A semi‐parametric within‐subject mixture approach to the analyses of responses and response times

• Published in: British journal of mathematical & statistical psychology Vol. 71; no. 2; pp. 205 - 228
• Main Authors: Molenaar, Dylan, Bolsinova, Maria, Vermunt, Jeroen K.
• Format: Journal Article
• Language: English
• Published: England British Psychological Society 01.05.2018
• Subjects: Algorithms; Bias; Computer Simulation; Data Interpretation, Statistical; False Positive Reactions; Humans; Item response theory; mixture modelling; Models, Psychological; Models, Statistical; Parameter estimation; Psychometrics - methods; Reaction Time; Response time; response times; mixture modelling; item response theory; response times
• ISSN: 0007-1102; 2044-8317; 2044-8317
• DOI: 10.1111/bmsp.12117

In item response theory, modelling the item response times in addition to the item responses may improve the detection of possible between‐ and within‐subject differences in the process that resulted in the responses. For instance, if respondents rely on rapid guessing on some items but not on all, the joint distribution of the responses and response times will be a multivariate within‐subject mixture distribution. Suitable parametric methods to detect these within‐subject differences have been proposed. In these approaches, a distribution needs to be assumed for the within‐class response times. In this paper, it is demonstrated that these parametric within‐subject approaches may produce false positives and biased parameter estimates if the assumption concerning the response time distribution is violated. A semi‐parametric approach is proposed which resorts to categorized response times. This approach is shown to hardly produce false positives and parameter bias. In addition, the semi‐parametric approach results in approximately the same power as the parametric approach.