When the highest-way association is present in a 3-way cross-classification of frequencies, standard logit and loglinear models have an many parameters as there are cells in the table; that is, the models are "saturated." Extensions of logit and loglinear models are described here that provide more parsimonious alternatives to saturated…

This study formulates a property of a quantification method, the principle of equivalent partitioning. When used with Guttman's principle of internal consistency, the combination allows the analysis of correlational data in terms of the variate(s) chosen by the investigator. Applications to multiple-choice, rank-order, and paired comparison data…

Statistical methods are presented to facilitate a more complete analysis of results obtained when a scaling model is applied to data from two or more groups. Various kinds of scaling models are considered here in the multiple-group context. (Author/LMO)

Ideal point discriminant analysis (IPDA) is proposed for the analysis of contingency tables of cross-classified data. Several data sets illustrate IPDA, which combines log-linear and dual scaling models to provide a spatial representation of row and column categories and allow statistical evaluation of various structural hypotheses about…

An approximate relationship is devised between the unidimensional model used in data analysis and a multidimensional model hypothesized to be generating the item responses. Scale shrinkage is successfully predicted for several sets of simulated data. (Author/LMO)

Outlines the general techniques of Guttman scale analysis and briefly describes its uses in social science research. To illustrate the potential application to library science, a Guttman scale of restrictiveness in dealing with overdue books is developed and data from a 1986 survey of public libraries are fitted into the scale. (23 references)…

Given "T" joint observations on "K" variables, it is frequently useful to consider the weighted average or scaled score. L-scaling is introduced as a technique for determining the weights. The technique is so named because of its resemblance to the Leontief matrix of mathematical economics. L-scaling is compared to two…

A scaling technique known as the Method of Reciprocal Averages has been in use since the early 1930's. This technique yields a set of item response weights for a psychological inventory which maximizes the internal consistency of the inventory for a group of subjects. Although the technique has been used for many years, its mathematical…

This special issues describes multidimensional scaling (MDS), with emphasis on proximity and preference models. An introduction and six papers review statistical developments in MDS study design and scrutinize MDS research in four areas of application (consumer, social, cognitive, and vocational psychology). (SLD)

A formal analysis is presented of the effects of item deletion on equating/scaling functions and reported score distributions. The phrase "item deletion" refers to the process of changing the original key of a flawed item to either all options correct, including omits, or to no options correct, i.e., not scoring the flawed item. There…

This study examined how four commonly used test equating procedures (linear, equipercentile, Rasch Model, and three-parameter) would respond to situations in which the properties or the two tests being equated were different. Data for two tests plus an external anchor test were generated from a three parameter model in which mean test differences…

A generalized Rasch model is presented for measuring attitudes; it is based on the concepts of Thurstone's method of successive intervals. Benefits of the model are illustrated with a study of students' (N=4,035 fifth through ninth graders) interest in physics. (SLD)

Three item response models were evaluated for estimating item parameters and equating test scores. The models, which approximated the traditional three-parameter model, included: (1) the Rasch one-parameter model, operationalized in the BICAL computer program; (2) an approximate three-parameter logistic model based on coarse group data divided…

The 1990 National Assessment of Educational Progress (NAEP) will mark the first time that state-level comparisons will be possible with NAEP data. The 1990 data will contain, as a trial component, state-level assessments of eighth graders in mathematics. Mathematics and reading comparisons for fourth graders will be added in 1992. Statistical…

This paper focuses on the questions which arise as test practitioners monitor score scales derived from latent trait theory. Large scale assessment programs are dynamic and constantly challenge the assumptions and limits of latent trait models. Even though testing programs evolve, test scores must remain reliable indicators of progress.…