“…Reference to a four‐parameter model (4PM) has appeared sporadically in the literature (Barton & Lord, 1981; Hambleton & Swaminathan, 1985; Linacre, 2004; Rupp, 2003). However, this model has rarely been used in practice and until recently (see Osgood et al , 2002; Reise & Waller, 2003; Tavares, de Andrade, & Pereira, 2004; Waller & Reise, 2009) was often dismissed as offering little practical benefit and as difficult to estimate. We address each of these issues in turn.…”