A latent trait model for response times on tests employing the proportional hazards model

Ranger, Jochen; Ortner, Tuulia M.

doi:10.1111/j.2044-8317.2011.02032.x

Cited by 21 publications

(36 citation statements)

References 42 publications

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“…The estimates resulting from the new rank correlation-based approach were compared with estimates resulting from a discrete version of the proportional hazards model fitted with standard marginal maximum likelihood estimation (Douglas et al, 1999) and with estimates resulting from a marginal profile likelihood approach (Ranger & Ortner, 2012). Altogether, the performance of the rank-based estimator was good.…”

Section: Discussionmentioning

confidence: 99%

“…An advanced approach to the estimation of the proportional hazards model with random effects is based on marginal maximum likelihood estimation and was first suggested by Klein (1992) and Parner (1997). Ranger and Ortner (2012) adapted this estimator to test data with normally distributed latent traits. The approach uses a profile likelihood function where the unknown baseline hazard function of the response times is profiled out.…”

Section: Please Scroll Down For Articlementioning

confidence: 99%

“…Response times of 10 items from the Egotism scale of the questionnaire were used. These response times have already been analyzed by Ranger and Ortner (2012), who fitted a proportional hazards model by maximizing the marginal profile likelihood. Their analysis revealed good fit of the proportional hazards model.…”

Section: Empirical Data Applicationmentioning

confidence: 99%

“…This generated four approximately equiprobable response time categories. And third, the marginal profile likelihood approach of Ranger and Ortner (2012) was used. In all estimators, work pace was assumed to be standard normally distributed.…”

Section: Simulation Studymentioning

confidence: 99%

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Response Time Modeling Based on the Proportional Hazards Model

Ranger

Ortner

2013

Multivariate Behavioral Research

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Response time data are regularly analyzed in psychology. When several response times are assessed per participant, it is common practice to use latent trait models in order to account for the dependency of the response times from the same participant. One such model is the proportional hazards model with random effects. Despite its popularity in survival analysis, this model is rarely used in psychology because of the difficulty of model estimation when latent variables are present. In this article, a new estimation method is proposed. This method is based on the rank correlation matrix containing Kendall's Tau coefficients and unweighted least squares estimation ( Kendall, 1938 ). Compared with marginal maximum likelihood estimation, the new estimation approach is simple, not computationally intensive, and almost as efficient. Additionally, the approach allows the implementation of a test for model fit. Feasibility of the estimation method and validity of the fit test is demonstrated with a simulation study. An application of the model to a real data set is provided.

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Section: Discussionmentioning

confidence: 99%

Section: Please Scroll Down For Articlementioning

confidence: 99%

Section: Empirical Data Applicationmentioning

confidence: 99%

Section: Simulation Studymentioning

confidence: 99%

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Response Time Modeling Based on the Proportional Hazards Model

Ranger

Ortner

2013

Multivariate Behavioral Research

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“…Assuming such proportionality may not be realistic in all circumstances as item response distributions can differ considerably even in similar tests (Ranger & Kuhn, ). Other recent proposals in the semi‐parametric PH framework (Ranger & Ortner, ; Wang et al ., ), specify the hazard as

h_{ij} (t) = h_{0 j} (t) \exp (β_{j} v_{1 i}),

where, similar to model (2),

v_{1 i}

can be viewed as a speed parameter. While the latter model allows for a different functional form for the hazard for each item and a discrimination parameter (

β_{j}

), the stratified baseline hazard would not allow the effect of an item‐specific characteristic

x_{ij}

(e.g., neutral vs. pleasant pictures) on the response time to be quantified.…”

Section: Bayesian Estimation In a Semi‐parametric Proportional Hazardmentioning

confidence: 99%

Semi‐parametric proportional hazards models with crossed random effects for psychometric response times

Loeys

Legrand²,

Schettino

2013

Brit J Math & Statis

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The semi-parametric proportional hazards model with crossed random effects shares two important characteristics: it avoids explicit specification of the response time distribution by using semi-parametric models, and heterogeneity that is due to subjects and items is captured. The proposed model has a proportionality parameter for the speed of each test taker, for the time intensity of each item, and for subject or item characteristics of interest. It is shown how all these parameters can be estimated by Markov Chain Monte Carlo methods (Gibbs sampling). The performance of the estimation procedure is assessed with simulations and the model is further illustrated with the analysis of response times from a visual recognition task.

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A latent space accumulator model for response time: Applications to cognitive assessment data

Jin,

Yun,

Kim

et al. 2023

Stat

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Response time has attracted increased interest in educational and psychological assessment for, for example, measuring test takers' processing speed, improving the measurement accuracy of ability and understanding aberrant response behaviour. Most models for response time analysis are based on a parametric assumption about the response time distribution. The Cox proportional hazard model has been utilized for response time analysis for the advantages of not requiring a distributional assumption of response time and enabling meaningful interpretations with respect to response processes. In this paper, we present a new version of the proportional hazard model, called a latent space accumulator model, for cognitive assessment data based on accumulators for two competing response outcomes, such as correct versus incorrect responses. The proposed model extends a previous accumulator model by capturing dependencies between respondents and test items across accumulators in the form of distances in a two‐dimensional Euclidean space. A fully Bayesian approach is developed to estimate the proposed model. The utilities of the proposed model are illustrated with two real data examples.

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A latent trait model for response times on tests employing the proportional hazards model

Cited by 21 publications

References 42 publications

Response Time Modeling Based on the Proportional Hazards Model

Response Time Modeling Based on the Proportional Hazards Model

Semi‐parametric proportional hazards models with crossed random effects for psychometric response times

A latent space accumulator model for response time: Applications to cognitive assessment data

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