The Relationship between Parameters from Two Polytomous Item Response Theory Models
ثبت نشده
چکیده
RESPONSE THEORY MODELS Various polytomous IRT models parameterize the probability of response categories differently from each other. For example, the graded response model (GRM) (Samejima, 1969) is based on the cumulative log-odds principle, whereas the generalized partial credit model (GPCM) (Muraki, 1992) is based on the adjacent log-odds principle. It is widely known that these two polytomous IRT models do not produce directly comparable parameters (e.g., Ostini & Nering, 2005). However, to our knowledge, it has not been clearly pointed out that how discrimination parameters (a-parameters, hereafter) from these two polytomous IRT models are affected by the number of response categories. Thus, this study investigates the relationship between the a-parameters and the number of response categories for polytomous item response theory models, specifically for the GRM and GPCM. The relationships are first explored algebraically. More specifically, the cumulative category response functions of the investigated models are solved with respect to the a-parameter. Then, the algebraically derived relationships are empirically demonstrated with simulated data sets. Finally, practical importance of the findings is discussed. Method Algebraic Demonstrations The formulas for the a-parameters based on the cumulative category response functions were derived for the GRM and GPCM. The category response functions of Samejima’s
منابع مشابه
Evaluation Psychometric Characteristics of the Persian Version of the Colorado Learning Attitudes about Science Survey Using polytomous Item Response Model
Goal: Researchers in the field of science education believe that peoplechr(chr('39')39chr('39'))s attitudes about learning will have a significant impact on their future learning and what they learn from science will not be unrelated to their views and attitudes. Accordingly, most questionnaires have been developed to measure attitudes toward science, especially about physics learning attitudes...
متن کامل%lrasch mml: A SAS Macro for Marginal Maximum Likelihood Estimation in Longitudinal Polytomous Rasch Models
Item response theory models are often applied when a number items are used to measure a unidimensional latent variable. Originally proposed and used within educational research, they are also used when focus is on physical functioning or psychological wellbeing. Modern applications often need more general models, typically models for multidimensional latent variables or longitudinal models for ...
متن کاملItem Response Theory: past Performance, Present Developments, and Future Expectations
We give a historical introduction to item response theory, which places the work of Thurstone, Lord, Guttman and Coombs in a present-day perspective. The general assumptions of modern item response theory, local independence and monotonicity of response functions, are discussed, followed by a general framework for estimating item response models. Six classes of well-known item response models a...
متن کاملThe effects of the violation of local independence assumption on the person measures under the Rasch model
Local independence of test items is an assumption in all Item Response Theory (IRT) models. That is, the items in a test should not be related to each other. Sharing a common passage, which is prevalent in reading comprehension tests, cloze tests and C-Tests, can be a potential source of local item dependence (LID). It is argued in the literature that LID results in biased parameter estimation ...
متن کاملsimpolycat: an SAS program for conducting CAT simulation based on polytomous IRT models.
A real-data simulation of computerized adaptive testing (CAT) is an important step in real-life CAT applications. Such a simulation allows CAT developers to evaluate important features of the CAT system, such as item selection and stopping rules, before live testing. SIMPOLYCAT, an SAS macro program, was created by the authors to conduct real-data CAT simulations based on polytomous item respon...
متن کامل