This paper uses log-linear models with latent variables (Hagenaars, in "Loglinear Models with Latent Variables," 1993) to define a family of cognitive diagnosis models. In doing so, the relationship between many common models is explicitly defined and discussed. In addition, because the log-linear model with latent variables is a general model for…

After a brief review of recent advances in sequential analysis involving sequential generalized likelihood ratio tests, we discuss their use in psychometric testing and extend the asymptotic optimality theory of these sequential tests to the case of sequentially generated experiments, of particular interest in computerized adaptive testing. We…

A new direct and short proof is offered for the monotone likelihood ratio for the sum of independent Bernoulli random variables through use of an inequality by Marcus and Lopes (1957) on elementary symmetric functions. (SLD)

In this paper, we apply sequential one-sided confidence interval estimation procedures with beta-protection to adaptive mastery testing. The procedures of fixed-width and fixed proportional accuracy confidence interval estimation can be viewed as extensions of one-sided confidence interval procedures. It can be shown that the adaptive mastery…

The use of Cohen's kappa index as a measure of the reliability of multiple classifications is developed. Special cases of the index as well as the effects of test length on the index are also explored. (JKS)

A model for the setting of mastery cut scores is presented. The model, based on the beta-binomial test distribution, allows for hand calculation of cut scores. The model provides a simple way to explore the consequences of selecting a particular cut score. (Author/JKS)

Several Bayesian approaches to the simultaneous estimation of the means of k binomial populations are discussed. This has particular applicability to criterion-referenced or mastery testing. (Author/JKS)

A procedure for estimating the rates of false positive and false negative classification in a mastery testing situation is described. Formulas and tables are described for the computations of the standard errors. (Author/JKS)

A Bayesian framework for making mastery/nonmastery decisions based on multivariate test data is described. Overall, mastery is granted if the posterion expected loss associated with such action is smaller than the one incurred by denying mastery. (Author/JKS)

A nonrandomized minimax solution is presented for passing scores on mastery tests using the binomial error model. The computation does not require prior knowledge regarding an individual examinee or group test data for a population of examinees. A scheme which allows for correction for guessing is also described. (Author/JKS)

Decision rules for assigning students to treatments based upon aptitudes or criterion scores are discussed. Popular procedures are criticized and a Bayesian approach is recommended. The effect of unreliability of aptitude or criterion scores is also discussed. (JKS)

The problem of determining an optimal passing score for a mastery test is discussed, when the purpose of the test is to predict success on an external criterion. For the case of constant losses for the two possible error types, a method for determining passing scores is derived. (Author/JKS)