This paper focuses on two estimators of ability with logistic item response theory models: the Bayesian modal (BM) estimator and the weighted likelihood (WL) estimator. For the BM estimator, Jeffreys' prior distribution is considered, and the corresponding estimator is referred to as the Jeffreys modal (JM) estimator. It is established that under…

In this paper, optimal designs will be derived for estimating the ability parameters of the Rasch model when difficulty parameters are known. It is well established that a design is locally D-optimal if the ability and difficulty coincide. But locally optimal designs require that the ability parameters to be estimated are known. To attenuate this…

As examples of models that are not based on normality or its approximation, the logistic positive exponent family of models is discussed. These models include the item task complexity as the third parameter, which determines the single principle of ordering individuals on the ability scale. (SLD)

Three counterexamples demonstrate that the Dutch Identity conjecture of P. Holland about examinee ability (1990) does not hold in general. The counterexamples suggest that only under strong assumptions can it be true that the limits of log-manifest probabilities are quadratic. Three propositions giving such strong conditions are given. (Author/SLD)

A similarity-based smoothing approach to nondimensional item analysis was studied. Simulated and actual data are presented to show that when responses are determined by a latent ability variable, this similarity-based smoothing procedure can reveal the dimensionality of ability satisfactorily. (SLD)

Rasch's multiplicative Poisson model is extended so that parameters for individuals in the prior gamma distribution have continuous covariates. Parameters for individuals are integrated out, and hyperparameters in the prior distribution are estimated by a numerical method separately from difficulty parameters that are treated as fixed parameters…

Examined the assumption that matching difficulty levels of test items with an examinee's ability makes a test more efficient and challenged this assumption through a class of one-parameter item response theory models. Found the validity of the fundamental assumption to be closely related to the van Zwet tail ordering of symmetric distributions (W.…

Proposed and evaluated two new methods of improving the measurement precision of a general test factor. One provides a multidimensional item response theory estimate based on administrations of multiple-choice test items that span general and nuisance dimensions, and the other chooses items adaptively to maximize the precision of the general…

Discusses whether the tradition of accepting point-symmetric item characteristic curves is justified by uncovering the inconsistent relationship between the difficulties of items and the order of maximum likelihood estimates of ability. In this context, proposes a family of models, called the logistic positive exponent family, that provides…

A new model, the acceleration model, is proposed in the framework of the heterogeneous case of the graded response model, based on processing functions defined for a finite or enumerable number of steps. The model is expected to be useful in cognitive assessment. (SLD)

A multidimensional model is presented for measuring learning and change based on item response theory. The model specifies a Wiener simplex pattern for involvement of initial ability and one or more modifiabilities in response potential for successive measurement occasions. Properties of the model are explored for several classical issues. (SLD)

Introduces and discusses the rationale and procedures of two nonparametric approaches to estimating the operating characteristic of a discrete item response, or the conditional probability, given the latent trait, that the examinee's response be that specific response. (SLD)

A hypothesis testing and estimation procedure, Crossing SIBTEST, is presented for detecting crossing differential item functioning (DIF), which exists when the difference in probabilities of a correct answer for two examinee groups changes signs as ability level is varied. The procedure estimates the matching subtest score at which crossing…

Imposed a two-level regression model on the ability parameters in an item response theory (IRT) model. Uses a simulation study and an empirical data set to show that the parameters of the two-parameter normal ogive model and the multilevel model can be estimated in a Bayesian framework using Gibbs sampling. (SLD)

Smallest exact confidence intervals for the ability parameter of the Rasch model are derived and compared to the traditional asymptotically valid intervals based on Fisher information. Tables of exact confidence intervals, termed Clopper-Pearson intervals, can be drawn up with a computer program developed by K. Klauer. (SLD)