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Power Law Checks from formhub top-100 users
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<p>We&#39;ll be checking whether the top 100 users of formhub follow a power law distribution, or a log-normal distribution, using guidance from <a href="http://vserver1.cscs.lsa.umich.edu/%7Ecrshalizi/weblog/857.html">a blog post by CMU stats prof. Cosma Rohilla Shaliz</a>.</p>
<p>First, load up the dataset; I have included it here in case you want to re-produce it. Each value is a number of submissions on formhub for top 100 users.</p>
<pre><code class="r">source(&quot;~/Downloads/pli-R-v0.0.3-2007-07-25/pareto.R&quot;)
source(&quot;~/Downloads/pli-R-v0.0.3-2007-07-25/lnorm.R&quot;)
source(&quot;~/Downloads/pli-R-v0.0.3-2007-07-25/power-law-test.R&quot;)
users &lt;- c(220346L, 31099L, 28568L, 16573L, 14862L, 7531L, 6510L, 6138L, 4609L,
4435L, 4279L, 3899L, 3825L, 3532L, 3069L, 2790L, 2770L, 2632L, 2622L, 2589L,
2393L, 2371L, 2343L, 2251L, 2239L, 2053L, 1981L, 1963L, 1910L, 1839L, 1680L,
1661L, 1579L, 1438L, 1416L, 1387L, 1271L, 1250L, 1238L, 1044L, 985L, 906L,
904L, 837L, 778L, 765L, 636L, 628L, 623L, 601L, 558L, 521L, 474L, 472L,
441L, 434L, 433L, 431L, 428L, 398L, 395L, 381L, 380L, 364L, 343L, 320L,
301L, 300L, 292L, 284L, 275L, 274L, 269L, 268L, 265L, 256L, 246L, 228L,
219L, 213L, 207L, 205L, 201L, 198L, 184L, 182L, 175L, 173L, 168L, 164L,
156L, 148L, 147L, 146L, 142L, 136L, 134L, 130L, 130L, 127L)
</code></pre>
<p>Then, make a quick plot&hellip; is it roughly linear?</p>
<pre><code class="r">plot.eucdf.loglog(users, xlab = &quot;Submissions&quot;, ylab = &quot;Cumulative probability&quot;)
</code></pre>
<p><img 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" alt="plot of chunk unnamed-chunk-2"/> </p>
<p>Close enough. Lets throw the pareto and lognormal tests at the dataset, and plot the predicted fit on top of the ecdf.</p>
<pre><code class="r">users.pareto &lt;- pareto.fit(users, threshold = 3)
users.lnorm &lt;- lnorm.fit(users)
plot.eucdf.loglog(users, xlab = &quot;Submissions&quot;, ylab = &quot;Cumulative probability&quot;)
curve(ppareto(x, exponent = users.pareto$exponent, threshold = 3, lower.tail = FALSE),
add = TRUE, col = &quot;red&quot;)
curve(plnorm(x, meanlog = users.lnorm$meanlog, sdlog = users.lnorm$sdlog, lower.tail = FALSE)/plnorm(3,
meanlog = users.lnorm$meanlog, sdlog = users.lnorm$sdlog, lower.tail = FALSE),
add = TRUE, col = &quot;blue&quot;)
</code></pre>
<p><img 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" alt="plot of chunk unnamed-chunk-3"/> </p>
<p>Looks like a &ldquo;text-book&rdquo; log-normal fit to me. One more observation: Looks like five of the top users are &ldquo;outliers&rdquo; in this data, which makes sense if you know the users. </p>
<p>For a little more insight, I print below a typical &ldquo;scenario&rdquo; according to the model: the # of submissions from 100 typical (&ldquo;random&rdquo;) top-100 formhub users would look like the graph below:</p>
<pre><code class="r">qplot(rlnorm(100, meanlog = users.lnorm$meanlog, users.lnorm$sdlog)) + xlab(paste(&quot;# of submissions for modeled top-100 formhub users.\nLognormal with meanlog &quot;,
users.lnorm$meanlog, &quot; meansd &quot;, users.lnorm$sdlog))
</code></pre>
<p><img 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" alt="plot of chunk unnamed-chunk-4"/> </p>
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Raw
index.Rmd
We'll be checking whether the top 100 users of formhub follow a power law distribution, or a log-normal distribution, using guidance from [a blog post by CMU stats prof. Cosma Rohilla Shaliz](http://vserver1.cscs.lsa.umich.edu/~crshalizi/weblog/857.html).
First, load up the dataset; I have included it here in case you want to re-produce it. Each value is a number of submissions on formhub for top 100 users.
```{r}
source("~/Downloads/pli-R-v0.0.3-2007-07-25/pareto.R")
source("~/Downloads/pli-R-v0.0.3-2007-07-25/lnorm.R")
source("~/Downloads/pli-R-v0.0.3-2007-07-25/power-law-test.R")
users <- c(220346L, 31099L, 28568L, 16573L, 14862L, 7531L, 6510L, 6138L,
4609L, 4435L, 4279L, 3899L, 3825L, 3532L, 3069L, 2790L, 2770L,
2632L, 2622L, 2589L, 2393L, 2371L, 2343L, 2251L, 2239L, 2053L,
1981L, 1963L, 1910L, 1839L, 1680L, 1661L, 1579L, 1438L, 1416L,
1387L, 1271L, 1250L, 1238L, 1044L, 985L, 906L, 904L, 837L, 778L,
765L, 636L, 628L, 623L, 601L, 558L, 521L, 474L, 472L, 441L, 434L,
433L, 431L, 428L, 398L, 395L, 381L, 380L, 364L, 343L, 320L, 301L,
300L, 292L, 284L, 275L, 274L, 269L, 268L, 265L, 256L, 246L, 228L,
219L, 213L, 207L, 205L, 201L, 198L, 184L, 182L, 175L, 173L, 168L,
164L, 156L, 148L, 147L, 146L, 142L, 136L, 134L, 130L, 130L, 127L
)
```
Then, make a quick plot... is it roughly linear?
```{r}
plot.eucdf.loglog(users,xlab="Submissions", ylab="Cumulative probability")
```
Close enough. Lets throw the pareto and lognormal tests at the dataset, and plot the predicted fit on top of the ecdf.
```{r warning=FALSE, message=FALSE}
users.pareto <- pareto.fit(users,threshold=3)
users.lnorm <- lnorm.fit(users)
plot.eucdf.loglog(users,xlab="Submissions", ylab="Cumulative probability")
curve(ppareto(x,exponent=users.pareto$exponent,threshold=3,lower.tail=FALSE),
add=TRUE,col="red")
curve(plnorm(x,meanlog=users.lnorm$meanlog,sdlog=users.lnorm$sdlog,
lower.tail=FALSE)/plnorm(3,meanlog=users.lnorm$meanlog,
sdlog=users.lnorm$sdlog,lower.tail=FALSE),add=TRUE,col="blue")
```
Looks like a "text-book" log-normal fit to me. One more observation: Looks like five of the top users are "outliers" in this data, which makes sense if you know the users.
For a little more insight, I print below a typical "scenario" according to the model: the # of submissions from 100 typical ("random") top-100 formhub users would look like the graph below:
```{r message=FALSE}
qplot(rlnorm(100, meanlog=users.lnorm$meanlog, users.lnorm$sdlog)) + xlab(paste("# of submissions for modeled top-100 formhub users.\nLognormal with meanlog ", users.lnorm$meanlog, " meansd ", users.lnorm$sdlog))
```
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