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    <h1>Categorical regression with softmax link density (univariate, discrete, bounded space)</h1>
    <small class="dont-index">Source: <a href='https://github.com/luisdamiano/BayesHMM//blob/master/R/densityRegCategoricalSoftmax.R'><code>R/densityRegCategoricalSoftmax.R</code></a></small>
    <div class="hidden name"><code>RegCategoricalSoftmax.Rd</code></div>
    </div>

    <div class="ref-description">
    
    <p>It can be used to specify either a
prior distribution for a model parameter or a likelihood function for an
observation model.</p>
    
    </div>

    <pre class="usage"><span class='fu'>RegCategoricalSoftmax</span>(<span class='kw'>xBeta</span> <span class='kw'>=</span> <span class='kw'>NULL</span>, <span class='kw'>M</span> <span class='kw'>=</span> <span class='kw'>NULL</span>, <span class='kw'>N</span> <span class='kw'>=</span> <span class='kw'>NULL</span>,
  <span class='kw'>ordered</span> <span class='kw'>=</span> <span class='kw'>NULL</span>, <span class='kw'>equal</span> <span class='kw'>=</span> <span class='kw'>NULL</span>, <span class='kw'>bounds</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>NULL</span>, <span class='kw'>NULL</span>),
  <span class='kw'>trunc</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>NULL</span>, <span class='kw'>NULL</span>), <span class='kw'>k</span> <span class='kw'>=</span> <span class='kw'>NULL</span>, <span class='kw'>r</span> <span class='kw'>=</span> <span class='kw'>NULL</span>, <span class='kw'>param</span> <span class='kw'>=</span> <span class='kw'>NULL</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>xBeta</th>
      <td><p>Either a fixed value or a prior density for the parameter of the regression.</p></td>
    </tr>
    <tr>
      <th>M</th>
      <td><p>An integer with the number of covariates in the observation regression model.</p></td>
    </tr>
    <tr>
      <th>N</th>
      <td><p>An integer with the number of trials (fixed quantity).</p></td>
    </tr>
    <tr>
      <th>ordered</th>
      <td><p>(optional) A logical setting an increasing ordering constraint on any univariate parameter and any unconstrained parameter vector. Ordered simplices (e.g. <code><a href='Categorical.html'>Categorical</a></code>, <code><a href='Multinomial.html'>Multinomial</a></code>, <code><a href='Dirichlet.html'>Dirichlet</a></code>) are currently not implemented. Most useful for location parameters to break symmetries and fix label switching as shown in Betancourt (2017). It defaults to unordered parameters.</p></td>
    </tr>
    <tr>
      <th>equal</th>
      <td><p>(optional) A logical setting whether the parameter takes the same value in every hidden state, i.e. the parameter is shared across states. It defaults to unequal parameters.</p></td>
    </tr>
    <tr>
      <th>bounds</th>
      <td><p>(optional) A list with two elements specifying the lower and upper bound for the parameter space. Use either a fixed value for a finite bound or NULL for no bounds. It defaults to an unbounded parameter space.</p></td>
    </tr>
    <tr>
      <th>trunc</th>
      <td><p>(optional) A list with two elements specifying the lower and upper bound for the domain of the density function. Use either a fixed value for a finite bound or NULL for no truncation. It defaults to an unbounded domain.</p></td>
    </tr>
    <tr>
      <th>k</th>
      <td><p>(optional) The number of the hidden state for which this density should be used. This argument is mostly for internal use: you should not use it unless you are acquainted with the internals of this software.</p></td>
    </tr>
    <tr>
      <th>r</th>
      <td><p>(optional) The dimension of the observation vector dimension for which this density should be used. This argument is mostly for internal use: you should not use it unless you are acquainted with the internals of this software.</p></td>
    </tr>
    <tr>
      <th>param</th>
      <td><p>(optional) The name of the parameter. This argument is mostly for internal use: you should not use it unless you are acquainted with the internals of this software.</p></td>
    </tr>
    </table>
    
    <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>

    <p>A <code><a href='Density.html'>Density</a></code> object.</p>
    
    <h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>

    <p>Betancourt, Michael (2017) Identifying Bayesian Mixture Models <em>Stan Case Studies</em> <b>Volume 4</b>. <a href='https://mc-stan.org/users/documentation/case-studies/identifying_mixture_models.html'>Link</a>.</p>
    
    <h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>

    <div class='dont-index'><p>Other Density: <code><a href='Bernoulli.html'>Bernoulli</a></code>, <code><a href='Beta.html'>Beta</a></code>,
  <code><a href='Binomial.html'>Binomial</a></code>, <code><a href='Categorical.html'>Categorical</a></code>,
  <code><a href='Cauchy.html'>Cauchy</a></code>, <code><a href='CholeskyLKJCor.html'>CholeskyLKJCor</a></code>,
  <code><a href='Density.html'>Density</a></code>, <code><a href='Dirichlet.html'>Dirichlet</a></code>,
  <code><a href='Exponential.html'>Exponential</a></code>, <code><a href='GammaDensity.html'>GammaDensity</a></code>,
  <code><a href='Gaussian.html'>Gaussian</a></code>, <code><a href='ImproperUniform.html'>ImproperUniform</a></code>,
  <code><a href='InitialFixed.html'>InitialFixed</a></code>, <code><a href='InitialSoftmax.html'>InitialSoftmax</a></code>,
  <code><a href='InverseWishart.html'>InverseWishart</a></code>,
  <code><a href='MVGaussianCholeskyCor.html'>MVGaussianCholeskyCor</a></code>,
  <code><a href='MVGaussian.html'>MVGaussian</a></code>, <code><a href='MVStudent.html'>MVStudent</a></code>,
  <code><a href='Multinomial.html'>Multinomial</a></code>,
  <code><a href='NegativeBinomialLocation.html'>NegativeBinomialLocation</a></code>,
  <code><a href='NegativeBinomial.html'>NegativeBinomial</a></code>, <code><a href='Poisson.html'>Poisson</a></code>,
  <code><a href='RegBernoulliLogit.html'>RegBernoulliLogit</a></code>,
  <code><a href='RegBinomialLogit.html'>RegBinomialLogit</a></code>,
  <code><a href='RegBinomialProbit.html'>RegBinomialProbit</a></code>,
  <code><a href='RegGaussian.html'>RegGaussian</a></code>, <code><a href='Student.html'>Student</a></code>,
  <code><a href='TransitionFixed.html'>TransitionFixed</a></code>,
  <code><a href='TransitionSoftmax.html'>TransitionSoftmax</a></code>, <code><a href='Wishart.html'>Wishart</a></code></p></div>
    

    <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
    <pre class="examples"><div class='input'><span class='fu'>RegCategoricalSoftmax</span>(
  <span class='kw'>xBeta</span> <span class='kw'>=</span> <span class='fu'><a href='Gaussian.html'>Gaussian</a></span>(<span class='fl'>0</span>, <span class='fl'>10</span>),
  <span class='kw'>M</span>     <span class='kw'>=</span> <span class='fl'>3</span>,
  <span class='kw'>N</span>     <span class='kw'>=</span> <span class='fl'>10</span>
)</div><div class='output co'>#&gt; Variable Density: RegCategoricalSoftmax (-infty, infty)
#&gt; 	Free parameters: 1 (xBeta)
#&gt; 		xBeta : 
#&gt; 						Variable Density: Gaussian (-infty, infty)
#&gt; 									Fixed parameters: 2 (mu = 0, sigma = 10)</div></pre>
  </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>

      <li><a href="#references">References</a></li>

      <li><a href="#see-also">See also</a></li>
      
      <li><a href="#examples">Examples</a></li>
    </ul>

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