A maximum likelihood estimation procedure was developed to fit unweighted and weighted additive models to conjoint data obtained by the categorical rating, the pair comparison or the directional ranking method. The scoring algorithm used to fit the models was found to be both reliable and efficient, and the program MAXADD is capable of handling up to 300 parameters to be estimated. Practical uses of the procedure are reported to demonstrate various advantages of the procedure as a statistical method.

In the last decade several authors discussed the so-called minimum trace factor analysis (MTFA), which provides the greatest lower bound (g.l.b.) to reliability. However, the MTFA fails to be scale free. In this paper we propose to solve the scale problem by maximization of the g.l.b. as the function of weights. Closely related to the primal problem of the g.l.b. maximization is the dual problem. We investigate the primal and dual problems utilizing convex analysis techniques. The asymptotic distribution of the maximal g.l.b. is obtained provided the population covariance matrix satisfies sone uniqueness and regularity assumptions. Finally we outline computational algorithms and consider numerical examples.

The importance of appropriate test selection for a given research endeavor cannot be overemphasized. Using samples drawn from eleven populations (differing in shape, peakedness, and density in the tails), this study investigates the small sample empirical powers of nine k-sample tests against ordered location alternatives under completely randomized designs. The results then are intended to aid the researcher in the selection of a particular procedure appropriate for a given endeavor. To highlight this an industrial psychology application involving work productivity is presented.

Bounds are here developed for the multiple correlation of common factors with the items whose factors they are. It is then easy to see, under broad but not completely general conditions, the circumstances under which an infinite item domain does or does not perfectly determine selected subsets of its common factors.

This paper is concerned with the study of covariance structural models in several populations. Estimation theory of the parameters that are subject to general functional restraints is developed based on the generalized least squares approach. Asymptotic properties of the constrained estimator are studied; and asymptotic chi-square tests are presented to evaluate appropriate model comparisons. The method of multipliers and the standard reparametrization technique are discussed in obtaining the estimates. The methodology is demonstrated by a set of real data.

A Bayesian framework for making mastery/nonmastery decisions based on multivariate test data is described in this study. Overall, mastery is granted (or denied) if the posterior expected loss associated with such action is smaller than the one incurred by the denial (or grant) of mastery. An explicit form for the cutting contour which separates mastery and nonmastery states in the test score space is given for multivariate normal test scores and for a constant loss ratio. For multiple cutting scores in the true ability space, the test score cutting contour will resemble the boundary defined by multiple test cutting scores when the test reliabilities are reasonably close to unity. For tests with low reliabilities, decisions may very well be based simply on a suitably chosen composite score.

The concept of sequential estimation is introduced in multidimensional scaling (MDS). The sequential estimation method developed in this paper refers to continually updating estimates of a configuration as new observations are added. This method has a number of advantages, such as a locally optimal design of the experiment can be easily constructed, and dynamic experimentation is made possible. Using artificial data, the performance of our sequential method is illustrated.

The polyserial and point polyserial correlations are discussed as generalizations of the biserial and point biserial correlations. The relationship between the polyserial and point polyserial correlation is derived. The maximum likelihood estimator of the polyserial correlation is compared with a two-step estimator and with a computationally convenient ad hoc estimator. All three estimators perform reasonably well in a Monte Carlo simulation. Some practical applications of the polyserial correlation are described.

An algorithm, using a short cut due to Feldman and Klingler, for the Fisher-Yates exact test is presented: the algorithm is quick, simple and accurate.

A Monte Carlo study was conducted to investigate the ability of three estimation criteria to recover the parameters of Case V and Case III models from comparative judgment data. Significant differences in recovery are shown to exist.