In experiments with paired comparisons, judges are occasionally allowed to express indifference between alternatives. For the analysis of such data, models for paired comparisons with ties are needed. Several models with tie parameters are reviewed. All are extensions of the basic models of L. L. Thurstone (1927) and R. A. Bradley and M. E. Terry…

This paper is concerned with estimation and hypothesis testing of treatment effects in nonequivalent control group designs with the assumption that in the absence of treatment effects, natural growth conforms to a particular class of continuous growth models. Point estimation, interval estimation, and hypothesis testing procedures were developed…

A general model for the homogeneous case of the continuous response is proposed. The model is an expansion and generalization of the one proposed by the author in 1974, in which the open response situation is dealt with. In this generalized model, the closed response situation is dealt with, and it includes the model for the open response…

The usefulness of path analysis as a means of better understanding various linear models is demonstrated. First, two linear models are presented in matrix form using linear structural relations (LISREL) notation. The two models, regression and factor analysis, are shown to be identical although the research question and data matrix to which these…

Reparameterization is used to find the maximum likelihood estimates of parameters in a multivariate model having some component variable observable only in polychotomous form. Maximum likelihood estimates are found by a Fletcher Powell algorithm. In addition, the partition maximum likelihood method is proposed and illustrated. (Author/GDC)

The most familiar models of item response theory are defined at the level of individual subjects. It is possible, however, to define such models for groups of subjects. This paper discusses group-level item response models, their uses, and their relationships to subject-level models. (Author/JKS)

A constrained quadratic spline is proposed as an estimator of the hazard function of a random variable. A maximum penalized likelihood procedure is used to fit the estimator to a sample of psychological response times. (Author/LMO)

Decomposable models, which allow for the interdependence of structure among observable variables, are described. Each model is fully characterized by a set of conditional interdependence restrictions and can be visualized with an undirected as well as a special type of directed graph. (Author/JKS)

Formulas for estimating the population measure of effect strength are based on the assumption that sample sizes are proportional to the sizes of their respective treatment populations. Because this assumption is frequently violated, a general method of estimating effect strength for the one-factor, fixed-effects design is presented. (Author/BW)

Generalizations of L. A. Goodman's RC(M) association model (1991 and earlier) are presented for three-way tables. These three-mode association models use L. R. Tucker's three-mode components model (1964, 1966) to represent the three-factor interaction or the combined effects of two- and three-factor interactions. (SLD)

Parameter recovery in the graded-response model was investigated using the MULTILOG computer program under default conditions. Results from 36 simulated data sets suggest that at least 500 examinees are needed to achieve adequate calibration under the graded model. Sample size had little influence on the true ability parameter's recovery. (SLD)

The concept of consensus ordering is defined, and formulas for exact and approximate posterior probabilities for consensus ordering are developed under the assumption of a generalized Mallows' model with a diffuse conjugate prior. These methods are applied to a data set concerning 98 college students. (SLD)

A Bayes estimation procedure for Rasch-type model estimation that has statistical and computational advantages over existing methods is described. It involves constructing posterior distributions based on sample data and artificial data reflecting prior information. Its use for some Rasch-type cases, and how it can improve parameter estimation are…

An alternating least squares algorithm is offered for fitting the DEcomposition into DIrectional COMponents (DEDICOM) model for representing asymmetric relations among a set of objects via a set of coordinates for the objects on a limited number of dimensions. An algorithm is presented for fitting the IDIOSCAL model in the least squares sense.…

Formulas for computing the exact signed and unsigned areas between two item characteristic curves (ICCs) are presented. It is further shown that when the "c" parameters are unequal, the area between two ICCs is infinite. The significance of the exact area measures for item bias research is discussed. (Author)