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A general approach is proposed for modeling the structure of a two-way contingency table, and for drawing inferences about the marginal and interaction effects, cell parameters, and conditional probabilities. The prior distribution expresses uncertainty in a simple reduced model, in particular the independence model. The posterior estimates of the cell parameters then provide compromises between the cell frequencies and fitted values obtained under the reduced model. In a mental test context, the reduced independece model is identical to Rasch's multiplicative Poisson model, and we therefore incorporate a procedure for checking the adequacy of this model. Using some general ideas on marginalization, it is possible to compute reasonable approximations to the full posterior densities of many parameters of interest thus permitting thorough parametric inference and statistical modeling. It is possible to proceed with the full interaction model even in the presence of zero cell frequencies. All prior parameters are evaluated with the assistance of the data via a hierarchical Bayes procedure, thus permitting the sensible analysis of data sets. An r x s cross classification of 5648 Marine Corps clerical students by school and test grade is analyzed in detail and the posterior densities of the 96 possible interactions are used to suggest a simplified structure partitioning and collapsing the table into a meaningful 3 x 2 table. Keywords include: Contingency tables, Marginalization.

Allan Birnbaum made two historical contributions to the theories of statistics and educational testing. The first was his famous 1962 proof that the sufficiency and conditionality principles together imply the likelihood principle, thus justifying conditional, e.g., Bayesian, inference when compared with frequentist inference. The second was his famous mental test model introduced in Lord and Novick (1968). This proposal attempts to follow in Birnbaum's tradition by using Bayesian ideas to show that his mental test model possesses even broader applicability than hitherto realized. A conditional maximization procedure is used to approximate numerical integrations thus broadening the scope of Bayesian inference and model checking. Additional keywords: Exchangeability, Computer programs, Normal distribution.

The presence of differences between prediction systems for males and females is investigated through a detailed study of clerical specialties in the Marine Corps. When various aptitude composites are used to predict success of recruits in training, sizeable differences in regression functions are found between male and female groups. The paper shows that selected deletion of extraneous ASVAB(Armed Services Vocational Aptitude Battery) variables maintains overall predictive efficiency but does not remove the differences between male and female regressions. However, when the attainment of a high school diploma is considered, differential prediction is substantially reduced. Implications of these empirical results for the general problem of military personnel selection are discussed. Originator-supplied key words include: Differential prediction, Johnson-Neyman technique, and Personnel selection.

This paper considers the application of Bayesian techniques for simultaneous estimation to the specification of regression weights for selection tests used in various technical training courses in the Marine Corps. Results of a method for m-group regression developed by Molenaar and Lewis (1979) suggest that common weights for training courses belonging to certain general categories are justified in many cases. However, such commonality of regression weights does not appear to hold for all courses in these categories--weights for some training courses remain distinct even after the application of the simultaneous estimation procedure. Thus, a hypothesis of validity generalization across training courses in a given category would only be retained for a carefully selected subset of courses and not for all groups included in the analyses. Keywords include: simultaneous estimation; m-group regression; personnel selection.

THIS REPORT ESTIMATES THE HEAT LOSSES FROM THE HEAT DISTRIBUTION SYSTEM AT Fort Wainwright, Alaska. Specific data on the Fort Wainwright heat and power plant are given and a method is then developed to calculate the heat losses from buried utilidor systems, such as the one at Fort Wainwright. This method is programmed for computer execution and estimates are made for the Fort Wainwright system, where heat losses are found to be 204,500 MBtu/yr. Possible improvements to the system to reduce heat losses are examined. Of the possible combinations of additional pipe insulation investigated, the addition of 1 in. of insulation to the steam pipe only is the most economically favorable. The results also indicate that insulating only the generally larger pipes found in larger utilidors would be the most economically favorable approach. Possible reductions in heat losses due to reduced steam temperature are also given, as well as recommendations for refinement of the predictions. (Author)