Differential Item Functioning Assessment in Cognitive Diagnostic Modeling: Application of the Wald Test to Investigate DIF in the DINA Model

Analyzing examinees’ responses using cognitive diagnostic models (CDMs) has the advantage of providing diagnostic information. To ensure the validity of the results from these models, differential item functioning (DIF) in CDMs needs to be investigated. In this article, the Wald test is proposed to examine DIF in the context of CDMs. This study explored the effectiveness of the Wald test in detecting both uniform and nonuniform DIF in the DINA model through a simulation study. Results of this study suggest that for relatively discriminating items, the Wald test had Type I error rates close to the nominal level. Moreover, its viability was underscored by the medium to high power rates for most investigated DIF types when DIF size was large. Furthermore, the performance of the Wald test in detecting uniform DIF was compared to that of the traditional Mantel‐Haenszel (MH) and SIBTEST procedures. The results of the comparison study showed that the Wald test was comparable to or outperformed the MH and SIBTEST procedures. Finally, the strengths and limitations of the proposed method and suggestions for future studies are discussed.     

Traditional Dimensionality Versus Essential Dimensionality

This article addresses testing the hypothesis of one versus more than one dominant (essential) dimension in the possible presence of minor dimensions. The method used is Stout's statistical test of essential unidimensionality, which is based on the theory of essential unidimensionality. Differences between the traditional definition of dimensionality provided by item response theory, which counts all dimensions present, and essential dimensionality, which counts only dominant dimensions, are discussed. As Monte Carlo studies demonstrate, Stout's test of essential unidimensionality tends to indicate essential unidimensionality in the presence of one dominant dimension and one or more minor dimensions that have a relatively small influence on item scores. As the influence of the minor dimensions increases, Stout's test is more likely to reject the hypothesis of essential unidimensionality. To assist in interpreting these studies, a rough index of the deviation from essential unidimensionality is proposed.     

Public Education and Multicultural Policy in Canada: The Special Case of Quebec

Education is a provincial responsibility in Canada, but there is a sharing of expenditure and strong support of public education, health and other welfare programs between the provinces and the federal government. Although the federal policy of multiculturalism has been aimed at making Canada a just society, the implementation of this policy in education in English-speaking Canada has been far from satisfactory, and there is great variation among the provinces in educational programs. In Quebec, the federal policy of multiculturalism is ideologically opposed to the vision of French-Québécois nationalism. While the federal policy of intercultural education has made some attempts to integrate immigrant populations, the focus remains on linguistic programs. In facing the dramatic changes driven by internationalization and a globalized economy, Canadians must respond – so the conclusion of the present study – to the urgent need to redefine the meaning of multiculturalism with radical educational programs.     

Exploring Elementary Pre-service Teachers’ Beliefs About Science Teaching and Learning as Revealed in Their Metaphor Writing

This study examined elementary preservice teachers’ beliefs about the role/image of a science teacher and science teaching and how these beliefs change during an elementary science methods course; this examination was conducted through an analysis of their metaphor writing. Data included personal metaphors and rationale papers for supporting them collected from 106 participants at the start and end of the semester. Data were analyzed using the constant comparative method and also quantified for statistical analysis. Results indicate that most participants came to the course with traditional views and developed more constructivist views during the course. However, they tended to keep their traditional views and added new constructivist perspectives into their original belief systems. This study suggests that metaphor writing can be used as both a reflection tool for preservice teachers to clarify and refine their beliefs about science teaching and learning and a diagnostic assessment tool for teacher educators to understand their students for tailoring a methods course accordingly.     

Poly-Detect for Quantifying the Degree of Multidimensionality of Item Response Data

This study investigated the validity of the Poly-Detect procedure to determine the approximate simple dimensionality structure and to quantify the degree of multidimensionality present in polytomous data through simulation and real data analysis. Both unidimensional and two-dimensional data were generated in the simulation study for the complete and the BIB data. The simulation results showed that the dimensionality structures were similar between the corresponding complete data and the BIB data as identified by the Poly-Detect procedure. Also, the simulation results indicated that the number of response categories of items did not affect the performance of the Poly-Detect procedure in quantifying the degree of multidimensionality of polytomous data. Based on the simulation results, a subjective scale of the degree of multidimensionality of a data set was developed. Application of the Poly-Detect procedure on the 1992 NAEP eighth-grade reading data indicated that the degree of multidimensionality of the entire 1992 NAEP eighth-grade reading item pool was moderate at most.     

Assessing Dimensionality of a Set of Item Responses-Comparison of Different Approaches

This study compares the performance of three methodologies for assessing unidi-mensionality: DIMTEST, Holland and Rosenbaum's approach, and nonlinear factor analysis. Each method is examined and compared with other methods on simulated and real data sets. Seven data sets, all with 2,000 examinees, were generated: three unidimensional and four two-dimensional data sets. Two levels of correlation between abilities were considered:ρ= 3 and ρ= . 7. Eight different real data sets were used: Four of them were expected to be unidimensional, and the other four were expected to be two-dimensional. Findings suggest that all three methods correctly confirmed unidimensionality but differed in their ability to detect lack of unidimensionality. DIMTEST showed excellent power in detecting lack of unidimensionality; Holland and Rosenbaum's and nonlinear factor analysis approaches showed good power, provided the correlation between abilities was low.