Data evolving from processes which are developmental or hierarchical in nature are often analyzed by using latent class or latent structure models. A procedure for estimating such models when the model is not "identifiable" is presented. (JKS)

Examines the main mathematical approaches to information retrieval, including both algebraic and probabilistic models, and describes difficulties which impede formalization of information retrieval processes. A number of developments are covered where new theoretical understandings have directly led to improved retrieval techniques and operations.…

Recent advances in item analysis have provided greater capabilities for the analysis of tests, but have also significantly increased the gap between the theory and practice of item analysis. This paper traces the lines of development in item analysis under latent trait theory. (MV)

Proposes a mathematical model using the probability formalism to explain why a geometrical law is observed in distributions related to library circulation data. Highlights include techniques based on convolution theory; Lotka's law; and Bradford's law. (Author/LRW)

Presents a formal method for making important one-shot decisions based on an elimination process which uses sequentially acquired information and is based on a conditional belief structure. The routine updating of the structure as information accumulates is based on Dempster's rule of combination. (15 references) (EAM)

Describes habituation and addiction, both psychological and physiological, using simple equations of mathematical model of ideodynamics, optimized to smoking data from Multiple Risk Factor Intervention Trial (MRFIT) program. With only four constant parameters, it was possible to calculate accurate time trends for recidivism to smoking among…

Describes several activities of the Data and Chance program involving third and fourth graders. Students use real-life situations to investigate probability. (MKR)

This paper proposes a generalization of Thurstonian probabilistic choice models for analyzing both multiple preference responses and their relationships. The approach is illustrated by modeling data from two multivariate preference experiments. Preliminary data analyses show that the extension can yield an adequate representation of multivariate…

We focus on the problem of ignoring statistical independence. A binomial experiment is used to determine whether judges could match, based on looks alone, dogs to their owners. The experimental design introduces dependencies such that the probability of a given judge correctly matching a dog and an owner changes from trial to trial. We show how…

Methodological issues of using a class of neural networks called Mixture Density Networks (MDN) for discriminant analysis are discussed. MDN models have the advantage of having a rigorous probabilistic interpretation, and they have proven to be a viable alternative as a classification procedure in discrete domains. Both classification and…

The probability integral of the multivariate normal distribution (ND) has received considerable attention since W. F. Sheppard's (1900) and K. Pearson's (1901) seminal work on the bivariate ND. This paper evaluates the formula that represents the "n x n" correlation matrix of the "chi(sub i)" and the standardized multivariate…

The use of a Bayesian approach in evaluating data from clinical trials with many treatment centers and from many studies is discussed. The main distinction between a metaanalysis and an analysis of a multicenter trial is that different studies may have very different designs, while the centers in a multicenter trial usually follow the same…

A method of estimating the parameters of the Rasch Model removing the effect of ramdom guessing is presented. The procedure is an application of the ARRG (Abilities Removing Random Guessing) model recently developed for two parameter latent trait models. Under the Rasch model ARRG provides for estimation of abilities, removing the effects of…

This paper explains the concept of models, their construction, and their use. It is suggested that mathematics is a helpful tool in model construction, and that models in general are indispensable in science. Models identify variables and illustrate causal relationships among the variables. An attempt is made to classify models from the point of…

The area investigated in the present study is the comparison of the permutation t-test with Student's t-test and the Mann-Whitney U-test. The comparison was made for small samples for three distributions, including a normal distribution, a uniform distribution, and a skewed distribution. The properties of each test compared were the probability of…