Modeling of Responses and Response Times with the Package cirt

In computerized testing, the test takers' responses as well as their response times on the items are recorded. The relationship between response times and response accuracies is complex and varies over levels of observation. For example, it takes the form of a tradeoff between speed and accuracy at the level of a fixed person but may become a positive correlation for a population of test takers. In order to explore such relationships and test hypotheses about them, a conjoint model is proposed. Item responses are modeled by a two-parameter normal-ogive IRT model and response times by a lognormal model. The two models are combined using a hierarchical framework based on the fact that response times and responses are nested within individuals. All parameters can be estimated simultaneously using an MCMC estimation approach. A R-package for the MCMC algorithm is presented and explained.

[1]  W. Wong,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[2]  Wim J. van der Linden,et al.  Using Response-Time Constraints to Control for Differential Speededness in Computerized Adaptive Testing , 1999 .

[3]  R. Hambleton,et al.  Handbook of Modern Item Response Theory , 1997 .

[4]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[5]  J. Albert.  Bayesian Estimation of Normal Ogive Item Response Curves Using Gibbs Sampling , 1992 .

[6]  D. Lindley,et al.  Bayes Estimates for the Linear Model , 1972 .

[7]  Edward E. Roskam,et al.  Models for Speed and Time-Limit Tests , 1997 .

[8]  Deborah L. Schnipke,et al.  Representing Response-Time Information in Item Banks. Law School Admission Council Computerized Testing Report. LSAC Research Report Series. , 1999 .

[9]  Eric Maris,et al.  Additive and multiplicative models for gamma distributed random variables, and their application as psychometric models for response times , 1993 .

[10]  Hartmann Scheiblechner,et al.  Specifically objective stochastic latency mechanisms , 1979 .

[11]  M. R. Novick,et al.  Statistical Theories of Mental Test Scores. , 1971 .

[12]  van der Linden,et al.  A hierarchical framework for modeling speed and accuracy on test items , 2007 .

[13]  Richard J. Patz,et al.  Making the Most of What We Have: A Practical Application of Multidimensional Item Response Theory in Test Scoring , 2005 .

[14]  Willem J. van der Linden,et al.  A lognormal model for response times on test items , 2006 .

[15]  N. D. Verhelst,et al.  A Logistic Model for Time-Limit Tests , 1992 .

[16]  F. Samejima.  Homogeneous case of the continuous response model , 1973 .

[17]  Peter E. Rossi,et al.  A Bayesian analysis of the multinomial probit model with fully identified parameters , 2000 .

[18]  F. Samejima.  A General Model for the Homogeneous Case of the Continuous Response. , 1983 .

[19]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  David Thissen,et al.  Timed Testing: An Approach Using Item Response Theory , 1983 .

[21]  Jerry Nedelman,et al.  Book review: “Bayesian Data Analysis,” Second Edition by A. Gelman, J.B. Carlin, H.S. Stern, and D.B. Rubin Chapman & Hall/CRC, 2004 , 2005, Comput. Stat..

[22]  Jian Qing Shi,et al.  Bayesian sampling‐based approach for factor analysis models with continuous and polytomous data , 1998 .