Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models that are widely used in educational and psychological measurement. A key component of CDMs is the Q-matrix characterizing the dependence structure between the items and the latent attributes. Additionally, researchers also assume in many applications certain…

Item response theory (IRT) refers to a family of mathematical models which describe the relationship between latent continuous variables (attributes or characteristics) and their manifestations (dichotomous/polytomous observed outcomes or responses) with regard to a set of item characteristics. Researchers typically use parametric IRT (PIRT)…

Topic models are mathematical and statistical models used to analyze textual data. The objective of topic models is to gain information about the latent semantic space of a set of related textual data. The semantic space of a set of textual data contains the relationship between documents and words and how they are used. Topic models are becoming…

Many organizations utilize some form of automation in the test assembly process; either fully algorithmic or heuristically constructed. However, one issue with heuristic models is that when the test assembly problem changes the entire model may need to be re-conceptualized and recoded. In contrast, mixed-integer programming (MIP) is a mathematical…

The objective of this research was to better understand the transfer of learning between different variations of pre-algebra problems. While the authors could have addressed a specific variation that might address transfer, they were interested in developing a general model of transfer, so we gathered data from multiple problem types and their…

The online deployment of Technology Engineered online Student Ratings of Instruction (SRIs) by colleges and universities in the United States has dynamically changed the deployment of course evaluation. This research investigation is the fourth part of a post hoc study that analytically and psychometrically examines the design, reliability, and…

In this study, psychometric properties of the test of the three-mathematical minds (M3) were investigated. The M3 test was developed based on a multidimensional conception of giftedness to identify mathematically talented students. Participants included 291 middle-school students. Data analysis indicated that the M3 had a 0.73 coefficient as a…

Computerized adaptive testing is subject to security problems, as the item bank content remains operative over long periods and administration time is flexible for examinees. Spreading the content of a part of the item bank could lead to an overestimation of the examinees' trait level. The most common way of reducing this risk is to impose a…

Various factors which influence the relationship between the Rasch item characteristic curve and the actual performance of an item are identified. The Rasch item characteristic curve is a new concept in test design and analysis. The Rasch test model provides information concerning the percent of students with a specified achievement level who…

INVESTIGATION IS CONTINUED INTO VARIOUS EFFECTS OF NON-INDEPENDENT ERROR INTRODUCED INTO MULTIPLE-CHOICE TEST SCORES AS A RESULT OF CHANCE GUESSING SUCCESS. A MODEL IS DEVELOPED IN WHICH THE CONCEPT OF THEORETICAL COMPONENTS OF SCORES IS NOT INTRODUCED AND IN WHICH, THEREFORE, NO ASSUMPTIONS REGARDING ANY RELATIONSHIP BETWEEN SUCH COMPONENTS NEED…

It is shown that if a behavior domain can be described by the common factor model with a finite number of factors, the squared correlation between the sum of a selection of items and the domain total score is actually greater than coefficient alpha. (Author/JKS)

The problem of characterizing the manifest probabilities of a latent trait model is considered. The approach taken here differs from the standard approach in that a population of examinees is being considered as opposed to a single examinee. Particular attention is given to the Rasch model. (Author/JKS)

The magnitude of statistical bias for the phi-coefficient was investigated, using computer simulated examinations in which all the students had equal knowledge. Several modifications of phi were tested, but when applied to real examinations, none succeeded in improving its reproducibility when items are re-used on equivalent student groups.…

A basic description of the Rasch model and a brief review of the work previously done on the model is related. Simulated data was used to test goodness of fit to the Rasch model. It was found that data with near perfect fit to the Guttman model provides perfect fit to the Rasch model, though a perfect Guttman scale collapses. Random data also…