I've been using MPlus for IRM for psychiatric (DSM-based) measures and a query that almost always arises is how best to use screening/stem questions. Assuming I am conducting IRT of alcohol dependence criteria - these items are structurally missing in those who have never drunk alcohol - however, once we subset on them the ICC are not population-representative. The alternative is to code those who have never drunk alcohol as '0' and adjust the thresholds by including ever used alcohol as an item whose threshold is assessed but is not used in the CFA. Are their alternative approaches for adjusting the thresholds so that they are population-representative?
Thank you for the reference! We are currently approaching the model as ML under MAR - we've used an ordinal 'upstream' measure (e.g. 0=never used, 1=used x times, 2=used x+n times) and the 'downstream' dependence measure can be measured in levels 1 and 2 of the screen. How both the screen/upstream measure and the downstream measures can be jointly modeled while allowing for dependence to be structurally missing in those with screen=0. Would this be a reasonable approach?
MIRT can be done in Mplus if you don't have guessing. Both logit and probit (normal ogive) link is available in ML estimation and probit in WLSMV estimation. There is nothing special about it, just define factors as say