A joint maximum likelihood estimation procedure for the hyperbolic cosine model for single-stimulus responses

Joint maximum likelihood estimation (JMLE) for the hyperbolic cosine model (Andrich & Luo, 1993) is extended to the situation in which the units of it ems are allowed to vary. Four issues were considered in developing this JML E procedure: (1) the indeterminacy caused by the unit parameter of each ite m, (2) a necessary constraint to eliminate this indeterminacy, (3) the init ial estimates of the unit and location parameters of the items, and (4) a p ractical correction procedure to account for inconsistency in parameter est imates. Four estimation cycles were designed to address these issues. Resul ts from two sets of simulation studies (ideal and non-ideal situations) ind icated that the algorithm yielded reasonably accurate recovery of the param eters.