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The primary purpose of this paper is to improve on the specification of job experience as measured by current age, minus age at completion of formal schooling. The process of acquiring productive job skills was modeled by first focusing on the determination of the level of first-job occupation and then, given initial occupation, examining the determinants of occupational advancement. The impact of initial occupational level and occupational change on current (1966) wage rates were then examined. In the empirical analysis, separate equations for middle-aged black and white men were estimated to focus on racial differences in the acquisition of labor market experience. The primary finding is that it is work experience accompanied by occupational advancement, rather than work experience per se, that has an effect on the distribution of wage rates. (Author/HD)

The logical and psychological bases for setting cutting scores for criterion-referenced tests are examined; they are found to be intrinsically arbitrary and are often examples of misdirected precision and axiomatization. The term, criterion referenced, originally referred to a technique for making test scores meaningful by controlling the test development process. It has since been applied to a variety of mathematical techniques for setting cutting scores. However, because of the nature of tests and the nature of education, no process of quantification will alter the critical concern, the definition of mastery or of minimal competence, which remains either unanswered or vaguely approximate. Different methods of setting cutting scores may provide widely divergent solutions to a given problem. It is important to recognize that cutting scores are arbitrary. However, no criticism is implied with respect to criterion reference or domain reference as techniques of test construction. (CTM)

A discussion is presented concerning variables associated with children's representation of certain addition and subtraction problems. Problem components are classified as physical, pictorial, sensual, verbal-spoken, verbal-written, symbolic, or internal. Problems are discussed as abstract (symbolic) or nonsymbolic. Three problem components are identified and discussed: (1) measurable entities, (2) contextual relationships or actions on entities, and (3) characteristics of the missing number. The second component is further broken down into joining, separating, equalizing, part-part-whole, and comparison. Problem structure is also discussed. (MK)

An important class of applications of measurement error or constrained factor analytic models consists of comparing models for several populations. In such cases, it is appropriate to make explicit statistical tests of model similarity across groups and to constrain some parameters of the models to be equal across groups using a priori substantive information. This paper discusses a statistical model developed by K. G. Joreskog for these purposes. The model is applied to children's and parents' reports of parental socioeconomic statuses for several grade levels. The analysis, which includes data from sons' reports of the schooling and occupations of their mothers and fathers, suggests that children do not approach their parents' level of reporting accuracy at the same rate for all characteristics; however, by twelfth grade, sons and parents are equally reliable for all characteristics considered. (Author/GC)

A general process for testing the feasibility of applying alternative mathematical or statistical models to the solution of a practical problem is presented and flowcharted. The system is used to develop a plan to compare models for test equating. The five alternative models to be considered for equating are: (1) anchor test equating using classical test theory; (2) anchor test equating using the one-parameter logistic model; (3) anchor test equating using the three-parameter logistic model; (4) preequating using the one-parameter logistic model; and (5) preequating using the three-parameter logistic model. Sources of estimation instability are identified for the logistic models. Various practical and theoretical problems associated with the general process and test equating are discussed. The equating problem is of interest in its own right and serves to explicate the general process. (Author/RL)

Comparative applications of simple and complex faculty flow models are examined to determine (1) their relative demands for data and calculations, (2) the divergence of their projections, especially when modelling a no-growth faculty, and (3) an estimate of the error incurred (i.e., the cost to analysis) when a simple model is used. The results support the view that academic personnel policy changes have delayed effects and are nonlinear. It is suggested that simple models may mislead analysts by being insensitive, for example, to backlogs of term appointees who expect promotion. Similarly, it may be that no model is needed at all if one is only looking for estimates on a two-year horizon. (Author/SW)

In this paper, logistic response models of the effects of parental socioeconomic characteristics and family structure on the probability of making selected school transitions for white American males are estimated by maximum likelihood. Transition levels examined include: (l) completion of elementary school; (2) attendance at high school; (3) graduation from high school; (4) college attendance; (5) college graduation; and (6) graduate level education. It is shown that, as a consequence of the pattern of differential attrition, parental socioeconomic effects decline sharply from the earliest school transitions to the latest. Implications of differential socioeconomic background effects over schooling levels for understanding changes in level and distribution of schooling are discussed. (Author/GC)

In this paper, a theory of the academic achievement process of learning is proposed. Learning is seen as the outcome of the utilization of learning opportunities created in the teaching process by students themselves. These students are characterized by a certain level of ability and effort. The theory is first formulated in a single equation model for learning in which students' ability and effort is assumed constant over time. This model is then modified to take into account an interdependency between effort and achievement. Implications are derived of the proposed conceptions of the learning process for research on school effects and on inequality of educational opportunity. (Author/GC)

The development of a planning/budgeting model as an integral component of a decision support system is described. The case study approach is used to describe how Grambling State University (GSU) developed the model to improve its financial planning and budgeting processes. The model can be used for tactical and/or strategic planning. The model is discussed as an example of GSU's simulation/forecasting capability. The following four basic computerized data files are used to make extrapolations: credit hours, enrollment, personnel, and fee table. With the data files and output generated from other models, the model can be used to prepare simulations and forecasts about students, faculty, staff, state appropriations, other revenues, expenditures, surpluses, and deficits. An important feature of the planning/budgeting model is that the user can change the data elements. In addition the planning/budgeting model integrates data generated by other models, i.e., the salary planning, enrollment/recruitment, and institutional cost index models. Appendices provide detailed descriptions of the various data elements that are contained in the four basic files. Also included are a list of outputs generated by the planning/budgeting model, and examples of calculations that are performed by the model. (SW)

A mathematical model designed to identify admitted college applicants who pay a tuition deposit but fail to attend the college was tested. A two-group discriminant model was built using 486 Trinity University students who paid deposits and enrolled as freshmen during the 1983-1984 academic year, and 72 persons who paid tuition deposits but did not enroll as freshmen. The variables included in the discriminant model were: verbal and mathematics Scholastic Aptitude Test scores, high school rank, high school grade point average, sex, amount of financial aid provided, and place of residence (in-state or out-of-state). For the 1983-1984 year, a significant difference was found between the two groups. The discriminant weights from this model were then applied to persons who paid deposits for entrance into the 1984-1985 freshman class. In this academic year, the model tested 610 students who paid deposits and enrolled and 79 persons who paid deposits but did not enroll. The second statistical analysis validated the previous year findings of a significant difference between the two groups. The accuracy of prediction was 75 percent for the 1983-1984 group and 68 percent for the 1984-1985 group. (SW)

Analytical techniques used in responding to a series of four substantial budget reductions imposed at Oregon State University are described. Over a 2-year period, each of the budget reductions demanded increasingly severe institutional action to meet the specified monetary targets. Different analytical techniques were required to meet the changing circumstances. For the first modest budget cut in June 1980, the analytical tool employed was the log-linear plot, line graphs of the student credit hour (SCH) trends for each of the university's schools and colleges. A logarithmic scale was used to identify academic units that would receive differential budget cuts. After severe budget cuts during 18 months, a computerized budget reduction model was developed that was designed to differentiate among various major categories of expense within overall budgets. Two sets of weighting factors were used for this mathematical model. Finally, in cases where program reduction or elimination was indicated, an effort was made to act equitably among affected units. The analytical tool used to define such equity was the Induced Work Load Matrix, which shows the way in which students majoring in one discipline generate SCH (and thus workload and resource requirements) in other departments. Illustrations of the use of these techniques are included. (SW)

This study develops a weighted least squares method for transforming a logistic scale in such a way that the estimates of ability parameters on the tranformed scale are as comparable as possible with those on another scale. This scale tranformation process is referred to as equating of scales. Equating is an important procedure in studies involving the logistic model and the latent trait model in general; the equating method presented deals with situations in which there are two separately scaled tests that have only some items in common (vertical equating or horizontal equating) or all items in common (horizontal equating). The necessity for equating in the later case arises when two scales have been derived by using two different groups of examinees which may have different characteristics pertinent to the results of scaling. In the former case (only some items common), the groups of examinees may or may not be overlapped. As one of the optimum estimation procedures, a weighted least squares method is introduced and applied to an achievement scale and an intelligence test. An advantage of the method over previously proposed methods is that highly discriminating items tend to affect equating more strongly than less discriminating items. (Author/RL)

This study developed a two-parameter linear probabilistic model of criterion referenced measurement, which relates an examinee's observed ability to his true ability through a guessing parameter and a carelessness parameter, both of which are probabilities. This model was applied to a survey of 10- and 14-year-old Australian students to estimate the proportion who had been able to master basic skills in mathematics and literacy. The estimates were derived by using a Bayesian inferential procedure incorporating the developed measurement model within a beta-binomial, decision-theoretic framework based on a two-state conception of mastery and non-mastery. The results of a computer simulation of the model indicate that guessing and carelessness may markedly affect the determination of passing scores, and hence the accuracy of decision about mastery. The computer program for calculating cutting scores, posterior probabilities, and prior and posterior distribution statistics is appended. (Author/CTM)

Designed for educational planners and decision makers, this report describes the application of mathematical procedures to depict the relationship of elements within models which represent the flow of students through an educational system. The introductory section includes a discussion of the history of the use of planning models in education and the steps in model development (variable identification, identification of variable interconnections, and operationalization and verification of the model). The next section reviews classification schemes for mathematical models of educational processes and presents a classification scheme developed for this report. Following this, examples of several classes of mathematical models of student flow are presented: extrapolation models; regression methods (simple first-order, polynomial, and multiple linear regression); and simultaneous equation models (non-optimizing models including the Markov Chain and optimizing models). Finally, the present utility of available mathematical models is discussed from the viewpoint of what effects these models have had on actual educational policy decision making. (Two related documents are also available in ERIC: Demography and Educational Planning [CE 019 499] and State and Local Responsibilities for Planning Occupational Education [ED 133 479].) (JH)

When several ability scales in item response models are separately derived from different test forms administered to different samples of examinees, these scales must be equated to a common scale because their units and origins are arbitrarily determined and generally different from scale to scale. A general method for equating logistic ability scales was developed that uses a least squares method with weights reflecting the relative importance of correct equating at the various values on the ability continuum. The method is characterized by explicit definition of the equating error on the probability scale, minimization of the overall error, and coherence of the equating in all directions. It is applicable when the test forms are linked by common items, and various linkage patterns can be used. When there are more than m - 1 links among m test forms, a restricted solution is provided to insure an internally consistent system of equatings. Results of the application of the method to many computer-generated data sets indicated that the accuracy of the obtained estimates of the equating constants was generally satisfactory and that the number of common items in the linked pairs of test forms was the most important factor in determining the accuracy of estimation. (Author/GK)

The Feldt-Gilmer congeneric reliability coefficients make it possible to estimate the reliability of a test composed of parts of unequal, unknown length. The approximate standard errors of the Feldt-Gilmer coefficients are derived via a method using the multivariate Taylor's expansion. Monte Carlo simulation is employed to corroborate the theoretical approximations for eight hypothetical tests. The Feldt-Gilmer coefficients are shown to be appropriate with both congeneric and tau-equivalent parts. Their superiority over the special case of Kristof's coefficient increases with the number of parts. Their standard errors also compare favorably to that of Cronbach's alpha coefficient when applied to tests with tau-equivalent parts. Tables illustrate the charts. (Author/CM)

Confirmatory factor analysis is presented as providing appropriate techniques for the analysis and evaluation of questionnaires and tests if the content of the measure can be identified as consisting of groups of items, with each group measuring only a single trait. This approach is contrasted with latent trait theory which assumes (and does not test) the assumption of unidimensionality. The first step in the analysis is the partitioning of the items into distinct scales or clusters, preferably on the basis of an a priori analysis of item content, although blind exploratory statistical methods may be substituted. The parameters of the model are estimated by oblique multiple groups factor analysis and include the correlations between items and factors, the correlations between the factors, and the communality of each item. This analysis will confirm, or disconfirm, the measurement model specified by the user. Chi square tests are provided for unidimensionality of clusters and parallelism. Appendices contain proofs and computer programs. (Author/CTM)

This document consists of seven chapters. The first chapter analyzes the modeling process and gives reasons for introducing a modeling approach in classrooms, arguing that students will develop more confident and positive attitudes toward mathematics. The next five chapters contain case studies, which focus, respectively on: whether it is more economical to rent or buy a television set; how pricing policy affects profit; how a rear window wiper should be positioned on an automobile to sweep the maximum area; the mathematics of the long jump; and which of three schools should be shut due to declining enrollments (by calculating traveling time by different modes of transportation). Each of these chapters includes: an introduction to the problem to be modeled, with prerequisites and the target age-range (and learning objectives, when applicable); list of assumptions on which the model is based; an influence diagram showing the relationship between factors; model development (which may consist of several parts); and a concluding section which draws out implications and gives ideas for further work. Assessment items are included for several models. The final chapter contains a list of models which could be used in the classroom together with a list of references and a bibliography. (JN)

A study was conducted to describe the segments of the U.S. labor force that have been affected by the recent deterioration in U.S. trade. The methodology involved computer modeling of the effects of eliminating the 1987 merchandise trade deficit on employment by detailed industry and occupation, by geographic region, and by wage group. This was done by calculating the number of jobs of different characteristics and in different industries that are required for the production of merchandise exports and those that would be required for the domestic production of imports. All computations were made with an input-output model of the U.S. economy using the most recent trade data (1987), providing a consistent framework for simultaneously computing the detailed production requirements of every industry. The advantage of this approach was that it allowed the calculation of all production requirements for satisfying a given bill of final deliveries, in this case, imports and exports. Specific findings were as follows: (1) the record trade deficit in 1987 represented a loss of 5.1 million job opportunities, 2 million of which were lost between 1984 and 1987; (2) 60 percent, or 3.1 million of the total 5.1 million jobs lost, were in manufacturing, and the remaining 2 million jobs were lost in industries closely related to manufacturing, primarily in business services; (3) each of the four regions lost over 1 million jobs because of the trade deficit, with the Midwest and the West each losing 1.4 million jobs; and (4) the wages of the jobs from trade were more likely to be high-wage jobs. The most important conclusions were that the employment effects of the trade deficit are large and more dispersed in the economy than commonly believed. (A 14-item reference list and two appendices, one on U.S. Merchandise Trade in 1987 and one on methodology and classifications, are attached.) (NLL)