Abstract
This paper concerns items that consist of several item steps to be responded to sequentially. The item scoreX is defined as the number of correct responses until the first failure. Samejima's graded response model states that each steph=1,...,m is characterized by a parameterb h , and, for a subject with abilityθ, Pr(X≥h; θ)=F(θ−b h ). Tutz's general sequential model associates with each step a parameterdh, and it states that Pr(X≥h;θ)=Π =1h r G(θ−d r ). Tutz's (1991, 1997) conjectures that the models are equivalent if and only ifF(x)=G(x) is an extreme value distribution. This paper presents a proof for this conjecture.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Castillo, Ron E. (1996).Algunas applicacionces de las ecuaciones functionales [Some applications of functional equations] (Apertura del Curso Académico 1996/97). Santander, Spain: Universidad de Cantabria.
Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores.Psychometric Monograph Supplement, No. 17.
Tutz, G. (1990). Sequential item response models with an ordered response.British Journal of Mathematical and Statistical Psychology, 43, 39–55.
Tutz, G. (1991). Sequential models in categorical regression.Computational Statistics & Data Analysis, 11, 275–295.
Tutz, G. (1997). Sequential models for ordered responses. In W.J. van der Linden & R. Hambleton (Eds.),Modern handbook of item response theory (pp. 139–152). New-York, NY: Springer.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bechger, T.M., Akkermans, W. A note on the equivalence of the graded response model and the sequential model. Psychometrika 66, 461–463 (2001). https://doi.org/10.1007/BF02294445
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02294445