The cognitive diagnosis model is an emerging evaluation theory. The mastery of fine-grained knowledge points of students can be obtained via the cognitive diagnostic model (CDM), which can subsequently describe the learning trajectory. The latter is a description of the learning progress of students in a specific area, through which teaching and learning can be linked. This research is based on nine statistical items in the Program for International Student Assessment (PISA) 2012 and an analysis of the response data of 30,092 students from 14 countries from four attributes based on CDM. Then, it obtains the learning trajectory of students in statistical knowledge. The study found that Bulgaria, Costa Rica, Peru, Mexico, and Serbia have the same learning trajectories. The learning trajectories of almost 14 countries are as follows: (1) uncertainty, (2) data handling, (3) statistical chart, and (4) average.

Item response models often cannot calculate true individual response probabilities because of the existence of response disturbances (such as guessing and cheating). Many studies on aberrant responses under item response theory (IRT) framework had been conducted. Some of them focused on how to reduce the effect of aberrant responses, and others focused on how to detect aberrant examinees, such as person fit analysis. The purpose of this research was to derive a generalized formula of bias with/without aberrant responses, that showed the effect of both non-aberrant and aberrant response data on the bias of capability estimation mathematically. A new evaluation criterion, named aberrant absolute bias (|ABIAS|), was proposed to detect aberrant examinees. Simulation studies and application to a real dataset were conducted to demonstrate the efficiency and the utility of |ABIAS|.

Sequence labeling has wide applications in many areas. For example, most of named entity recognition tasks, which extract named entities or events from unstructured data, can be formalized as sequence labeling problems. Sequence labeling has been studied extensively in different communities, such as data mining, natural language processing or machine learning. Many powerful and popular models have been developed, such as hidden Markov models (HMMs) [4], conditional Markov models (CMMs) [3], and conditional random fields (CRFs) [2]. Despite their successes, they suffer from some known problems: (i) HMMs are generative models which suffer from the mismatch problem, and also it is difficult to incorporate overlapping, non-independent features into a HMM explicitly. (ii) CMMs suffer from the label bias problem; (iii) CRFs overcome the problems of HMMs and CMMs, but the global normalization of CRFs can be very expensive. This prevents CRFs from being applied to big datasets (e.g. Tweets).In this paper, we propose the empirical Co-occurrence Rate Networks (ECRNs) [5] for sequence labeling. CRNs avoid the problems of the existing models mentioned above. To make the training of CRNs as efficient as possible, we simply use the empirical distribution as the parameter estimation. This results in the ECRNs which can be trained orders of magnitude faster and still obtain competitive accuracy to the existing models. ECRN has been applied as a component to the University of Twente system [1] for concept extraction challenge at #MSM2013, which won the best challenge submission awards. ECRNs can be very useful for practitioners on big data.

The quality of multiple-choice questions (MCQs) as well as the student's solve behavior in MCQs are educational concerns. MCQs cover wide educational content and can be immediately and accurately scored. However, many studies have found some flawed items in this exam type, thereby possibly resulting in misleading insights into students’ performance and affecting important decisions. This research sought to determine the characteristics of MCQs and factors that may affect the quality of MCQs by using item response theory (IRT) to evaluate data. For this, four samples of different sizes from US and China in secondary and higher education were chosen. Item difficulty and discrimination were determined using item response theory statistical item analysis models. Results were as follows. First, only a few guessing behaviors are included in MCQ exams because all data fit the two-parameter logistic model better than the three-parameter logistic model. Second, the quality of MCQs depended more on the degree of training of examiners and less on middle or higher education levels. Lastly, MCQs must be evaluated to ensure that high-quality items can be used as bases of inference in middle and higher education. Keywords: higher education, item evaluation, item response theory, multiple-choice test, secondary education

A three-parameter logistic (3PL) model variant, named the two-parameter logistic extension (2PLE) model, was developed. This new model employs a function that integrates item features according to an examinee’s ability level instead of a fixed guessing parameter used in the 3PL model to quantify guessing behavior. Correct response probabilities from a solution behavior and guessing behavior increase as the level of ability increases. At extreme cases in which the level of ability is close to negative infinity, the 2PLE model degenerates into a 3PL model with a guessing probability at chance level (i.e., 1/ m, where m is the number of options). The properties of the 2PLE model were described and compared with those of other guessing models. Then, a simulation study comparing the performance of the 2PLE model with that of the 3PL model under three scenarios was conducted. Results showed that the 2PLE model generally outperforms the 3PL model. Finally, the application of the new model in comparison with several existing models was demonstrated by using two real data sets.