Handbook of Modern Item Response Theory pp 169-185 | Cite as

# A Logistic Model for Time-Limit Tests

## Abstract

The purpose of the present chapter is to introduce a psychometric model for time-limit tests. Our point of departure is a practical one. The main problem involved in the use of time-limit tests may be illustrated by the following example. Assume that a test consists of a large number of equally difficult items, and that examinees are allowed to answer the items during a fixed amount of time *τ*. Suppose person A and person B both have the same proportion of correct answers, but have completed a different number of items. Should the ability estimates of A and B be equal? It may be argued that for several reasons the answer should be no. The most practical reason may be that if only the proportion correct is important, the optimal strategy in answering the test is to spend all the allotted time on the first item. But also in realistic settings, where examinees are urged to work fast but accurately, a response style which favors accuracy at the expense of speed is advantageous. It might seem that using the number of correct responses reflects both speed and accuracy, and is therefore a more sensible way of scoring the test performance. But with this approach, another problem crops up. If the test consists of *n* items, the number of correct responses can be expressed as a proportion relative to *n*, implying that items not reached and wrong responses are treated in the same way, an approach which may prejudice to persons working slowly but accurately.

## Keywords

Item Parameter Response Style Precision Parameter Conditional Likelihood Rank Number## Preview

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## References

- Andersen, E.B. (1970). Asymptotic properties of conditional maximum likelihood estimation.
*Journal of the Royal Statistical Society B***32**, 283–301.MATHGoogle Scholar - Amemiya, T. (1986).
*Advanced Econometrics*. Oxford: Blackwell.Google Scholar - Arnold, B.C. and Strauss, D. (1988).
*Pseudolikelihood Estimation*(Technical Report No. 164 ). Riverside: University of California, Department of Statistics.Google Scholar - Dubey, S.D. (1969). A new derivation of the logistic distribution.
*Naval Research Logistics Quarterly***16**, 37–40.Google Scholar - Fischer, G.H. (1974).
*Einfiihrung in die Theorie psychologischer Tests*[Introduction to the Theory of Psychological Tests]. Bern: Huber.Google Scholar - Glas, C.A.W. and Verhelst, N.D. (1995). Testing the Rasch model. In G.H. Fischer and I.W. Molenaar (Eds.),
*Rasch Models: Foundations, Recent Developments and Applications (pp*. 69–95 ). New York: Springer-Verlag.Google Scholar - Lord, F.M. (1983). Unbiased estimation of ability parameters, of their variance, and of their parallel-forms reliability.
*Psychometrika***48**, 233–245.MathSciNetMATHCrossRefGoogle Scholar - Masters, G.N. (1982). A Rasch model for partial credit scoring.
*Psychometrika***47**, 149–174.MATHCrossRefGoogle Scholar - Rasch, G. (1980).
*Probabilistic Models for Some Intelligence and Attainment Tests*. Chicago: The University of Chicago Press (original work published in 1960 ).Google Scholar - Roskam, E.E.Ch.I. (1987). Towards a psychometric theory of intelligence. In E.E.Ch.I. Roskam and R. Suck (Eds.),
*Progress in Mathematical Psychology, Vol*.*1*(pp. 151–174 ). Amsterdam: North-Holland.Google Scholar - Van Breukelen, G.J.P. (1989).
*Concentration, Speed and Precision in Mental Tests: A Psychometric Approach*. Doctoral dissertation, University of Nijmegen, The Netherlands.Google Scholar - Verhelst, N.D. and Kamphuis, F.H. (1989).
*Statistiek met Theta-Dak*[Statistics with Theta-hat] (Bulletin series, 77 ). Arnhem: Cito.Google Scholar - Verhelst, N.D., Glas, C.A.W., and Verstralen, H.H.F.M. (1995).
*OPLM: One Parameter Logistic Model. Computer Program and Manual*. Arnhem: Cito.Google Scholar - Verhelst, N.D. and Glas, C.A.W. (1995). The one-parameter logistic model. In G.H. Fischer and I.W. Molenaar (Eds.),
*Rasch Models: Foundations, Recent Developments and Applications*(pp. 215–237 ). New York: Springer.Google Scholar - Verhelst, N.D., Verstralen, H.H.F.M., and Jansen, M.G.H. (1992).
*A Logistic Model for Time Limit Tests*. (Measurement and Research Department Reports, 92–1 ). Arnhem: Cito.Google Scholar - Warm, Th.A. (1989). Weighted likelihood estimation of ability in item response theory.
*Psychometrika***54**, 427–450.MathSciNetCrossRefGoogle Scholar