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...

The most probable distribution method is applied to derive the logistic model as the distribution accounting for the maximum number of possible outcomes in a dichotomous test while introducing latent traits and item characteristics as constraints to the system. The item response theory logistic...

In measuring latent variables, marketing research currently defines measurement as the assignment of numerals to objects. On this basis, marketing researchers utilize a multitude of avenues to measurement. However, the scientific concept of measurement requires the discovery of a specific...

Item response theory models are measurement models for categorical responses. Traditionally, the models are used in educational testing, where responses to test items can be viewed as indirect measures of latent ability. The test items are scored either dichotomously (correct–incorrect) or by...

Analyzing latent variables is becoming more and more important in several fields, such as clinical research, psychology, educational sciences, ecology, and epidemiology. The item response theory allows analyzing latent variables measured by questionnaires of items with binary or ordinal...

The statistical measures used by the U.S. Department of Agriculture since 1995 to monitor the food security of the Nation’s households—the extent to which they can consistently acquire adequate food for active healthy living—are based on a single-parameter logistic latent-trait measurement...