. a lt- 2
• Operations on those data types e.g. area(polygon)
• Control structures e.g. sequence, iteration, and
  conditions.
• Logic is an important part of programming, but it
  is often implicit and external to the language.
  Some languages like SQL are quite close to logic.

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Starting R Programs consists of Data,
Operations etc.

• The basic components of current languages are
• Concrete data types e.g. Integer, String,
  Polygon.
• Variables to refer to data types e.g. a lt- 2
• Operations on those data types e.g. area(polygon)
• Control structures e.g. sequence, iteration, and
  conditions.
• Logic is an important part of programming, but it
  is often implicit and external to the language.
  Some languages like SQL are quite close to logic.

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Starting R Variables

• Variables provide a means of accessing the data
  stored in computer memory. R provides a number of
  specialized data structures or objects (also
  called data types). These objects are referenced
  in your programs using variables.
• Store a lt- 2 Access a
• Store b lt-Pat Access b
• Assigns the variable a the number 2 and the
  variable b the string Pat.

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Starting R Data types

• A data type represents a constraint placed upon
  the interpretation of data in a type system,
  describing representation, interpretation, legal
  operations and structure of values.
• Data types are a way to limit the kind of data
  that can be used by a particular program or
  stored in a database table. Types restrict the
  data to a certain set of values (e.g. 1,2,3,..for
  Integers).
• Data types also are restricted to certain
  operations on the type (e.g. addition for
  Integers). R comes with a range of standard data
  types that can be used to represent strings,
  integers, real numbers, and dates, but R also has
  types that are especially suited to statistics
  such as vectors and tables.

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Starting R Data types
The c() function combines its argument into a
vector. In R the term modes is used to describe
data types. There are 4 basic types or modes
numeric, character, complex , and logical. These
can be combined to form collections or what are
called objects in R.
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Starting R Data types (Objects)
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Starting R Data types (Objects)
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Starting R Data types (Objects)
12
Starting R Finding data types
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Starting R Data types

• Numbers 1, 1.4.
• Strings ABC or abc
• Vector
• Arrays are vectors plus dimension vector (dim)
• Factors for nominal ordered categorical data
• Data Frames matrix-like for data of different
  types
• Tables
• One Way Tables
• Two Way Tables

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Starting R Data types- Numbers

• a lt- 3
• b lt- sqrt(aa3)
• List of the defined variables/objects
• gt ls()
• We can add 1 to every element of a list
• gt a lt- c(1,2,3,4,5)
• gt a1
• We can get the mean, variance, and standard
  deviation from a list of numbers
• gt mean(a)
• gt var(a)
• gt sd(a)

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Starting R Data types- Strings

• gt a lt- "hello"
• gt a 1 "hello"
• gt b lt- c("hello","there")
• gt b 1
• gt b 2

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Starting R Data types-Vector

• R operates on named data structures. The simplest
  such structure is the numeric vector, which is a
  single entity consisting of an ordered collection
  of numbers. To set up a vector named x use the R
  command
• gt x lt- c(10.4, 5.6, 3.1, 6.4, 21.7)
• gt x2
• Variable assignment can be written as lt- in R.
  The above assignment uses the function c() which
  can take an arbitrary number of vector arguments
  and whose value is a vector got by concatenating
  its arguments end to end.
• A number occurring by itself in an expression is
  taken as a vector of length one.

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Starting R Data types-Arrays

• Arrays are vectors plus the dim attribute
  (dimension vector), matrices are arrays with a
  dim attribute of length 2. Arrays are ordered
  column major order

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Starting R Data types-Matrices

• Arrays are vectors plus the dim attribute
  (dimension vector), matrices are arrays with a
  dim attribute of length 2. Arrays are ordered
  column major order

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Starting R Data types-Tables

• xc("Yes","No","No","Yes","Yes")
• gt table(x)
• x
• No Yes
• 2 3

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Types of Categorical data

• Nominal Mutually exclusive categories
  male/female, dead/alive, smoker/non-smoker,
  bus/car/train. Tends to be unordered or have no
  logical hierarchy
• Ordinal Can be ranked in a meaningful order.
  Distance between values is not relevant as there
  is no distance information race positions (1st,
  2nd, 3rd), grouped amounts (1-5, 6-10, 11-15 per
  day). Unlike nominal data, ordinal data can be
  compared against each other.

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Starting R Data types- Factor

• When looking at the impact of carbon dioxide
  (CO2) on the growth rate of a tree you might try
  to observe how different trees grow when exposed
  to different preset concentrations of CO2. The
  different levels are often called categories or
  factors. CO2 is measured in parts per million by
  volume (ppmv). Levels could be L1 0-3, L23-6,
  L36-9, L49-12 ppmv (ignoring double inclusion
  of boundaries).

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Starting R Data types- Factor

• Categorical data is often used to classify data
  into various levels or factors. For example,
  smoking data could be a factor in a broader
  survey on health issues. R has a special class
  for working with factors, R will adapt itself
  when it knows it has a factor.
• gt xc("Yes","No","No","Yes","Yes")
• gt factor(x)
• 1 Yes No No Yes Yes
• Levels No Yes

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Starting R Data types- Factor

• We will assume that your data files are stored in
  C\My-R-Dir\
• Load in the file tree91.csv.
• tree lt- read.csv(file"C\\My-R-Dir\\trees91.csv"
  ,headerTRUE,sep",")
• The summary operation prints out the possible
  values and the frequency that they occur. Find
  summary of the chamber identification label
  (CHBR)
• summary(treeCHBR)

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Starting R Data types- Factor

• summary(treeCHBR)
• Note the output of the summary operation produces
  quartiles. A quartile is one of three points
  (including the median), that divide a data set
  into four equal groups, each representing a
  fourth of the distributed sampled population.

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Starting R Data types- Factor

• A nominal value is represented as a factor in R.
  The factor stores the nominal values as a vector
  of integers in the range 1... k
• where k is the number of unique values in the
  nominal variable e.g. male1,female2,
• and an internal vector of character strings (the
  original values) mapped to these integers.

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Starting R Data types- Factor

• Consider variable gender with 20 male entries and
  30 female
• gender lt- c(rep("male",20), rep("female", 30))
• gender lt- factor(gender)
• Stores gender as 20 1s and 30 2s, where 1female,
  2male internally (alphabetically)
• R now treats gender as a nominal variable
• summary(gender)
• What does rep() do? How would you find out?
• Type ? rep() into R and see.

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Starting R Data types- Factor

• An ordered factor is used to represent an ordinal
  variable. Consider a variable rating coded as
  large, medium, small
• rating lt- c(rep("large",10), rep("medium",
  10),rep("small", 10) )
• rating lt- ordered(rating)
• R codes rating to 1,2,3 and associates 1large,
  2medium, 3small internally
• R uses factor for nominal variables and ordered
  for ordinal variables in statistical procedures
  and graphical analyses.
• Try the command plot(rating)

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Starting R Data types- Factor

• A factor is a vector object used to specify a
  discrete classification (grouping) of the
  components of other vectors of the same length. R
  provides both ordered and unordered factors. The
  application of factors is with model formulae. A
  sample of 30 tax accountants from all the states
  of Australia by a character vectors as
• state lt- c("tas", "sa", "qld", "nsw", "nsw",
  "nt", "wa", "wa", "qld", "vic", "nsw", "vic",
  "qld", "qld", "sa", "tas", "sa", "nt", "wa",
  "vic", "qld", "nsw", "nsw", "wa", "sa", "act",
  "nsw", "vic", "vic", "act")
• A factor is created using the factor() function
• statef lt- factor(state)
• summary(statef)
• To find out the levels of a factor the function
  levels() can be used.
• levels(statef) 1 "act" "nsw" "nt" "qld" "sa"
  "tas" "vic" "wa"

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Starting R Data types- Matrix

• A matrix is a collection of data elements
  arranged in a two-dimensional rectangular layout.
  The following is an example of a matrix with 2
  rows and 3 columns.

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Starting R Data types- Matrix

• gt A  matrix(    c(2, 4, 3, 1, 5, 7),  the data
   elements    nrow2,               number of ro
  ws    ncol3,               number of columns 
     byrow  TRUE)         fill matrix by rows  
• gt A    print the matrix      ,1 ,2 ,3 1,
      2    4    3 2,    1    5    7
• An element at the mth row, nth column of A can be
  accessed by the expression Am, n.
• gt A2, 3       element at 2nd row, 3rd column 
  1 7
• The entire mth row A can be extracted as Am, .
• gt A2,         the 2nd row 1 1 5 7
• Similarly, the entire nth column A can be
  extracted as A ,n.
• gt A ,3        the 3rd column 1 3 7

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Starting R Data types- Dataframe

• A dataframe is more general than a matrix, in
  that different columns can have different modes
  (numeric, character, factor, etc.). It is a bit
  like an SQL table.
• d lt- c(1,2,3,4)e lt- c("red", "white", "red",
  NA)f lt- c(TRUE,TRUE,TRUE,FALSE)mydata lt-
  data.frame(d,e,f)names(mydata) lt-
  c("ID","Color","Passed")
• There are a variety of ways to identify the
  elements of a dataframe .
• mydata23 columns 2,3 of dataframe
• mydatac("ID",Color") columns ID,Color
• myframeID name in dataframe

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Starting R Data types- data.frame

• Here we create a data.frame called d.
• L3 lt- LETTERS13
• (d lt- data.frame(cbind(x1, y110),
• facsample(L3, 10, replaceTRUE)))
• To view four rows df14,
• To view a column dy, dy, dfac
• Alternative way to view a column d,3

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Starting R Data types- Table

• One way tables are created with table command,
  its arguments are a vector of factors, and it
  calculates the frequency that each factor occurs.

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Starting R Data types- one-way Table

• gt a lt- factor(c("A","A","B","A","B","B","C","A","C
  "))
• gt results lt- table(a)
• gt results
• gta
• A B C
• 4 3 2
• gt attributes(results)
• gtattributes(results) dimnamesa
• gtattributes(results) dim
• gtattributes(results) class
• gt summary(results)

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Starting R Data types- two-way Table

• Say we want to put the results of two questions
  into a table
• First question responses are Never, Sometimes,
  Always,
• Second question responses are Yes, No, and
  Maybe. Two vectors a and b contain the response
  for each measurement.
• In the vectors, responses are represented by
  position. The third item in a is how the third
  person responded to the first question, and the
  third item in b is how the third person responded
  to the second question.
• In the following we can see that two people who
  said "Maybe" to the first question also said
  "Sometimes" to the second question.

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Starting R Data types- two-way Table
ROW COLUMN

• a lt-
• c("Sometimes","Sometimes","Never","Always","Always
  ","Sometimes","Sometimes","Never")
• b lt- c("Maybe","Maybe","Yes","Maybe","Maybe","No",
  "Yes","No")
• results lt- table(a,b)
• gt results
• b
• a Maybe No Yes
• Always 2 0 0
• Never 0 1 1
• Sometimes 2 1 1
• The table shows that two people who said Maybe to
  the first question
• also said Sometimes to the second question.
• The elements are accessed like a matrix
  (result(,1). )
• How many people responded?

The third item in a is how the third person
responded to the first question, and the third
item in b is how the third person responded to
the second question.
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Useful functions

• length(object) number of elements or
  componentsstr(object)     structure of an
  object class(object)   class or type of an
  objectnames(object)   namesc(object,object,...)
  combine objects into a vectorcbind(object,
  object, ...) combine objects as
  columnsrbind(object, object, ...) combine
  objects as rows

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Useful functions

• object()      prints the
  objectls(),objects()    list current
  objectsrm(object) delete an
  objectnewobjectlt-edit(object) edit,copy,save
• fix(object)    edit in place
• data.entry(result) GUI edit in place
• mode(object) type of the object.

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Starting R Input-Output IO

• There are many ways to data into R. We focus on
  just three
• Assignment
• Reading a CSV File (writing later)
• Loading data from PostgreSQL (later)

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Starting R IO-Assignment

• Assignment (RHS lt- LHS) allows an expression on
  the RHS to be stored in a name object on the LHS.
  In R
• gt a lt- c(3,5,7,9) gt
• The above assignment uses the combine command.
  (c means combine). This makes a vector called a.
  No output is produced yet. Now we can retrieve
  the contents of a just by typing it in.
• gt a
• gt a3
• The command gives all of a the second command
  gives the third element of a . 3 is called the
  index. The zero entry hold the data type of the a
  vector. Try
• b lt- c("one","two","three")

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Starting R IO-Assignment

• cells lt- c(1,26,24,68)
• rnames lt- c("R1", "R2")
• cnames lt- c("C1", "C2")
• mymatrix lt-
• matrix(cells, nrow2, ncol2,
• byrowTRUE,
• dimnames
• list(rnames, cnames))

Type gtattributes(mymatrix) Type gthelp(array) to
find more details on Arrays
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Starting R Input File

• Place the file simple.csv in a directory
  (folder).
• Load the file into R using
• h lt- read.csv(fileC\\My-R-Dir\\simple.csv,head
  TRUE,sep,)
• View the contents of h
• Now the contents of the file are stored in R as
  the object named h.
• Type gtnames(h)

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Starting R Data types-Matrices

• All columns in a matrix must have the same data
  type (numeric, character, etc.) and the same
  length. The general format is
• mymatrix lt-
• matrix(vector, nrowr, ncolc,
• byrowFALSE,
• dimnameslist(char_vector_rownames,
• char_vector_colnames))
• byrowTRUE indicates that the matrix should be
  filled by rows. byrowFALSE indicates that the
  matrix should be filled by columns (the default).
  dimnames provides optional labels for the columns
  and rows.

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Review - vectors, lists, matrices, data frames

• To make vectors x, y, year, names
• x lt- c(2,3,7,9)
• y lt- c(9,7,3,2)
• year lt- 19901993
• names lt- c("payal", "shraddha", "kritika",
  "itida")
• Accessing last element
• ylength(y)
• To make a list person
• person lt- list(name"payal", x2, y9, year1990)
• Accessing personname, personx , person1
• names(person)

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Review - vectors, lists, matrices, data frames

• To make a matrix, pasting together the columns
  year , x, y using column bind.
• m lt- cbind(year, x, y)
• To make a data frame, which is a list of vectors
  of the same length
• D lt- data.frame(names, year, x, y)
• nrow(D)
• Accessing one of these vectors
• Dnames
• Accessing the last element of this vector
  Dnamesnrow(D)
• Dnameslength(Dnames)

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Finding the type and class

• gt g lt- c(1,3,2)
• gt class(g)
• 1 "numeric"
• gt typeof(g)
• 1 "double
• gt is(g)
• 1 "numeric" "vector"

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Sorting

• The variable i is a vector of integers, then the
  data frame Di, picks up rows from D based on
  the values found in i'. The order() function
  makes an integer vector which is a correct
  ordering for the purpose of sorting.
• D lt- data.frame(xc(1,2,3,1), yc(7,19,2,2))
• Sort on x
• indexes lt- order(Dx)
• Dindexes,
• Print out sorted dataset, sorted in reverse by y
  Drev(order(Dy)),

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Logical constants variables

• TRUE and FALSE are logical constants
• T and F are logical variables
• T and F are quite not synonyms for TRUE and FALSE
  but variables that have the expected values by
  default
• TRUE TRUE
• T T
• Normally give the expected result.

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Missing Values NA

• Not Available or Missing Values are represented
  as NA, which is a logical constant (either T or
  F) which contains a missing value indicator.
• Examples
• is.na(c(1, NA)) FALSE TRUE
• is.na(c(NA, NA)) TRUE TRUE
• is.na(paste(c(1, NA))) FALSE FALSE
• xx lt- c(04)
• is.na(xx) lt- c(2, 4)
• xx 0 NA 2 NA 4

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Writing your own functions.

• R comes with a built-in median function.
• Usage median(x, na.rm FALSE)
• Where x an object for which a method has been
  defined, or a numeric vector containing the
  values whose median is to be computed.
• na.rm a logical value indicating whether NA
  values should be removed before the computation
  proceeds.

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Control - If

• gt if (T) print("Hello") else print("Good Bye")
• 1 "Hello"
• gt if (F) print("Hello") else print("Good Bye")
• 1 "Good Bye"

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Control - Sequence

• a lt- c(1,2,3,4,5)
• b lt- c(2,3,4,5)
• odd.even lt- length(a) 2
• if (odd.even 0)
• (sort(a)length(a)/2
• sort(a)1 length(a)/2)/2 else
• sort(a)ceiling(length(a)/2)
• If we want to find the median of b we have to
  type the whole thing again.
• gt if (odd.even 0) (sort(b)length(b)/2
  sort(b)1 length(b)/2)/2 else
  sort(b)ceiling(length(b)/2)
• It would be better to write a function.

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User Written - Functions

• a lt- c(1,2,3,4,5)
• b lt- c(2,3,4,5)
• mymedian lt- function(x)
• odd.even lt- length(x) 2
• if (odd.even 0)
• (sort(x)length(x)/2
• sort(x)1 length(x)/2)/2 else
• sort(x)ceiling(length(x)/2)
• Now we can call, run, execute or invoke my median
  on any vector.
• gt mymedian(a)
• gt mymedian(b)

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References
Applied Spatial Data Analysis with R Bivand,
Pebesma, Gómez-Rubio
Lloyd Spatial Data Analysis
http//www.manning.com/obe/
http//www.spatial.cs.umn.edu/Book/