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<title>Objective function — Q_theta • sail</title>
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<meta property="og:description" content="calculates likelihood function. Used to assess convergence of
fitting algorithm. This corresponds to the Q(theta) function in the paper" />
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<h1>Objective function</h1>
<div class="hidden name"><code>Q_theta.Rd</code></div>
</div>
<div class="ref-description">
<p>calculates likelihood function. Used to assess convergence of
fitting algorithm. This corresponds to the Q(theta) function in the paper</p>
</div>
<pre class="usage"><span class='fu'>Q_theta</span>(<span class='no'>R</span>, <span class='no'>nobs</span>, <span class='no'>lambda</span>, <span class='no'>alpha</span>, <span class='no'>we</span>, <span class='no'>wj</span>, <span class='no'>wje</span>, <span class='no'>betaE</span>, <span class='no'>theta_list</span>, <span class='no'>gamma</span>)</pre>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>R</th>
<td><p>residual</p></td>
</tr>
<tr>
<th>nobs</th>
<td><p>number of observations</p></td>
</tr>
<tr>
<th>lambda</th>
<td><p>a user supplied lambda sequence. Typically, by leaving this
option unspecified users can have the program compute its own lambda
sequence based on <code>nlambda</code> and <code>lambda.factor</code>. Supplying a
value of lambda overrides this. It is better to supply a decreasing
sequence of lambda values than a single (small) value, if not, the program
will sort user-defined lambda sequence in decreasing order automatically.
Default: <code>NULL</code>.</p></td>
</tr>
<tr>
<th>alpha</th>
<td><p>the mixing tuning parameter, with \(0<\alpha<1\). It controls
the penalization strength between the main effects and the interactions.
The penalty is defined as $$\lambda(1-\alpha)(w_e|\beta_e|+ \sum w_j
||\beta_j||_2) + \lambda\alpha(\sum w_{je} |\gamma_j|)$$Larger values of
<code>alpha</code> will favor selection of main effects over interactions.
Smaller values of <code>alpha</code> will allow more interactions to enter the
final model. Default: <code>0.5</code></p></td>
</tr>
<tr>
<th>we</th>
<td><p>penalty factor for exposure variable</p></td>
</tr>
<tr>
<th>wj</th>
<td><p>penalty factor for main effects</p></td>
</tr>
<tr>
<th>wje</th>
<td><p>penalty factor for interactions</p></td>
</tr>
<tr>
<th>betaE</th>
<td><p>estimate of exposure effect</p></td>
</tr>
<tr>
<th>theta_list</th>
<td><p>estimates of main effects</p></td>
</tr>
<tr>
<th>gamma</th>
<td><p>estimates of gamma parameter</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>value of the objective function</p>
</div>
<div class="col-md-3 hidden-xs hidden-sm" id="sidebar">
<h2>Contents</h2>
<ul class="nav nav-pills nav-stacked">
<li><a href="#arguments">Arguments</a></li>
<li><a href="#value">Value</a></li>
</ul>
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