A general program for item-response analysis is described that uses the stabilized Newton-Raphson algorithm. This program is written to be compliant with Fortran 2003 standards and is sufficiently general to handle independent variables, multidimensional ability parameters, and matrix sampling. The ability variables may be either polytomous or…

Continuous exponential families may be employed to find continuous distributions with the same initial moments as the discrete distributions encountered in typical applications of classical equating. These continuous distributions provide distribution functions and quantile functions that may be employed in equating. To illustrate, an application…

Continuous exponential families are applied to linking forms via a single-group design. In this application, a distribution from the continuous bivariate exponential family is used that has selected moments that match those of the bivariate distribution of scores on the forms to be linked. The selected continuous bivariate distribution then yields…

Some probabilistic illustrations of the reliability coefficient are provided to assist in interpretation of this measure. All explanations are derived under the assumption that the joint distribution of examinee scores from two parallel tests is well approximated by a bivariate normal distribution.

Latent-class item response models with small numbers of latent classes are quite competitive in terms of model fit to corresponding item-response models, at least for one- and two-parameter logistic (1PL and 2PL) models. Provided that care is taken in terms of computational procedures and in terms of use of only limited numbers of latent classes,…

Criteria for prediction of multinomial responses are examined in terms of estimation bias. Logarithmic penalty and least squares are quite similar in behavior but quite different from maximum probability. The differences ultimately reflect deficiencies in the behavior of the criterion of maximum probability.

Multinomial-response models are available that correspond implicitly to tests in which a total score is computed as the sum of polytomous item scores. For these models, joint and conditional estimation may be considered in much the same way as for the Rasch model for right-scored tests. As in the Rasch model, joint estimation is only attractive if…

When a simple random sample of size n is employed to establish a classification rule for prediction of a polytomous variable by an independent variable, the best achievable rate of misclassification is higher than the corresponding best achievable rate if the conditional probability distribution is known for the predicted variable given the…