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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. 98

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To examine whether children (mean age 34 months) can fast map and extend novel action labels to actions for which they do not already have names, the comprehension of familiar and novel verbs was tested using colored drawings of Sesame Street characters performing both familiar and unfamiliar actions. Children were asked to point to the character "verbing," from among sets of 4 drawings. With familiar words and actions, children made correct choices 97% of the time. With novel action words, children performed at levels mostly significantly above chance, selecting a previously unlabeled action or another token of a just-names action. In a second, control experiment children were asked to select an action from among the same sets of 4 drawings, but they were not given a novel action name. Here children mainly demonstrated performance at levels not significantly different from chance, showing that the results from the main experiment were attributable to the presence of a word in the request. Results of these studies are interpreted as support for the availability of principles to ease verb acquisition.

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.