Biased (conditional) parameter estimation of a Rasch model calibrated item pool administered according to a branched testing design

With reference to Glas (1988), this paper deals with the problem of biased conditional maximum likelihood (CML) Rasch model item parameter estimation when administering the items of a test according to any branched testing design. Specifically, the design of the widely used intelligence test-battery AID (Adaptive Intelligence Diagnosticum; see the last edition by Kubinger, 2009) is focused. The paper illustrates, firstly, why CML estimation leads to biased item parameter estimations given the branched testing design. Secondly, it highlights how big the bias is, and thirdly, in turn, how the biased item parameter estimations influence ability parameter estimation and therefore also the respective percentiles and T-scores of the testees. The results support the recommendation that any branched testing design should be examined in advance as to whether or not the resulting CML-based ability parameter estimations are biased in a relevant manner – before being used for psychological consultations.