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<h1>Poisson and Negative Binomial Regression</h1>
<blockquote>
<p><em>Poisson regression</em> models count variables that assumes poisson distribution. When the count variable is over dispersed, having to much variation, <em>Negative Binomial</em> regression is more suitable.</p>
</blockquote>
<h2>Introduction</h2>
<p>A count variable is something that can take only non-negative integer values. Some examples of count variables could be: 1. Number of vehicles manufactured. 1. Number of phone calls arriving at a call center. 1. Number of patents granted.</p>
<h2>How to Implement Poisson Regression?</h2>
<p>Poisson regression can be implemented in a similar manner as other <em>Generalised Linear Models (GLMs)</em>, by adjusting the family argument to <code>poisson</code>.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span> (MASS)
poissonModel <-<span class="st"> </span><span class="kw">glm</span>(countResponse ~<span class="st"> </span>pred1 +<span class="st"> </span>pred2, <span class="dt">family=</span><span class="st">"poisson"</span>, <span class="dt">data=</span>inputData) <span class="co"># poisson Model</span>
<span class="kw">summary</span> (poissonModel) <span class="co"># model summary</span>
<span class="kw">predict</span>(poissonModel, newdata, <span class="dt">type=</span><span class="st">"response"</span>) <span class="co"># predict on new data </span></code></pre></div>
<h2>How to Implement Negative Binomial Regression?</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span> (MASS)
negBinomModel <-<span class="st"> </span><span class="kw">glm.nb</span>(countResponse ~<span class="st"> </span>pred1 +<span class="st"> </span>pred2, <span class="dt">data =</span> inputData)<span class="er">)</span> <span class="co"># negative Binomial model</span>
<span class="kw">summary</span> (negBinomModel) <span class="co"># Model summary</span>
<span class="kw">predict</span> (negBinomModel, newdata, <span class="dt">type=</span><span class="st">"response"</span>) <span class="co"># predict on new data </span></code></pre></div>
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