Population-level behavior and extensions of the MaxMI framework

Determine, under an Independent Latent Class Item Response Theory population with rapid-responding-behaviour and solution-behaviour components, whether a MaxMI-32 threshold can identify rapid-responding behaviour, whether a threshold can divide solution-behaviour test-takers into two subpopulations, how raw responses should be modelled to study MaxMI-2Q, how MaxMI-2Q behaves under a suitable raw-response model, and whether MaxMI-3Q or MaxMI-42 provide viable alternatives.

Background

The paper introduces the Maximal Mutual Information (MaxMI) framework for identifying rapid-responding behaviour (RRB) from response times and responses. MaxMI-22 uses binary response correctness and a binary discretised response-time variable; MaxMI-32 uses binary correctness and a ternary discretised response-time variable; and MaxMI-2Q uses a binary discretised response-time variable together with the raw response, which may have more than two nominal categories.

The study investigates MaxMI-22 in an Independent Latent Class Item Response Theory setting but does not analyze the population-level behavior of the other methods. The authors therefore leave unresolved whether MaxMI-32 can distinguish RRB from solution behaviour or further partition solution-behaviour respondents, how an appropriate model for nominal raw responses could be constructed for MaxMI-2Q, how MaxMI-2Q would perform under such a model, and whether additional variants such as MaxMI-3Q and MaxMI-42 are useful.

References

This line of research still has much to offer. First, the behaviour of MaxMI methods other than MaxMI-22 at the population level remains to be seen. The following questions remain unanswered: When the population is characterised by ILC-IRT with two explicit components in the distribution, could one of the MaxMI-32 thresholds be suitable for identifying RRB? Could one of the thresholds also be used to split SB test-takers into two subpopulations? In addition, how could a population of raw responses be modelled to study MaxMI-2Q? \citet{bock_1972_nrm}'s nominal response model could be useful for this purpose. If a suitable model is discovered, how would MaxMI-2Q behave? Finally, could other methods within the MaxMI framework, such as MaxMI-3Q or MaxMI-42, be viable alternatives?

— Mutual Information as a Tool for Optimal Classification: Application to Identifying Rapid-Responding Behaviour  (2609.19781 - Holopainen et al., 17 Sep 2026) in Discussion, first paragraph beginning “This line of research still has much to offer”