An IRT Model with a Parameter-Driven Process for Change

• Published in: Psychometrika Vol. 70; no. 4; pp. 651 - 669
• Main Authors: Rijmen, Frank, De Boeck, Paul, van der Maas, Han L. J.
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01.12.2005; Springer Nature B.V
• Subjects: Biological and medical sciences; Change; Feedback (Response); Fundamental and applied biological sciences. Psychology; Individual Differences; Item Response Theory; Latent class analysis; Longitudinal studies; Markov analysis; Markov Processes; Observation; Probability; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Psychometrics; Psychometrics. Statistics. Methodology; Rasch model; Research Methodology; Scientific Research; Statistics. Mathematics; Variables; Psychometrics; Panel data; Change; Markov model; Item response theory; latent markov model
• ISSN: 0033-3123; 1860-0980
• DOI: 10.1007/s11336-002-1047-z

An IRT model with a parameter-driven process for change is proposed. Quantitative differences between persons are taken into account by a continuous latent variable, as in common IRT models. In addition, qualitative interindividual differences and autodependencies are accounted for by assuming within-subject variability with respect to the parameters of the IRT model. In particular, the parameters of the IRT model are governed by an unobserved or “hidden'” homogeneous Markov process. The model includes the mixture linear logistic test model (Mislevy & Verhelst, 1990), the mixture Rasch model (Rost, 1990), and the Saltus model (Wilson, 1989) as specific instances. The model is applied to a longitudinal experiment on discontinuity in conservation acquisition (van der Maas, 1993).