Asymmetry in fixed-precision M-CAT: Multidimensional selection versus marginal stopping

Standard implementations of a Multidimensional Computerized Adaptive Testing (M-CAT) algorithm have item selection rules that are searching for items that optimize the Fisher information volume. A variable-length M-CAT would usually include a stopping rule requiring all dimensions being measured with a fixed minimum precision. In contrast to the inherently multidimensional selection rule, this stopping rule is defined at the marginal levels of the latent traits distribution: standard error smaller than a pre-determined threshold value for each dimension. This asymmetry between selection rule and stopping rule leads to side-effects that might not always be anticipated at first glance. We will first revisit and discuss the issue from a distribution and practical perspective, subsequently propose some work-arounds in the form of alternative selection rules, and elaborate on their effectivity to tackle the issue in practice.