ArticleEducational and psychological measurement2020
Modeling Responses and Response Times in Tests With the Hierarchical Model and the Three-Parameter Lognormal Distribution.
Article in Educational and psychological measurement, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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5 citing papers in PubMed.
- Joint partial credit and time model.Behavior research methods · 2026Article
- Angry facial expressions elicit a late attentional withdrawal.Scientific reports · 2025Article
- A New Fit Assessment Framework for Common Factor Models Using Generalized Residuals.Psychometrika · 2025Article
- Comparing Likert and visual analogue scales in ecological momentary assessment.Behavior research methods · 2025Article
- Semiparametric Factor Analysis for Item-Level Response Time Data.Psychometrika · 2022Article
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3 authors.
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Abstract
The hierarchical model of van der Linden is the most popular model for responses and response times in tests. It is composed of two separate submodels-one for the responses and one for the response times-that are joined at a higher level. The submodel for the response times is based on the lognormal distribution. The lognormal distribution is a skew distribution with a support from zero to infinity. Such a support is unrealistic as the solution process demands a minimal processing time that sets a response time threshold. Ignoring this response time threshold misspecifies the model and threatens the validity of model-based inferences. In this article, the response time model of van der Linden is replaced by a model that is based on the three-parameter lognormal distribution. The three-parameter lognormal distribution extends the lognormal distribution by an additional location parameter that bounds the support away from zero. Two different approaches to model fitting are proposed and evaluated with regard to parameter recovery in a simulation study. The extended model is applied to two data sets. In both data sets, the extension improves the fit of the hierarchical model.
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