</p>
<p>The number of free parameters required to specify a <span class="math inline">\(K \times K\)</span> correlation matrix is <span class="math inline">\(\binom{K}{2}\)</span>.</p>
<p>There is more than one way to map from <span class="math inline">\(\binom{K}{2}\)</span> unconstrained parameters to a <span class="math inline">\(K \times K\)</span> correlation matrix. Stan implements the Lewandowski-Kurowicka-Joe (LKJ) transform <span class="citation">Lewandowski, Kurowicka, and Joe (<a href="#ref-Lewan