Applications of polytomous IRT models in applied fields (e.g., health, education, psychology) are abound. However, little is known about the impact of the number of categories and sample size requirements for precise parameter recovery. In a simulation study, we investigated the impact of the number of response categories and required sample size…

The application of diagnostic classification models (DCMs) in the field of educational measurement is getting more attention in recent years. To make a valid inference from the model, it is important to ensure that the model fits the data. The purpose of the present study was to investigate the performance of the limited information…

S-X[superscript 2] is a popular item fit index that is available in commercial software packages such as "flex"MIRT. However, no research has systematically examined the performance of S-X[superscript 2] for detecting item misfit within the context of the multidimensional graded response model (MGRM). The primary goal of this study was…

This study analysed polytomous items' psychometric properties according to nonparametric item response theory (NIRT) models. Thus, simulated datasets--three different test lengths (10, 20 and 30 items), three sample distributions (normal, right and left skewed) and three samples sizes (100, 250 and 500)--were generated by conducting 20…

As item response theory has been more widely applied, investigating the fit of a parametric model becomes an important part of the measurement process. There is a lack of promising solutions to the detection of model misfit in IRT. Douglas and Cohen introduced a general nonparametric approach, RISE (Root Integrated Squared Error), for detecting…

This dissertation proposes two modified cognitive diagnostic models (CDMs), the deterministic, inputs, noisy, "and" gate with hierarchy (DINA-H) model and the deterministic, inputs, noisy, "or" gate with hierarchy (DINO-H) model. Both models incorporate the hierarchical structures of the cognitive skills in the model estimation…

In this study we examined procedures for assessing model-data fit of item response theory (IRT) models for mixed format data. The model fit indices used in this study include PARSCALE's G[superscript 2], Orlando and Thissen's S-X[superscript 2] and S-G[superscript 2], and Stone's chi[superscript 2*] and G[superscript 2*]. To investigate the…

Investigating the fit of a parametric model is an important part of the measurement process when implementing item response theory (IRT), but research examining it is limited. A general nonparametric approach for detecting model misfit, introduced by J. Douglas and A. S. Cohen (2001), has exhibited promising results for the two-parameter logistic…

Orlando and Thissen (2000, 2003) proposed an item-fit index, S-X[superscript 2], for dichotomous item response theory (IRT) models, which has performed better than traditional item-fit statistics such as Yen's (1981) Q[subscript 1] and McKinley and Mill's (1985) G[superscript 2]. This study extends the utility of S-X[superscript 2] to polytomous…

In the early 1970s A. Constantinople wrote a seminal article that led to the development of the construct of psychological androgyny. The Bem Sex-Role Inventory is a popular measure of the construct, but the measure remains controversial. The construct validity of scores from the measure was explored using confirmatory factor analysis on data from…