Description:
<jats:p>Diagnostic models combine multiple binary latent variables in an attempt to produce a latent structure that provides more information about test takers' performance than do unidimensional latent variable models. Recent developments in diagnostic modeling emphasize the possibility that multiple skills may interact in a conjunctive way within the item function, while individual skills still may retain separable additive effects. This extension of either the conjunctive deterministic‐input‐noisy‐and (<jats:styled-content style="fixed-case">DINA</jats:styled-content>) model to the generalized version (G‐<jats:styled-content style="fixed-case">DINA</jats:styled-content>) or the compensatory/additive general diagnostic model (<jats:styled-content style="fixed-case">GDM</jats:styled-content>) to the log‐linear cognitive diagnostic model (<jats:styled-content style="fixed-case">LCDM</jats:styled-content>) is aimed at integrating models with conjunctive skills and those that assume compensatory functioning of multiple skill variables. More recently, a result was proven mathematically that the fully conjunctive <jats:styled-content style="fixed-case">DINA</jats:styled-content> model, which combines all required skills in a single binary function, may be recast as a compensatory special case of the <jats:styled-content style="fixed-case">GDM</jats:styled-content>. This can be accomplished in more than one form such that the resulting transformed skill‐space definitions and design (Q) matrices are different from each other but mathematically equivalent to the <jats:styled-content style="fixed-case">DINA</jats:styled-content> model, producing identical model‐based response probabilities. In this report, I extend this equivalency result to the <jats:styled-content style="fixed-case">LCDM</jats:styled-content> and show that a mathematically equivalent, constrained <jats:styled-content style="fixed-case">GDM</jats:styled-content> can be defined that yields identical parameter estimates based on a transformed set of compensatory skills.</jats:p>