Controlling the Speededness of Assembled Test Forms: A Generalization to the Three-Parameter Lognormal Response Time Model

Abstract

When designing or modifying a test, an important challenge is controlling its speededness. To achieve this, van der Linden (2011a, 2011b) proposed using a lognormal response time model, more specifically the two-parameter lognormal model, and automated test assembly (ATA) via mixed integer linear programming. However, this approach has a severe limitation, in that the two-parameter lognormal model lacks a slope parameter. This means that the model assumes that all items are equally speed sensitive. From a conceptual perspective, this assumption seems very restrictive. Furthermore, various other empirical studies and new data analyses performed by us show that this assumption almost never holds in practice. To overcome this shortcoming, we bring together the already frequently used three-parameter lognormal model for response times, which contains a slope parameter, and the ATA approach for controlling speededness by van der Linden. Using multiple empirically based illustrations, the proposed extension is illustrated, including complete and documented R code. Both the original van der Linden approach and our newly proposed approach are available to practitioners in the freely available R package eatATA.