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The S- X2 statistic (Orlando & Thissen, 2000) is popular among researchers and practitioners who are interested in the assessment of item fit. However, the statistic suffers from the Chernoff–Lehmann problem (Chernoff & Lehmann, 1954) and hence does not have a known asymptotic null distribution. This paper suggests a modified version of the S- X2 statistic that is based on the modified Rao–Robson χ2 statistic (Rao & Robson, 1974). A simulation study and a real data analyses demonstrate that the use of the modified statistic instead of the S- X2 statistic would lead to fewer items being flagged for misfit.

Zinc is an essential minor element for the rice growth and the human health. Applying Zn fertilizer to rice ( Oryza sativa L.) is an effective way to boost yield and grain zinc content. As the most active component in soil, microorganisms can realize a virtuous cycle of soil nutrients and crop growth. However, current studies on the impacts of Zn fertilizer application on crop yield and grain Zn content are inconsistent. The mechanism during the process, especially concerning the soil bacterial community characteristics, is yet unclear. Therefore, it’s important to have a comprehensive understanding of the rice rhizosphere bacterial communities. We took advantage of 16S rRNA gene sequencing and co-occurrence network analysis to study the effects of Zn fertilizer application on the rice grain yield, Zn content and the soil bacterial community. Results showed that Zn application (ZS2, i.e., 10.35 kg ha Zn soil application + 3.10 kg ha foliar spraying) increased the grain yield (17.34%~19.52%) and enriched the Zn content of polished rice (1.40%~20.05%) compared with the control group (ZS0) treatments. This was closely correlated to the soil available Zn (AZ) contents (1.16%~85.69%). Furthermore, soil total nitrogen (TN) was considered as the primary driver which led to a community shift in the rice rhizosphere bacterial community. This was mainly due to the variation in the co-occurrence network which made more complex and stable caused by the Zn fertilizer application. Thus, the interaction between different species was strengthened. During the process, the most critical bacteria taxa were identified as Actinobacteria, Bacteroidetes, Proteobacteria, and Chloroflexi. KEGG metabolic pathway prediction demonstrated that Zn application may improve metabolism functions such as lipid metabolism, amino acid metabolism, carbohydrate metabolism, and xenobiotics biodegradation, which ultimately affected the yield and Zn content of rice grains. However, their positive effects were different among rice cultivars, of which Nanjing-9108 performed better. This study deepens the understanding of the interaction between Zn fertilizer, rice yield, Zn content of rice grain, and soil bacterial structure and further navigates the development of Zn-rich rice cultivation strategies.

In educational and psychological measurement when short test forms are used, the asymptotic normality of the maximum likelihood estimator of the person parameter of item response models does not hold. As a result, hypothesis tests or confidence intervals of the person parameter based on the normal distribution are likely to be problematic. Inferences based on the exact distribution, on the other hand, do not suffer from this limitation. However, the computation involved for the exact distribution approach is often prohibitively expensive. In this paper, we propose a general framework for constructing hypothesis tests and confidence intervals for IRT models within the exponential family based on exact distribution. In addition, an efficient branch and bound algorithm for calculating the exact p value is introduced. The type-I error rate and statistical power of the proposed exact test as well as the coverage rate and the lengths of the associated confidence interval are examined through a simulation. We also demonstrate its practical use by analyzing three real data sets.

The Programme for International Student Assessment (PISA) introduced the measurement of problem-solving skills in the 2012 cycle. The items in this new domain employ scenario-based environments in terms of students interacting with computers. Process data collected from log files are a record of students' interactions with the testing platform. This study suggests a two-stage approach for generating features from process data and selecting the features that predict students' responses using a released problem-solving item-the Climate Control Task. The primary objectives of the study are (1) introducing an approach for generating features from the process data and using them to predict the response to this item, and (2) finding out which features have the most predictive value. To achieve these goals, a tree-based ensemble method, the random forest algorithm, is used to explore the association between response data and predictive features. Also, features can be ranked by importance in terms of predictive performance. This study can be considered as providing an alternative way to analyze process data having a pedagogical purpose.

One of the primary goals in cognitive diagnosis is to use the item responses from a cognitive diagnostic assessment to make inferences about what skills a test-taker has. Much of the research to date has focused on parametric inference in cognitive diagnosis models (CDMs), which requires that the parametric model used for inference does an adequate job of describing the item response distribution of the population of examinees being studied. Whatever the type of model misspecification or misfit, users of CDMs need tools to investigate model-data misfit from a variety of angles. In this chapter we separate the model fit methods into four categories defined by two aspects of the methods: (1) the level of the fit analysis, i.e., global/test-level versus item-level; and (2) the choice of the alternative model for comparison, i.e., an alternative CDM (relative fit) or a saturated categorical model (absolute fit).