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A latent trait model for response times on tests employing the proportional hazards model
Author(s) -
Ranger Jochen,
Ortner Tuulia
Publication year - 2012
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.2011.02032.x
Subject(s) - estimator , statistics , latent variable model , proportional hazards model , mathematics , hazard , econometrics , variance (accounting) , latent variable , function (biology) , trait , computer science , chemistry , accounting , organic chemistry , evolutionary biology , business , biology , programming language
For computer‐administered tests, response times can be recorded conjointly with the corresponding responses. This broadens the scope of potential modelling approaches because response times can be analysed in addition to analysing the responses themselves. For this purpose, we present a new latent trait model for response times on tests. This model is based on the Cox proportional hazards model. According to this model, latent variables alter a baseline hazard function. Two different approaches to item parameter estimation are described: the first approach uses a variant of the Cox model for discrete time, whereas the second approach is based on a profile likelihood function. Properties of each estimator will be compared in a simulation study. Compared to the estimator for discrete time, the profile likelihood estimator is more efficient, that is, has smaller variance. Additionally, we show how the fit of the model can be evaluated and how the latent traits can be estimated. Finally, the applicability of the model to an empirical data set is demonstrated.