Abstract
With the widespread use of computerized tests in educational measurement and cognitive psychology, registration of response times has become feasible in many applications. Considering these response times helps provide a more complete picture of the performance and characteristics of persons beyond what is available based on response accuracy alone. Statistical models such as the hierarchical model (van der Linden, 2007) have been proposed that jointly model response time and accuracy. However, these models make restrictive assumptions about the response processes (RPs) that may not be realistic in practice, such as the assumption that the association between response time and accuracy is fully explained by taking speed and ability into account (conditional independence). Assuming conditional independence forces one to ignore that many relevant individual differences may play a role in the RPs beyond overall speed and ability. In this paper, we critically consider the assumption of conditional independence and the important ways in which it may be violated in practice from a substantive perspective. We consider both conditional dependences that may arise when all persons attempt to solve the items in similar ways (homogeneous RPs) and those that may be due to persons differing in fundamental ways in how they deal with the items (heterogeneous processes). The paper provides an overview of what we can learn from observed conditional dependences. We argue that explaining and modeling these differences in the RPs is crucial to increase both the validity of measurement and our understanding of the relevant RPs.
Highlights
Using the statistical tools of for example item response theory (IRT; see e.g. Hambleton and Swaminathan, 1985; van der Linden and Hambleton, 1997), responses to items from cognitive and educational tests are used to make inferences about the underlying abilities
An important indicator of those possible differences in response processes (RPs) is response time (RT), which due to the increasing popularity of computerized testing has become available in many applications of educational and cognitive testing
Within psychometrics effort has been devoted to developing suitable joint models for RT and RA to incorporate this additional source of information into the traditional measurement procedures (e.g., Thissen, 1983; van der Linden, 2007; Molenaar et al, 2015a,b)
Summary
Using the statistical tools of for example item response theory (IRT; see e.g. Hambleton and Swaminathan, 1985; van der Linden and Hambleton, 1997), responses to items from cognitive and educational tests are used to make inferences about the underlying abilities. An important indicator of those possible differences in response processes (RPs) is response time (RT), which due to the increasing popularity of computerized testing has become available in many applications of educational and cognitive testing Considering this additional information provides a more complete picture of the RPs. Within psychometrics effort has been devoted to developing suitable joint models for RT and RA to incorporate this additional source of information into the traditional measurement procedures (e.g., Thissen, 1983; van der Linden, 2007; Molenaar et al, 2015a,b). We take a careful look at the substantive assumptions about the RPs that are made by common joint models for RA and RT, and explore the ways in which these assumptions may be violated in practice These assumptions are the following: (1) there is no systematic within-person variation of speed and ability across items; (2) item characteristics are constant across persons; (3) responses come from the same process. The paper concludes with a discussion on what steps one could take to distinguish the different possible phenomena presented in this paper in practice
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