The item set consists of three items, \(Q = \{a, b, c\}\), and the knowledge structure is \(\mathcal{K}^{02} = \{\emptyset, \{a, b\}, Q\}\). The parameter vector is \(\theta' = (\beta_a, \beta_b, \beta_c, \pi_\emptyset, \pi_{ab})\), not allowing for guessing.
For the BLIM with knowledge structure \(\mathcal{K}^{02}\) and parameter vector \(\theta\) the parameters \(\beta_c\) and \(\pi_{ab}\) are not identifiable. Therefore, different pairs of values for these parameters predict the same response frequencies (plot on the right). The relation of \(\beta_c\) and \(\pi_{ab}\) is described by the indifference curve in the plot below.
The values for the identifiable parameters are \(\beta_a = 0.2\), \(\beta_b = 0.2\), and \(\pi_{\emptyset}= 0.4\).