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<h3 class="section">25.5 Models</h3>
<!-- ./statistics/models/logistic_regression.m -->
<p><a name="doc_002dlogistic_005fregression"></a>
<div class="defun">
— Function File: [<var>theta</var>, <var>beta</var>, <var>dev</var>, <var>dl</var>, <var>d2l</var>, <var>p</var>] = <b>logistic_regression</b> (<var>y, x, print, theta, beta</var>)<var><a name="index-logistic_005fregression-1890"></a></var><br>
<blockquote><p>Perform ordinal logistic regression.
<p>Suppose <var>y</var> takes values in <var>k</var> ordered categories, and let
<code>gamma_i (</code><var>x</var><code>)</code> be the cumulative probability that <var>y</var>
falls in one of the first <var>i</var> categories given the covariate
<var>x</var>. Then
<pre class="example"> [theta, beta] = logistic_regression (y, x)
</pre>
<p class="noindent">fits the model
<pre class="example"> logit (gamma_i (x)) = theta_i - beta' * x, i = 1 ... k-1
</pre>
<p>The number of ordinal categories, <var>k</var>, is taken to be the number
of distinct values of <code>round (</code><var>y</var><code>)</code>. If <var>k</var> equals 2,
<var>y</var> is binary and the model is ordinary logistic regression. The
matrix <var>x</var> is assumed to have full column rank.
<p>Given <var>y</var> only, <code>theta = logistic_regression (y)</code>
fits the model with baseline logit odds only.
<p>The full form is
<pre class="example"> [theta, beta, dev, dl, d2l, gamma]
= logistic_regression (y, x, print, theta, beta)
</pre>
<p class="noindent">in which all output arguments and all input arguments except <var>y</var>
are optional.
<p>Setting <var>print</var> to 1 requests summary information about the fitted
model to be displayed. Setting <var>print</var> to 2 requests information
about convergence at each iteration. Other values request no
information to be displayed. The input arguments <var>theta</var> and
<var>beta</var> give initial estimates for <var>theta</var> and <var>beta</var>.
<p>The returned value <var>dev</var> holds minus twice the log-likelihood.
<p>The returned values <var>dl</var> and <var>d2l</var> are the vector of first
and the matrix of second derivatives of the log-likelihood with
respect to <var>theta</var> and <var>beta</var>.
<p><var>p</var> holds estimates for the conditional distribution of <var>y</var>
given <var>x</var>.
</p></blockquote></div>
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