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<h1 class="title toc-ignore">R Data Structures</h1>
</div>
<p>As in many programming languages, understanding how data are stored and manipulated is important to getting the most out of the experience. In these next few sections, we will introduce some basic R data types and structures as well as some general approaches for working with them.</p>
<div id="vectors" class="section level1">
<h1>Vectors</h1>
<p>In R, even a single value is a vector with length=1.</p>
<pre class="r"><code>z = 1
z</code></pre>
<pre><code>## [1] 1</code></pre>
<pre class="r"><code>length(z)</code></pre>
<pre><code>## [1] 1</code></pre>
<p>In the code above, we “assigned” the value 1 to the variable named <code>z</code>. Typing <code>z</code> by itself is an “expression” that returns a result which is, in this case, the value that we just assigned. The <code>length</code> method takes an R object and returns the R length. There are numerous ways of asking R about what an object represents, and <code>length</code> is one of them.</p>
<p>Vectors can contain numbers, strings (character data), or logical values (<code>TRUE</code> and <code>FALSE</code>) or other “atomic” data types (table @ref(tab:simpletypes)). <em>Vectors cannot contain a mix of types!</em> We will introduce another data structure, the R <code>list</code> for situations when we need to store a mix of base R data types.</p>
<table>
<caption>(#tab:simpletypes) Atomic (simplest) data types in R.</caption>
<thead>
<tr class="header">
<th align="left">Data type</th>
<th align="left">Stores</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">numeric</td>
<td align="left">floating point numbers</td>
</tr>
<tr class="even">
<td align="left">integer</td>
<td align="left">integers</td>
</tr>
<tr class="odd">
<td align="left">complex</td>
<td align="left">complex numbers</td>
</tr>
<tr class="even">
<td align="left">factor</td>
<td align="left">categorical data</td>
</tr>
<tr class="odd">
<td align="left">character</td>
<td align="left">strings</td>
</tr>
<tr class="even">
<td align="left">logical</td>
<td align="left">TRUE or FALSE</td>
</tr>
<tr class="odd">
<td align="left">NA</td>
<td align="left">missing</td>
</tr>
<tr class="even">
<td align="left">NULL</td>
<td align="left">empty</td>
</tr>
<tr class="odd">
<td align="left">function</td>
<td align="left">function type</td>
</tr>
</tbody>
</table>
<div id="creating-vectors" class="section level2">
<h2>Creating vectors</h2>
<p>Character vectors (also sometimes called “string” vectors) are entered with each value surrounded by single or double quotes; either is acceptable, but they must match. They are always displayed by R with double quotes. Here are some examples of creating vectors:</p>
<pre class="r"><code># examples of vectors
c('hello','world')</code></pre>
<pre><code>## [1] "hello" "world"</code></pre>
<pre class="r"><code>c(1,3,4,5,1,2)</code></pre>
<pre><code>## [1] 1 3 4 5 1 2</code></pre>
<pre class="r"><code>c(1.12341e7,78234.126)</code></pre>
<pre><code>## [1] 11234100.00 78234.13</code></pre>
<pre class="r"><code>c(TRUE,FALSE,TRUE,TRUE)</code></pre>
<pre><code>## [1] TRUE FALSE TRUE TRUE</code></pre>
<pre class="r"><code># note how in the next case the TRUE is converted to "TRUE"
# with quotes around it.
c(TRUE,'hello')</code></pre>
<pre><code>## [1] "TRUE" "hello"</code></pre>
<p>We can also create vectors as “regular sequences” of numbers. For example:</p>
<pre class="r"><code># create a vector of integers from 1 to 10
x = 1:10
# and backwards
x = 10:1</code></pre>
<p>The <code>seq</code> function can create more flexible regular sequences.</p>
<pre class="r"><code># create a vector of numbers from 1 to 4 skipping by 0.3
y = seq(1,4,0.3)</code></pre>
<p>And creating a new vector by concatenating existing vectors is possible, as well.</p>
<pre class="r"><code># create a sequence by concatenating two other sequences
z = c(y,x)
z</code></pre>
<pre><code>## [1] 1.0 1.3 1.6 1.9 2.2 2.5 2.8 3.1 3.4 3.7 4.0 10.0 9.0 8.0 7.0
## [16] 6.0 5.0 4.0 3.0 2.0 1.0</code></pre>
</div>
<div id="vector-operations" class="section level2">
<h2>Vector Operations</h2>
<p>Operations on a single vector are typically done element-by-element. For example, we can add <code>2</code> to a vector, <code>2</code> is added to each element of the vector and a new vector of the same length is returned.</p>
<pre class="r"><code>x = 1:10
x + 2</code></pre>
<pre><code>## [1] 3 4 5 6 7 8 9 10 11 12</code></pre>
<p>If the operation involves two vectors, the following rules apply. If the vectors are the same length: R simply applies the operation to each pair of elements.</p>
<pre class="r"><code>x + x</code></pre>
<pre><code>## [1] 2 4 6 8 10 12 14 16 18 20</code></pre>
<p>If the vectors are different lengths, but one length a multiple of the other, R reuses the shorter vector as needed.</p>
<pre class="r"><code>x = 1:10
y = c(1,2)
x * y</code></pre>
<pre><code>## [1] 1 4 3 8 5 12 7 16 9 20</code></pre>
<p>If the vectors are different lengths, but one length <em>not</em> a multiple of the other, R reuses the shorter vector as needed <em>and</em> delivers a warning.</p>
<pre class="r"><code>x = 1:10
y = c(2,3,4)
x * y</code></pre>
<pre><code>## Warning in x * y: longer object length is not a multiple of shorter object
## length</code></pre>
<pre><code>## [1] 2 6 12 8 15 24 14 24 36 20</code></pre>
<p>Typical operations include multiplication (“*”), addition, subtraction, division, exponentiation (“^”), but many operations in R operate on vectors and are then called “vectorized”.</p>
</div>
<div id="logical-vectors" class="section level2">
<h2>Logical Vectors</h2>
<p>Logical vectors are vectors composed on only the values <code>TRUE</code> and <code>FALSE</code>. Note the all-upper-case and no quotation marks.</p>
<pre class="r"><code>a = c(TRUE,FALSE,TRUE)
# we can also create a logical vector from a numeric vector
# 0 = false, everything else is 1
b = c(1,0,217)
d = as.logical(b)
d</code></pre>
<pre><code>## [1] TRUE FALSE TRUE</code></pre>
<pre class="r"><code># test if a and d are the same at every element
all.equal(a,d)</code></pre>
<pre><code>## [1] TRUE</code></pre>
<pre class="r"><code># We can also convert from logical to numeric
as.numeric(a)</code></pre>
<pre><code>## [1] 1 0 1</code></pre>
<div id="logical-operators" class="section level3">
<h3>Logical Operators</h3>
<p>Some operators like <code><, >, ==, >=, <=, !=</code> can be used to create logical vectors.</p>
<pre class="r"><code># create a numeric vector
x = 1:10
# testing whether x > 5 creates a logical vector
x > 5</code></pre>
<pre><code>## [1] FALSE FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE</code></pre>
<pre class="r"><code>x <= 5</code></pre>
<pre><code>## [1] TRUE TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE FALSE</code></pre>
<pre class="r"><code>x != 5</code></pre>
<pre><code>## [1] TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE</code></pre>
<pre class="r"><code>x == 5</code></pre>
<pre><code>## [1] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE</code></pre>
<p>We can also assign the results to a variable:</p>
<pre class="r"><code>y = (x == 5)
y</code></pre>
<pre><code>## [1] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE</code></pre>
</div>
</div>
<div id="indexing-vectors" class="section level2">
<h2>Indexing Vectors</h2>
<p>In R, an index is used to refer to a specific element or set of elements in an vector (or other data structure). [R uses <code>[</code> and <code>]</code> to perform indexing, although other approaches to getting subsets of larger data structures are common in R.</p>
<pre class="r"><code>x = seq(0,1,0.1)
# create a new vector from the 4th element of x
x[4]</code></pre>
<pre><code>## [1] 0.3</code></pre>
<p>We can even use other vectors to perform the “indexing”.</p>
<pre class="r"><code>x[c(3,5,6)]</code></pre>
<pre><code>## [1] 0.2 0.4 0.5</code></pre>
<pre class="r"><code>y = 3:6
x[y]</code></pre>
<pre><code>## [1] 0.2 0.3 0.4 0.5</code></pre>
<p>Combining the concept of indexing with the concept of logical vectors results in a very power combination.</p>
<pre class="r"><code># use help('rnorm') to figure out what is happening next
myvec = rnorm(10)
# create logical vector that is TRUE where myvec is >0.25
gt1 = (myvec > 0.25)
sum(gt1)</code></pre>
<pre><code>## [1] 3</code></pre>
<pre class="r"><code># and use our logical vector to create a vector of myvec values that are >0.25
myvec[gt1]</code></pre>
<pre><code>## [1] 0.8690175 0.3469630 1.0568830</code></pre>
<pre class="r"><code># or <=0.25 using the logical "not" operator, "!"
myvec[!gt1]</code></pre>
<pre><code>## [1] -1.74087909 0.23290943 -1.45242500 0.02577602 0.05147477 -1.07679812
## [7] 0.24372313</code></pre>
<pre class="r"><code># shorter, one line approach
myvec[myvec > 0.25]</code></pre>
<pre><code>## [1] 0.8690175 0.3469630 1.0568830</code></pre>
</div>
<div id="character-vectors-a.k.a.-strings" class="section level2">
<h2>Character Vectors, A.K.A. Strings</h2>
<p>R uses the <code>paste</code> function to concatenate strings.</p>
<pre class="r"><code>paste("abc","def")</code></pre>
<pre><code>## [1] "abc def"</code></pre>
<pre class="r"><code>paste("abc","def",sep="THISSEP")</code></pre>
<pre><code>## [1] "abcTHISSEPdef"</code></pre>
<pre class="r"><code>paste0("abc","def")</code></pre>
<pre><code>## [1] "abcdef"</code></pre>
<pre class="r"><code>## [1] "abcdef"
paste(c("X","Y"),1:10)</code></pre>
<pre><code>## [1] "X 1" "Y 2" "X 3" "Y 4" "X 5" "Y 6" "X 7" "Y 8" "X 9" "Y 10"</code></pre>
<pre class="r"><code>paste(c("X","Y"),1:10,sep="_")</code></pre>
<pre><code>## [1] "X_1" "Y_2" "X_3" "Y_4" "X_5" "Y_6" "X_7" "Y_8" "X_9" "Y_10"</code></pre>
<p>We can count the number of characters in a string.</p>
<pre class="r"><code>nchar('abc')</code></pre>
<pre><code>## [1] 3</code></pre>
<pre class="r"><code>nchar(c('abc','d',123456))</code></pre>
<pre><code>## [1] 3 1 6</code></pre>
<p>Pulling out parts of strings is also sometimes useful.</p>
<pre class="r"><code>substr('This is a good sentence.',start=10,stop=15)</code></pre>
<pre><code>## [1] " good "</code></pre>
<p>Another common operation is to replace something in a string with something (a find-and-replace).</p>
<pre class="r"><code>sub('This','That','This is a good sentence.')</code></pre>
<pre><code>## [1] "That is a good sentence."</code></pre>
<p>When we want to find all strings that match some other string, we can use <code>grep</code>, or “grab regular expression”.</p>
<pre class="r"><code>grep('bcd',c('abcdef','abcd','bcde','cdef','defg'))</code></pre>
<pre><code>## [1] 1 2 3</code></pre>
<pre class="r"><code>grep('bcd',c('abcdef','abcd','bcde','cdef','defg'),value=TRUE)</code></pre>
<pre><code>## [1] "abcdef" "abcd" "bcde"</code></pre>
</div>
<div id="missing-values-aka-na" class="section level2">
<h2>Missing Values, AKA “NA”</h2>
<p>R has a special value, “NA”, that represents a “missing” value, or <em>Not Available</em>, in a vector or other data structure. Here, we just create a vector to experiment.</p>
<pre class="r"><code>x = 1:5
x</code></pre>
<pre><code>## [1] 1 2 3 4 5</code></pre>
<pre class="r"><code>length(x)</code></pre>
<pre><code>## [1] 5</code></pre>
<pre class="r"><code>is.na(x)</code></pre>
<pre><code>## [1] FALSE FALSE FALSE FALSE FALSE</code></pre>
<pre class="r"><code>x[2] = NA
x</code></pre>
<pre><code>## [1] 1 NA 3 4 5</code></pre>
<p>The length of <code>x</code> is unchanged, but there is one value that is marked as “missing” by virtue of being <code>NA</code>.</p>
<pre class="r"><code>length(x)</code></pre>
<pre><code>## [1] 5</code></pre>
<pre class="r"><code>is.na(x)</code></pre>
<pre><code>## [1] FALSE TRUE FALSE FALSE FALSE</code></pre>
<p>We can remove <code>NA</code> values by using indexing. In the following, <code>is.na(x)</code> returns a logical vector the length of <code>x</code>. The <code>!</code> is the logical <em>NOT</em> operator and converts <code>TRUE</code> to <code>FALSE</code> and vice-versa.</p>
<pre class="r"><code>x[!is.na(x)]</code></pre>
<pre><code>## [1] 1 3 4 5</code></pre>
</div>
<div id="factors" class="section level2">
<h2>Factors</h2>
<p>A factor is a special type of vector, normally used to hold a categorical variable–such as smoker/nonsmoker, state of residency, zipcode–in many statistical functions. Such vectors have class “factor”. Factors are primarily used in Analysis of Variance (ANOVA) or other situations when “categories” are needed. When a factor is used as a predictor variable, the corresponding indicator variables are created (more later).</p>
<p>Note of caution that factors in R often <em>appear</em> to be character vectors when printed, but you will notice that they do not have double quotes around them. They are stored in R as numbers with a key name, so sometimes you will note that the factor <em>behaves</em> like a numeric vector.</p>
<pre class="r"><code># create the character vector
citizen<-c("uk","us","no","au","uk","us","us","no","au")
# convert to factor
citizenf<-factor(citizen)
citizen </code></pre>
<pre><code>## [1] "uk" "us" "no" "au" "uk" "us" "us" "no" "au"</code></pre>
<pre class="r"><code>citizenf</code></pre>
<pre><code>## [1] uk us no au uk us us no au
## Levels: au no uk us</code></pre>
<pre class="r"><code># convert factor back to character vector
as.character(citizenf)</code></pre>
<pre><code>## [1] "uk" "us" "no" "au" "uk" "us" "us" "no" "au"</code></pre>
<pre class="r"><code># convert to numeric vector
as.numeric(citizenf)</code></pre>
<pre><code>## [1] 3 4 2 1 3 4 4 2 1</code></pre>
<p>R stores many data structures as vectors with “attributes” and “class” (just so you have seen this).</p>
<pre class="r"><code>attributes(citizenf)</code></pre>
<pre><code>## $levels
## [1] "au" "no" "uk" "us"
##
## $class
## [1] "factor"</code></pre>
<pre class="r"><code>class(citizenf)</code></pre>
<pre><code>## [1] "factor"</code></pre>
<pre class="r"><code># note that after unclassing, we can see the
# underlying numeric structure again
unclass(citizenf)</code></pre>
<pre><code>## [1] 3 4 2 1 3 4 4 2 1
## attr(,"levels")
## [1] "au" "no" "uk" "us"</code></pre>
<p>Tabulating factors is a useful way to get a sense of the “sample” set available.</p>
<pre class="r"><code>table(citizenf)</code></pre>
<pre><code>## citizenf
## au no uk us
## 2 2 2 3</code></pre>
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