In the human sciences, a common assumption is that latent traits have a hierarchical structure. Higher order item response theory models have been developed to account for this hierarchy. In this study, computerized adaptive testing (CAT) algorithms based on these kinds of models were implemented, and their performance under a variety of situations was examined using simulations. The results showed that the CAT algorithms were very effective. The progressive method for item selection, the Sympson and Hetter method with online and freeze procedure for item exposure control, and the multinomial model for content balancing can simultaneously maintain good measurement precision, item exposure control, content balance, test security, and pool usage.

Many latent traits in the human sciences have a hierarchical structure. This study aimed to develop a new class of higher order item response theory models for hierarchical latent traits that are flexible in accommodating both dichotomous and polytomous items, to estimate both item and person parameters jointly, to allow users to specify customized item response functions, and to go beyond two orders of latent traits and the linear relationship between latent traits. Parameters of the new class of models can be estimated using the Bayesian approach with Markov chain Monte Carlo methods. Through a series of simulations, the authors demonstrated that the parameters in the new class of models can be well recovered with the computer software WinBUGS, and the joint estimation approach was more efficient than multistaged or consecutive approaches. Two empirical examples of achievement and personality assessments were given to demonstrate applications and implications of the new models.

When diagnostic assessments are administered to examinees, the mastery status of each examinee on a set of specified cognitive skills or attributes can be directly evaluated using cognitive diagnosis models (CDMs). Under certain circumstances, allowing the examinees to have at least one opportunity to correctly answer the questions and assessments, with repeated attempts on the items, provides many potential benefits. A sequential process model can be extended to model repeated attempts in diagnostic assessments. Two formulations of the sequential generalized deterministic-input noisy-“and”-gate (G-DINA) model were developed in this study. The first extension uses the latent transition analysis (LTA) approach to model changes in the attributes over attempts, and the second extension constructs a higher order structure of latent continuous variables and latent attributes to account for the dependences of the attributes over attempts. Accurate model parameter estimation and correct classifications of attributes were observed in a series of simulations using Bayesian estimation. The effectiveness of the developed sequential G-DINA model was demonstrated by fitting real data from a longitudinal mathematical test to the developed model and the longitudinal G-DINA model using the LTA approach. Finally, this article closes by discussing several important issues associated with the developed models and providing suggestions for future directions.

In imperfect production processes, this paper considers production correction and maintenance to break away out of control state. Production processes are classified into two types of state: one is the type I state (out-of-control state) and the other is the type II state (in-control state). The type I state involves adjustment of the production mechanism. Production correction is either imperfect; worsening a production system, or perfect, returning it to "in-control" conditions. After N type I states, the operating system must be maintained and returned to the beginning condition. At the beginning of the production of the each renewal cycle, the state of the process is not always to be restored to "in-control". The total cost until "in-control" state, is determined. The existence of a unique and finite optimal N for an imperfect process under certain reasonable conditions is shown. A numerical example is presented.