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<a name="Model-Comparison-1"></a>
<h3 class="section">4.15 Model Comparison</h3>

<dl>
<dt><a name="index-model_005fcomparison"></a>Command: <strong>model_comparison</strong> <em><var>FILENAME</var>[(<var>DOUBLE</var>)]&hellip;;</em></dt>
<dt><a name="index-model_005fcomparison-1"></a>Command: <strong>model_comparison</strong> <em>(marginal_density = laplace | modifiedharmonicmean) <var>FILENAME</var>[(<var>DOUBLE</var>)]&hellip;;</em></dt>
<dd><a name="model_005fcomparison"></a><p><em>Description</em>
</p>
<p>This command computes odds ratios and estimate a posterior density over a
collection of models (see <i>e.g.</i> <cite>Koop (2003), Ch. 1</cite>). The priors over
models can be specified as the <var>DOUBLE</var> values, otherwise a uniform prior
over all models is assumed.  In contrast to frequentist econometrics, the
models to be compared do not need to be nested.  However, as the computation of
posterior odds ratios is a Bayesian technique, the comparison of models
estimated with maximum likelihood is not supported.
</p>
<p>It is important to keep in mind that model comparison of this type is only
valid with proper priors.  If the prior does not integrate to one for all
compared models, the comparison is not valid. This may be the case if part of
the prior mass is implicitly truncated because Blanchard and Kahn conditions
(instability or indeterminacy of the model) are not fulfilled, or because for
some regions of the parameters space the deterministic steady state is
undefined (or Dynare is unable to find it). The compared marginal densities
should be renormalized by the effective prior mass, but this not done by
Dynare: it is the user&rsquo;s responsibility to make sure that model comparison is
based on proper priors. Note that, for obvious reasons, this is not an issue if
the compared marginal densities are based on Laplace approximations.
</p>
<p><em>Options</em>
</p>
<dl compact="compact">
<dt><code>marginal_density = <var>ESTIMATOR</var></code></dt>
<dd><p>Specifies the estimator for computing the marginal data density. <var>ESTIMATOR</var> can 
take one of the following two values:
<code>laplace</code> for the Laplace estimator or <code>modifiedharmonicmean</code> for the 
<cite>Geweke (1999)</cite> Modified Harmonic Mean estimator. Default value: <code>laplace</code>
</p></dd>
</dl>

<p><em>Output</em>
</p>
<p>The results are stored in <code>oo_.Model_Comparison</code>, which is described below.
</p>
<p><em>Example</em>
</p>
<div class="example">
<pre class="example">model_comparison my_model(0.7) alt_model(0.3);
</pre></div>
<p>This example attributes a 70% prior over <code>my_model</code> and 30% prior
over <code>alt_model</code>.
</p>
</dd></dl>

<dl>
<dt><a name="index-oo_005f_002eModel_005fComparison"></a>MATLAB/Octave variable: <strong>oo_.Model_Comparison</strong></dt>
<dd><p>Variable set by the <code>model_comparison</code> command. Fields are of the form:
</p><div class="example">
<pre class="example"><code>oo_.Model_Comparison.<var>FILENAME</var>.<var>VARIABLE_NAME</var></code>
</pre></div>
<p>where <var>FILENAME</var> is the file name of the model and <var>VARIABLE_NAME</var> is one of the following:
</p>
<dl compact="compact">
<dt><code>Prior</code></dt>
<dd><p>(Normalized) prior density over the model
</p>
</dd>
<dt><code>Log_Marginal_Density</code></dt>
<dd><p>Logarithm of the marginal data density
</p>
</dd>
<dt><code>Bayes_Ratio</code></dt>
<dd><p>Ratio of the marginal data density of the model relative to the one of the first declared model
</p>
</dd>
<dt><code>Posterior_Model_Probability</code></dt>
<dd><p>Posterior probability of the respective model
</p>
</dd>
</dl>

</dd></dl>

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