il} q_{il}  \theta_{pl} - b_{il} ) $$
where \(i\), \(p\), \(l\) denote items, persons and dimensions
respectively.</p>
<p>The compensatory item response model (<code>irtmodel="comp"</code>) is defined by
$$P(X_{pi}=1 | \bold{\theta}_p )=c_i + (d_i - c_i )
invlogit( \sum_l  a_{il}  q_{il} \theta_{pl} - b_{i} ) $$
Using a design matrix <code>theta.kDES</code> the model can be made even more general
in a model which is linear in item parameters
$$P(X_{pi}=1 | \bold{\theta}_p )=c_i + (d_i - c_i )
invlogit( \sum