A Simplified Method for Predicting Pattern Match Ratio.

Cognitive diagnostic test design (CDTD) has a direct impact on the pattern match ratio (PMR) of the classification of examinees. It is more helpful to know the quality of a test during the stage of the test design than after the examination is taken. The theoretical construct validity (TCV) is an index of the test quality that can be calculated without testing, and the relationship between the PMR and the TCV will be revealed. The TCV captures the three aspects of the appeal of the test design as follows: (1) the TCV is a measure of test construct validity, and this index will navigate the processes of item construction and test design toward achieving the goal of measuring the intended objectives, (2) it is the upper bound of the PMR of the knowledge states of examinees, so it can predict the PMR, and (3) it can detect the defects of test design, revise the test in time, improve the efficiency of test design, and save the cost of test design. Furthermore, the TCV is related to the distribution of knowledge states and item categories and has nothing to do with the number of items.

A Semi-supervised Learning Method for Q-Matrix Specification Under the DINA and DINO Model With Independent Structure.

Cognitive diagnosis assessment (CDA) can be regarded as a kind of formative assessments because it is intended to promote assessment for learning and modify instruction and learning in classrooms by providing the formative diagnostic information about students' cognitive strengths and weaknesses. CDA has two phases, like a statistical pattern recognition. The first phase is feature generation, followed by classification stage. A Q-matrix, which describes the relationship between items and latent skills, corresponds to the feature generation phase in statistical pattern recognition. Feature generation is of paramount importance in any pattern recognition task. In practice, the Q-matrix is difficult to specify correctly in cognitive diagnosis and misspecification of the Q-matrix can seriously affect the accuracy of the classification of examinees. Based on the fact that any columns of a reduced Q-matrix can be expressed by the columns of a reachability R matrix under the logical OR operation, a semi-supervised learning approach and an optimal design for examinee sampling were proposed for Q-matrix specification under the conjunctive and disjunctive model with independent structure. This method only required subject matter experts specifying a R matrix corresponding to a small part of test items for the independent structure in which the R matrix is an identity matrix. Simulation and real data analysis showed that the new method with the optimal design is promising in terms of correct recovery rates of q-entries.

A Sequential Higher Order Latent Structural Model for Hierarchical Attributes in Cognitive Diagnostic Assessments.

The higher-order structure and attribute hierarchical structure are two popular approaches to defining the latent attribute space in cognitive diagnosis models. However, to our knowledge, it is still impossible to integrate them to accommodate the higher-order latent trait and hierarchical attributes simultaneously. To address this issue, this article proposed a sequential higher-order latent structural model (LSM) by incorporating various hierarchical structures into a higher-order latent structure. The feasibility of the proposed higher-order LSM was examined using simulated data. Results indicated that, in conjunction with the deterministic-inputs, noisy "and" gate model, the sequential higher-order LSM produced considerable improvement in person classification accuracy compared with the conventional higher-order LSM, when a certain attribute hierarchy existed. An empirical example was presented as well to illustrate the application of the proposed LSM.

Online Calibration of Polytomous Items Under the Graded Response Model.

Computerized adaptive testing (CAT) is an efficient testing mode, which allows each examinee to answer appropriate items according his or her latent trait level. The implementation of CAT requires a large-scale item pool, and item pool needs to be frequently replenished with new items to ensure test validity and security. Online calibration is a technique to calibrate the parameters of new items in CAT, which seeds new items in the process of answering operational items, and estimates the parameters of new items through the response data of examinees on new items. The most popular estimation methods include one EM cycle method (OEM) and multiple EM cycle method (MEM) under dichotomous item response theory models. This paper extends OEM and MEM to the graded response model (GRM), a popular model for polytomous data with ordered categories. Two simulation studies were carried out to explore online calibration under a variety of conditions, including calibration design, initial item parameter calculation methods, calibration methods, calibration sample size and the number of categories. Results show that the calibration accuracy of new items were acceptable, and which were affected by the interaction of some factors, therefore some conclusions were given.

Theorems and Methods of a Complete Q Matrix With Attribute Hierarchies Under Restricted Q-Matrix Design.

The design of test Q matrix can directly influence the classification accuracy of a cognitive diagnostic assessment. In this paper, we focus on Q matrix design when attribute hierarchies are known prior to test development. A complete Q matrix design is proposed and theorems are presented to demonstrate that it is a necessary and sufficient condition to guarantee the identifiability of ideal response patterns. A simulation study is also conducted to detect the effects of the proposed design on a family of conjunctive diagnostic models. The results revealed that the proposed Q matrix design is the key condition for guaranteeing classification accuracy. When only one type of item pattern in R matrix is missing from the associated test Q matrix, the related attribute-wise agreement rate will decrease dramatically. When the entire R matrix is missing, both the pattern-wise and attribute-wise agreement rates will decrease sharply. This indicates that the proposed procedures for complete Q matrix design with attribute hierarchies can serve as guidelines for test blueprint development prior to item writing in a cognitive diagnostic assessment.

An EM-Based Method for Q-Matrix Validation.

With the purpose to assist the subject matter experts in specifying their Q-matrices, the authors used expectation-maximization (EM)-based algorithm to investigate three alternative Q-matrix validation methods, namely, the maximum likelihood estimation (MLE), the marginal maximum likelihood estimation (MMLE), and the intersection and difference (ID) method. Their efficiency was compared, respectively, with that of the sequential EM-based δ method and its extension (ς2), the γ method, and the nonparametric method in terms of correct recovery rate, true negative rate, and true positive rate under the deterministic-inputs, noisy "and" gate (DINA) model and the reduced reparameterized unified model (rRUM). Simulation results showed that for the rRUM, the MLE performed better for low-quality tests, whereas the MMLE worked better for high-quality tests. For the DINA model, the ID method tended to produce better quality Q-matrix estimates than other methods for large sample sizes (i.e., 500 or 1,000). In addition, the Q-matrix was more precisely estimated under the discrete uniform distribution than under the multivariate normal threshold model for all the above methods. On average, the ς2 and ID method with higher true negative rates are better for correcting misspecified Q-entries, whereas the MLE with higher true positive rates is better for retaining the correct Q-entries. Experiment results on real data set confirmed the effectiveness of the MLE.

[Atomic absorption fingerprint and identification studies of Da Huo Luo pill. I. Exploration of inorganic elements fingerprint for establishment of industrial standard].

The fingerprints for most of Chinese medicines based on their organic compositions have been well established. Nevertheless, there are very few known fingerprints which are based on inorganic elements. In order to identify the Da Huo Luo Dan and its efficiency from other Chinese medicines, the authors attempted to set up a fingerprint which could be determined by the measurement of inorganic elements in Da Huo Luo Dan and other Chinese medicines. In the present study, the authors first employed 28 batches of Da Huo Luo Dan produced by Zhang-Shu Pharmatheutical Company in Jiang Xi Province to screen 12 kinds of inorganic elements measured by atomic absorption spectrophotometer and established the atomic absorption fingerprints. Secondly, the authors tried to identify Da Huo Luo Dan and other Chinese medicines by using the similarly analysis of vectors and the statistical analysis of compositional data. The result showed that the methods the authors used here were predictable to tell the efficiency of Da Huo Luo Dan from others. The authors' study also proves that establishment of standard for quality control by analysis of inorganic elements in Chinese medicines is feasible. The present study provides a new idea and a new technique that serve for the establishment of industrial standards for analysis of inorganic elements fingerprint to explore the effects of Chinese medicines.