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<title>Tutorial 4: Cleaning and Merging Data</title>
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<body>
<div class="slide titlepage">
<h1 class="title">Tutorial 4: Cleaning and Merging Data</h1>
<p class="author">
DPI R Bootcamp
</p>
<p class="date">Jared Knowles</p>
</div>
<div class="section slide level1" id="overview">
<h1>Overview</h1>
<p>In this lesson we hope to learn about:</p>
<ul class="incremental">
<li>The Strategic Data Project</li>
<li>Checking data for errors</li>
<li>Recoding data and changing data types</li>
<li>Diagnostics and error checks</li>
</ul>
<p align="center">
<img src="data:image/png;base64,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" height="81" width="138">
</p>
</div>
<div class="section slide level1" id="data-setup">
<h1>Data Setup</h1>
<ul class="incremental">
<li>Let's read in a new dataset now that has some messiness to it</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">load</span>(<span class="st">"data/Student_Attributes.rda"</span>)
<span class="kw">head</span>(stuatt[, <span class="dv">1</span>:<span class="dv">4</span>], <span class="dv">7</span>)</code></pre>
<pre><code> sid school_year male race_ethnicity
1 1 2004 1 B
2 1 2005 1 H
3 1 2006 1 H
4 1 2007 1 H
5 2 2006 0 W
6 2 2007 0 B
7 3 2006 1 H</code></pre>
<ul class="incremental">
<li>What's wrong with this?</li>
</ul>
</div>
<div class="section slide level1" id="how-can-r-help-correct-this">
<h1>How can R help correct this?</h1>
<ul class="incremental">
<li>Identify problems</li>
<li>Enforce business rules for messy data consistently</li>
<li>Build data cleaning into all analyses tasks across the workflow</li>
<li>Analyze inconsistencies and do reports</li>
</ul>
</div>
<div class="section slide level1" id="strategic-data-project">
<h1>Strategic Data Project</h1>
<ul class="incremental">
<li><a href="http://www.gse.harvard.edu/~pfpie/index.php/sdp/">The Strategic Data Project</a> is a project housed at Harvard Center for Education Policy Research aimed at bringing high quality research methods and data analysis to bear on strategic management and policy decisions in the education sector</li>
<li>SDP was formed on two fundamental premises:</li>
</ul>
<ol class="incremental" style="list-style-type: decimal">
<li>Policy and management decisions can directly influence schools' and teachers' ability to improve student achievement</li>
<li>Valid and reliable data analysis significantly improves the quality of decision making</li>
</ol>
<ul class="incremental">
<li>Their focus is on bringing together the right people, assembling the right data, and performing the right analysis because this will improve decisions made by leadership</li>
<li>They are smart folks who have done a lot of the important but unexciting work of systematically identifying how to clean, document, and transparently evaluate datasets</li>
</ul>
<p align="center">
<img 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zFGhBo1AwPRWg6VACBIkl5AUyHAjA7lA/U0EBHXU0o1BNXUBIdAAHlHEDFAAIega5pAAHKga2RAAATgXBTnUywoWmlYEFkVbQIxjHnZBvQHAFIQY1dJUV4AlTaAVrNFCLgolV8oEH6gV6wndAwQdXGAB3eInAyQBaY4EIWQBQXXAX4AlgzwBTiQBa/3iWrCZ4puoGogKBDfuXZrt14CYQMtQAQicADR2QZZIGEM1gY+QATUeRAu8AY/8J8XsAXYl4JvwAQaJxBPwARvoAMCsQVMUAWoyQQX0HEBcAFMUGwCcQLfhhDfKW/ayZ2VuQc9oIMaEHcnYAYFEAZqUHUJlgXquXZ1+VZxQAQTgEwE8QU9kAVptkk82qM++qNAGqRCOqREWqRGeqRImqRKuqRM2qRO+qRQGqVSOqVUWqVWeqVYmqVauqVc2qVe+qVgGqbFERAAOw==" height="112" width="329">
</p>
</div>
<div class="section slide level1" id="toolkit---data-cleaning">
<h1>Toolkit - Data Cleaning</h1>
<ul class="incremental">
<li>The SDP has come up with a great tutorial and guided analyses using a great synthetic data set to help walk through the process of cleaning data</li>
<li>This was written in Stata, we are porting it to R (you can contribute to this effort if you like), and are going to walk through just a single lesson of it here (Clean Data Building)</li>
<li>You can get the toolkit lesson that this tutorial is adapted from <a href="http://www.gse.harvard.edu/~pfpie/index.php/sdp/tools">online</a></li>
<li>There are five toolkits in addition to a data guide that are incredibly helpful, so we are just touching the tip of the iceberg</li>
<li>Other modules include:</li>
</ul>
<ol class="incremental" style="list-style-type: decimal">
<li>How to identify essential data elements for analyzing student achievement</li>
<li>Clean, check, and build variables in the dataset</li>
<li>Connect relevant datasets from different soruces</li>
<li>Analyze datasets</li>
<li>Adopt coding best practices to facilitate shared and replicable data analysis</li>
</ol>
</div>
<div class="section slide level1" id="sdp-task-1-student-attributes-intro">
<h1>SDP Task 1 Student Attributes Intro</h1>
<ul class="incremental">
<li>Drop the <code>first_9th_school_year_reported</code> variable</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r">stuatt$first_9th_year_reported <- <span class="ot">NULL</span></code></pre>
<ul class="incremental">
<li>To drop variables in R we assign them <code>NULL</code>, another R quirk</li>
</ul>
</div>
<div class="section slide level1" id="sdp-task-1---step-1-consistent-gender">
<h1>SDP Task 1 - Step 1: Consistent Gender</h1>
<ul class="incremental">
<li>Is gender unique for each student?</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">length</span>(<span class="kw">unique</span>(stuatt$sid))</code></pre>
<pre><code>[1] 21803</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">length</span>(<span class="kw">unique</span>(stuatt$sid, stuatt$male))</code></pre>
<pre><code>[1] 21806</code></pre>
<ul class="incremental">
<li>Nah, we have 21,803 unique students in our dataset, but <em>21,806</em> unique combinations of gender and student</li>
</ul>
</div>
<div class="section slide level1" id="testing-uniqueness">
<h1>Testing Uniqueness</h1>
<ul class="incremental">
<li>Below we write a small function that automates the check we did on the last slide</li>
<li>How does this work?</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r">testuniqueness <- function(id, group) {
<span class="kw">length</span>(<span class="kw">unique</span>(id)) == <span class="kw">length</span>(<span class="kw">unique</span>(id, group))
} <span class="co"># Need better varname and some optimization to the speed of this code</span>
<span class="kw">testuniqueness</span>(stuatt$sid, stuatt$male)</code></pre>
<pre><code>[1] FALSE</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">testuniqueness</span>(stuatt$sid, stuatt$race_ethnicity)</code></pre>
<pre><code>[1] FALSE</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">testuniqueness</span>(stuatt$sid, stuatt$birth_date)</code></pre>
<pre><code>[1] FALSE</code></pre>
<ul class="incremental">
<li>Messy...</li>
</ul>
</div>
<div class="section slide level1" id="where-is-the-data-messy">
<h1>Where is the data messy?</h1>
<pre class="sourceCode r"><code class="sourceCode r">stuatt[<span class="dv">17</span>:<span class="dv">21</span>, <span class="dv">1</span>:<span class="dv">3</span>]</code></pre>
<pre><code> sid school_year male
17 7 2004 1
18 7 2005 1
19 7 2006 1
20 7 2007 0
21 7 2008 1</code></pre>
<ul class="incremental">
<li>Student 7 has an inconsistently reported gender in our data</li>
<li>We need a business rule to handle fixing this, and a way to implement it</li>
<li>SDP provides the rule, R provides the systematic implementation</li>
</ul>
</div>
<div class="section slide level1" id="unifying-consistent-gender-values">
<h1>Unifying Consistent Gender Values</h1>
<ul class="incremental">
<li>First we create a variable with the number of unique values gender takes per student</li>
<li>In R to do this we create a summary table of student attributes by collapsing the data set into one row per student using the <code>plyr</code> strategy we learned in Tutorial 3</li>
<li>Then we ask R to tell us how many rows have what values for the length of gender</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(plyr)
sturow <- <span class="kw">ddply</span>(stuatt, .(sid), summarize, <span class="dt">nvals_gender =</span> <span class="kw">length</span>(<span class="kw">unique</span>(male)))
<span class="kw">table</span>(sturow$nvals_gender)</code></pre>
<pre><code>
1 2
21799 4 </code></pre>
<ul class="incremental">
<li>So 4 students have more than one unique value for gender</li>
</ul>
</div>
<div class="section slide level1" id="fixing-the-pesky-observations">
<h1>Fixing the pesky observations</h1>
<ul class="incremental">
<li>At this point there are a number of business rules we could adopt</li>
<li>We could assign students the most recent value, the most frequent value, or even a random value!</li>
<li>Let's see if replacing it with the most frequent value works</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="co"># A function to find the most frequent value</span>
<span class="kw">library</span>(eeptools)
sturow <- <span class="kw">ddply</span>(stuatt, .(sid), summarize, <span class="dt">nvals_gender =</span> <span class="kw">length</span>(<span class="kw">unique</span>(male)),
<span class="dt">gender_mode =</span> <span class="kw">statamode</span>(male), <span class="dt">gender_recent =</span> <span class="kw">tail</span>(male, <span class="dv">1</span>))
<span class="kw">head</span>(sturow[<span class="dv">7</span>:<span class="dv">10</span>, ])</code></pre>
<pre><code> sid nvals_gender gender_mode gender_recent
7 7 2 1 1
8 8 1 1 1
9 9 1 1 1
10 10 1 1 1</code></pre>
</div>
<div class="section slide level1" id="fixing-observations-ii">
<h1>Fixing observations II</h1>
<ul class="incremental">
<li>Now we have two objects <code>stuatt</code> and <code>sturow</code> and we need to replace some values from <code>stuatt</code> with some values from <code>sturow</code></li>
<li><code>merge</code> to the rescue!</li>
<li>Let's <code>merge</code> our two data objects into a temporary data object called <code>tempdf</code></li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r">tempdf <- <span class="kw">merge</span>(stuatt, sturow) <span class="co"># R finds the linking variable already</span>
<span class="kw">head</span>(tempdf[<span class="dv">17</span>:<span class="dv">21</span>, <span class="kw">c</span>(<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>, <span class="dv">10</span>, <span class="dv">11</span>)])</code></pre>
<pre><code> sid school_year male nvals_gender gender_mode
17 7 2004 1 2 1
18 7 2005 1 2 1
19 7 2006 1 2 1
20 7 2007 0 2 1
21 7 2008 1 2 1</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">print</span>(<span class="kw">subset</span>(tempdf[, <span class="kw">c</span>(<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>, <span class="dv">10</span>, <span class="dv">11</span>)], sid == <span class="dv">12506</span>))</code></pre>
<pre><code> sid school_year male nvals_gender gender_mode
50064 12506 2004 1 2 .
50065 12506 2005 0 2 .</code></pre>
<ul class="incremental">
<li>We fixed observation 7, but not observation 12506</li>
</ul>
</div>
<div class="section slide level1" id="fixing-where-the-mode-does-not-work">
<h1>Fixing where the mode does not work</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">print</span>(<span class="kw">subset</span>(tempdf[, <span class="kw">c</span>(<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>, <span class="dv">10</span>, <span class="dv">11</span>, <span class="dv">12</span>)], sid == <span class="dv">12506</span>))</code></pre>
<pre><code> sid school_year male nvals_gender gender_mode gender_recent
50064 12506 2004 1 2 . 0
50065 12506 2005 0 2 . 0</code></pre>
<ul class="incremental">
<li>Our next business rule is to assign the most recent value of gender from the <code>gender_recent</code> variable when there is not a value of <code>gender_mode</code> that is valid</li>
<li>This seems like a pretty simple job for <code>recoding</code> our variable!</li>
</ul>
</div>
<div class="section slide level1" id="recode-gender">
<h1>Recode Gender</h1>
<ul class="incremental">
<li>Two step process: first we assign <code>tempdf$male</code> to be the same as <code>tempdf$gender_mode</code></li>
<li>Then, where <code>tempdf$male</code> is now a "." indicating no modal category exists, we assign <code>tempdf$gender_recent</code> to be <code>tempdf$male</code></li>
<li>Go ahead and try this and use <code>testuniqueness(tempdf$id,tempdf$male)</code> to check if it worked</li>
</ul>
</div>
<div class="section slide level1" id="results">
<h1>Results</h1>
<pre class="sourceCode r"><code class="sourceCode r">tempdf$male <- tempdf$gender_mode
tempdf$male[tempdf$male == <span class="st">"."</span>] <- tempdf$gender_recent[tempdf$male == <span class="st">"."</span>]
<span class="co"># we have to put the filter on both sides of the assignment operator</span>
<span class="kw">testuniqueness</span>(tempdf$id, tempdf$male)</code></pre>
<pre><code>[1] TRUE</code></pre>
<ul class="incremental">
<li>Now let's clean up our workspace, we created a lot of temporary variables that we don't need</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">rm</span>(sturow)
stuatt <- tempdf
stuatt$nvals_gender <- <span class="ot">NULL</span>
stuatt$gender_mode <- <span class="ot">NULL</span>
stuatt$gender_recent <- <span class="ot">NULL</span>
<span class="co"># or just run stuatt<-tempdf[,1:9]</span>
<span class="kw">rm</span>(tempdf)</code></pre>
</div>
<div class="section slide level1" id="create-a-consistent-race-and-ethnicity-indicator">
<h1>Create a consistent race and ethnicity indicator</h1>
<ul class="incremental">
<li>Let's practice the same procedure on race</li>
</ul>
<h3 id="a-note-about-variable-types">A Note About Variable Types</h3>
<ul class="incremental">
<li>In the SDP Toolkit you are advised to convert the <code>race_ethnicity</code> variable to numeric and add labels to it</li>
<li>This is because Stata and other statistical packages don't have internal data structures that can handle the <code>factor</code> variable type like R can, and rely on numeric coding schemes</li>
<li>Why don't we need to do this in R?</li>
<li>In fact, in R, we should probably recode the <code>male</code> variable as a factor with values <code>M</code> and <code>F</code></li>
<li>One problem is that our datafile uses 'NA' for Native American and we do have to recode that... why?</li>
</ul>
</div>
<div class="section slide level1" id="recoding-race">
<h1>Recoding Race</h1>
<ul class="incremental">
<li>What's wrong with our race variable?</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">summary</span>(stuatt$race_ethnicity)</code></pre>
<pre><code> A B H M/O W NA's
7303 25321 30444 2809 20528 1129 </code></pre>
<ul class="incremental">
<li>How do we do this?</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">length</span>(stuatt$race_ethnicity[<span class="kw">is.na</span>(stuatt$race_ethnicity)])
stuatt$race_ethnicity[<span class="kw">is.na</span>(stuatt$race_ethnicity)] <- <span class="st">"AI"</span>
<span class="kw">summary</span>(stuatt$race_ethnicity)</code></pre>
<ul class="incremental">
<li>Why doesn't this work?</li>
</ul>
</div>
<div class="section slide level1" id="correct-conversion">
<h1>Correct conversion</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">length</span>(stuatt$race_ethnicity[<span class="kw">is.na</span>(stuatt$race_ethnicity)])</code></pre>
<pre><code>[1] 1129</code></pre>
<pre class="sourceCode r"><code class="sourceCode r">stuatt$race_ethnicity <- <span class="kw">as.character</span>(stuatt$race_ethnicity)
stuatt$race_ethnicity[<span class="kw">is.na</span>(stuatt$race_ethnicity)] <- <span class="st">"AI"</span>
stuatt$race_ethnicity <- <span class="kw">factor</span>(stuatt$race_ethnicity)
<span class="kw">summary</span>(stuatt$race_ethnicity)</code></pre>
<pre><code> A AI B H M/O W
7303 1129 25321 30444 2809 20528 </code></pre>
<ul class="incremental">
<li>Factors are pesky, even though they are useful and keep us from having to remember numeric representations of our data</li>
<li>In fact, if you read the toolkit, this is a big drawback of <em>Stata</em> because you must constantly refer back to the numbers to remember what number corresponds to "hispanic"</li>
</ul>
</div>
<div class="section slide level1" id="inconsistency-within-years">
<h1>Inconsistency Within Years</h1>
<ul class="incremental">
<li>Let's consider student 3 in our dataset</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r">stuatt[<span class="dv">7</span>:<span class="dv">9</span>, <span class="kw">c</span>(<span class="st">"sid"</span>, <span class="st">"school_year"</span>, <span class="st">"race_ethnicity"</span>)]</code></pre>
<pre><code> sid school_year race_ethnicity
7 3 2006 H
8 3 2006 B
9 3 2007 B</code></pre>
<ul class="incremental">
<li>How is this different from our prior problem?</li>
<li>Since student 3 was recorded twice in the same year and given a different <em>race/ethnicity</em> we now have to figure out some rules for assigning a consistent value</li>
</ul>
</div>
<div class="section slide level1" id="business-rule">
<h1>Business Rule</h1>
<ul class="incremental">
<li>Again, we are implementing a business rule which means we are making some arbitrary decisions about the data</li>
<li>In this case, if a student is <em>hispanic</em> we will code both values as hispanic</li>
<li>If the student is <em>not hispanic</em> in either observation, we will code the student as _multiple</li>
</ul>
</div>
<div class="section slide level1" id="lets-calculate-the-number-of-values-per-year">
<h1>Let's calculate the number of values per year</h1>
<pre class="sourceCode r"><code class="sourceCode r">nvals <- <span class="kw">ddply</span>(stuatt, .(sid, school_year), summarize, <span class="dt">nvals_race =</span> <span class="kw">length</span>(<span class="kw">unique</span>(race_ethnicity)),
<span class="dt">tmphispanic =</span> <span class="kw">length</span>(<span class="kw">which</span>(race_ethnicity == <span class="st">"H"</span>)))
tempdf <- <span class="kw">merge</span>(stuatt, nvals)
<span class="co"># Clean up</span>
<span class="kw">rm</span>(nvals)
<span class="co"># Recode race_ethnicity</span>
tempdf$race2 <- tempdf$race_ethnicity
tempdf$race2[tempdf$nvals_race > <span class="dv">1</span> & tempdf$tmphispanic == <span class="dv">1</span>] <- <span class="st">"H"</span>
tempdf$race2[tempdf$nvals_race > <span class="dv">1</span> & tempdf$tmphispanic != <span class="dv">1</span>] <- <span class="st">"M/O"</span>
tempdf$race_ethnicity <- tempdf$race2
<span class="co"># Clean up by removing old variables</span>
tempdf$race2 <- <span class="ot">NULL</span>
tempdf$nvals_race <- <span class="ot">NULL</span>
tempdf$tmphispanic <- <span class="ot">NULL</span>
<span class="co"># Resort our result</span>
tempdf <- tempdf[<span class="kw">order</span>(tempdf$sid, tempdf$school_year), ]</code></pre>
</div>
<div class="section slide level1" id="compare-them">
<h1>Compare them</h1>
<pre><code> sid school_year race_ethnicity
56201 3 2006 H
56202 3 2006 H
81064 8552 2005 W
81065 8552 2006 M/O
81066 8552 2006 M/O
6162 11382 2005 H
6163 11382 2005 H
6164 11382 2006 H</code></pre>
<pre><code> sid school_year race_ethnicity
7 3 2006 H
8 3 2006 B
34290 8552 2005 W
34291 8552 2006 A
34292 8552 2006 W
45674 11382 2005 H
45675 11382 2005 M/O
45676 11382 2006 H</code></pre>
</div>
<div class="section slide level1" id="ok">
<h1>OK</h1>
<ul class="incremental">
<li>Merge it back together</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r">stuatt <- tempdf
<span class="kw">rm</span>(tempdf)</code></pre>
</div>
<div class="section slide level1" id="break-in-case-of-emergency">
<h1>Break in Case of Emergency</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Stupid hack workaround of ddply bug when running too many of these</span>
<span class="co"># sequentially</span>
ddply_race <- function(x, y, z) {
NewColName <- <span class="st">"race_ethnicity"</span>
z <- <span class="kw">ddply</span>(x, .(y, z), <span class="dt">.fun =</span> function(xx, col) {
<span class="kw">c</span>(<span class="dt">nvals_race =</span> <span class="kw">length</span>(<span class="kw">unique</span>(xx[, col])))
}, NewColName)
z$sid <- z$y
z$school_year <- z$z
z$y <- <span class="ot">NULL</span>
z$z <- <span class="ot">NULL</span>
<span class="kw">return</span>(z)
}
nvals <- <span class="kw">ddply_race</span>(stuatt, stuatt$sid, stuatt$school_year)
tempdf <- <span class="kw">merge</span>(stuatt, nvals)
tempdf$temp_ishispanic <- <span class="ot">NA</span>
tempdf$temp_ishispanic[tempdf$race_ethnicity == <span class="st">"H"</span> & tempdf$nvals_race > <span class="dv">1</span>] <- <span class="dv">1</span></code></pre>
</div>
<div class="section slide level1" id="inconsistency-across-years">
<h1>Inconsistency across years</h1>
<ul class="incremental">
<li>So we are in the clear right?</li>
<li>No, our data still has messiness across years:</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">head</span>(stuatt[, <span class="kw">c</span>(<span class="st">"sid"</span>, <span class="st">"school_year"</span>, <span class="st">"race_ethnicity"</span>)])</code></pre>
<pre><code> sid school_year race_ethnicity
1 1 2004 B
2 1 2005 H
3 1 2006 H
4 1 2007 H
44618 2 2006 W
44619 2 2007 B</code></pre>
<ul class="incremental">
<li>Student 1 and 2 are both listed as black and hispanic at alternate times</li>
</ul>
</div>
<div class="section slide level1" id="so...">
<h1>So...</h1>
<h3 id="what-do-we-do">What do we do?</h3>
<h3 id="try-it-on-your-own">Try it on your own</h3>
<h3 id="remember-this-is-tough-stuff-so-feel-free-to-ask-for-help">Remember, this is tough stuff, so feel free to ask for help!</h3>
</div>
<div class="section slide level1" id="answer">
<h1>Answer</h1>
<pre class="sourceCode r"><code class="sourceCode r">tempdf <- <span class="kw">ddply</span>(stuatt, .(sid), summarize, <span class="dt">var_temp =</span> <span class="kw">statamode</span>(race_ethnicity),
<span class="dt">nvals =</span> <span class="kw">length</span>(<span class="kw">unique</span>(race_ethnicity)), <span class="dt">most_recent_year =</span> <span class="kw">max</span>(school_year),
<span class="dt">most_recent_var =</span> <span class="kw">tail</span>(race_ethnicity, <span class="dv">1</span>))
tempdf$race2[tempdf$var_temp != <span class="st">"."</span>] <- tempdf$var_temp[tempdf$var_temp != <span class="st">"."</span>]
tempdf$race2[tempdf$var_temp == <span class="st">"."</span>] <- <span class="kw">paste</span>(tempdf$most_recent_var[tempdf$var_temp ==
<span class="st">"."</span>])
tempdf <- <span class="kw">merge</span>(stuatt, tempdf)
<span class="kw">head</span>(tempdf[, <span class="kw">c</span>(<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">4</span>, <span class="dv">14</span>)], <span class="dv">7</span>)</code></pre>
<pre><code> sid school_year race_ethnicity race2
1 1 2004 B H
2 1 2005 H H
3 1 2006 H H
4 1 2007 H H
5 2 2006 W B
6 2 2007 B B
7 3 2006 H H</code></pre>
<ul class="incremental">
<li>Why do we have to do a paste command?</li>
<li>What other parts of this code are important to remember?</li>
<li>Always filter on both sides</li>
<li>Always use <code>summarize</code> in the <code>ddply</code> call in this situation</li>
</ul>
</div>
<div class="section slide level1" id="a-faster-way">
<h1>A Faster Way</h1>
<ul class="incremental">
<li>The nice thing about R is we can role processes together once we understand them</li>
<li>Let's build a script to do this more efficiently</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r">task1 <- function(df, id, year, var) {
<span class="kw">require</span>(plyr)
mdf <- <span class="kw">eval</span>(<span class="kw">parse</span>(<span class="dt">text =</span> <span class="kw">paste</span>(<span class="st">"ddply("</span>, df, <span class="st">",.("</span>, id, <span class="st">"),summarize,</span><span class="ch">\n</span><span class="st">var_temp=statamode("</span>,
var, <span class="st">"),</span><span class="ch">\n</span><span class="st">nvals=length(unique("</span>, var, <span class="st">")),most_recent_year=max("</span>, year,
<span class="st">"),</span><span class="ch">\n</span><span class="st">most_recent_var=tail("</span>, var, <span class="st">",1))"</span>, <span class="dt">sep =</span> <span class="st">""</span>)))
mdf$var2[mdf$var_temp != <span class="st">"."</span>] <- mdf$var_temp[mdf$var_temp != <span class="st">"."</span>]
mdf$var2[mdf$var_temp == <span class="st">"."</span>] <- <span class="kw">as.character</span>(mdf$most_recent_var[mdf$var_temp ==
<span class="st">"."</span>])
ndf <- <span class="kw">eval</span>(<span class="kw">parse</span>(<span class="dt">text =</span> <span class="kw">paste</span>(<span class="st">"merge("</span>, df, <span class="st">",mdf)"</span>, <span class="dt">sep =</span> <span class="st">""</span>)))
<span class="kw">rm</span>(mdf)
<span class="kw">return</span>(ndf)
}
<span class="co"># Note data must be sorted</span>
tempdf <- <span class="kw">task1</span>(stuatt, stuatt$sid, stuatt$school_year, stuatt$race_ethnicity)</code></pre>
</div>
<div class="section slide level1" id="other-references">
<h1>Other References</h1>
<ul class="incremental">
<li><a href="http://www.gse.harvard.edu/~pfpie/index.php/sdp/tools">The Strategic Data Project Toolkit</a></li>
<li><a href="http://www.ats.ucla.edu/stat/r/faq/default.htm">UCLA ATS: R FAQ on Data Management</a></li>
<li><a href="http://www.twotorials.com/">Video Tutorials</a></li>
<li><a href="http://www.jstatsoft.org/v40/i01">The Split-Apply-Combine Strategy for Data Analysis by Hadley Wickham</a> available in the Journal of Statistical Software vol 40, Issue 1, April 2011</li>
</ul>
</div>
<div class="section slide level1" id="session-info">
<h1>Session Info</h1>
<p>It is good to include the session info, e.g. this document is produced with <strong>knitr</strong> version 0.9.6. Here is my session info:</p>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">print</span>(<span class="kw">sessionInfo</span>(), <span class="dt">locale =</span> <span class="ot">FALSE</span>)</code></pre>
<pre><code>R version 2.15.2 (2012-10-26)
Platform: x86_64-w64-mingw32/x64 (64-bit)
attached base packages:
[1] grid stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] sandwich_2.2-9 quantreg_4.94 SparseM_0.96 gridExtra_0.9.1
[5] mgcv_1.7-22 eeptools_0.1 mapproj_1.2-0 maps_2.3-0
[9] proto_0.3-10 plyr_1.8 stringr_0.6.2 ggplot2_0.9.3
[13] lmtest_0.9-30 zoo_1.7-9 knitr_0.9.6
loaded via a namespace (and not attached):
[1] codetools_0.2-8 colorspace_1.2-0 dichromat_1.2-4
[4] digest_0.6.0 evaluate_0.4.3 formatR_0.7
[7] gtable_0.1.2 labeling_0.1 lattice_0.20-10
[10] MASS_7.3-22 Matrix_1.0-10 munsell_0.4
[13] nlme_3.1-106 RColorBrewer_1.0-5 reshape2_1.2.2
[16] scales_0.2.3 tools_2.15.2 </code></pre>
</div>
<div class="section slide level1" id="attribution-and-license">
<h1>Attribution and License</h1>
<p xmlns:dct="http://purl.org/dc/terms/">
<a rel="license" href="http://creativecommons.org/publicdomain/mark/1.0/"> <img src="data:image/png;base64,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" style="border-style: none;" alt="Public Domain Mark" /> </a> <br /> This work (<span property="dct:title">R Tutorial for Education</span>, by <a href="www.jaredknowles.com" rel="dct:creator"><span property="dct:title">Jared E. Knowles</span></a>), in service of the <a href="http://www.dpi.wi.gov" rel="dct:publisher"><span property="dct:title">Wisconsin Department of Public Instruction</span></a>, is free of known copyright restrictions.
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