The Gain-Loss model is a probabilistic skill multimap model for assessing learning processes. In practical applications, more than one skill multimap could be plausible, while none corresponds to the true one. The article investigates whether constraining the error probabilities is a way of uncovering the best skill assignment among a number of…

This paper is concerned with supplementing statistical tests for the Rasch model so that additionally to the probability of the error of the first kind (Type I probability) the probability of the error of the second kind (Type II probability) can be controlled at a predetermined level by basing the test on the appropriate number of observations.…

With reference to a questionnaire aimed at assessing the performance of Italian nursing homes on the basis of the health conditions of their patients, we investigate two relevant issues: dimensionality of the latent structure and discriminating power of the items composing the questionnaire. The approach is based on a multidimensional item…

Conjoint choice experiments are used widely in marketing to study consumer preferences amongst alternative products. We develop a class of choice models, belonging to the class of Poisson race models, that describe a "random utility" which lends itself to a process-based description of choice. The models incorporate a dependence structure which…

Most item response theory models are not robust to violations of conditional independence. However, several modeling approaches (e.g., conditioning on other responses, additional random effects) exist that try to incorporate local item dependencies, but they have some drawbacks such as the nonreproducibility of marginal probabilities and resulting…

The problem of selecting (from several bionomial populations) the one with the highest probability is discussed in this brief article. Several approximate solutions are offered and the solution is extended to bivariate correlation. (Author/JKS)

As the literature indicates, no method is presently available which takes explicitly into account that the parameters of Lazarsfeld's latent class analysis are defined as probabilities and are therefore restricted to the interval (0,1). An appropriate transform on the parameters is presented in order to satisfy this constraint. (Author/JKS)

This note extends and elaborates Hubert's attempt to provide an interpretation of Freeman's measure of association, theta. The theta measure is used in a contingency table when observations are ordered on one variable and unordered on the other. No attempt is made to explore the distribution of theta. (Author/RC)

Probabilistic assumptions are added to single and multidimensional versions of the Coombs unfolding model for preferential choice (Coombs, 1950) and practical ways of obtaining maximum likelihood estimates of the scale parameters and goodness-of-fit tests of the model are presented. A Monte Carlo experiment is discussed. (Author/RC)

Tukey's scheme for finding separations in univariate data strings is described and tested. It is found that one can use the size of a data gap coupled with its ordinal position in the distribution to determine the likelihood of its having arisen by chance. (Author/JKS)

A computational short cut suggested by Feldman and Klinger for the one-sided Fisher-Yates exact test is clarified and is extended to the calculation of probability values for certain two-sided tests when sample sizes are unequal. (Author)

It is shown that common factors are not subject to indeterminancy to the extent that has been claimed (Guttman, 1955), because the measure of indeterminancy that has been adopted is ill-founded. (Author/RC)

The small-world problem revolves around the tracing of a line of acquaintances linking any two persons chosen at random. Statistical analysis of data from two experimental studies of the problem and estimation of parameters in two previously proposed models is discussed along with the models' goodness of fit. (Author/RC)