An Expected Utility Model for "Optimal" Selection

Petersen, Nancy S.

doi:10.2307/1164987

Cited by 23 publications

(36 citation statements)

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“…The regression model is the most widely used model in fairness selection within the predictive context. Gross and Su (1975) and Petersen (1976) used threshold utility and derived the cut-scores from the posterior predictive distributions of the regression model. The following analysis demonstrates that these distributions are not always PSI and that the use of cut-scores is not necessarily justified in all cases.…”

Section: Cut-scores In Regression Modelsmentioning

confidence: 99%

“…Applications of Bayesian decision theory to the problems of personnel selection and classification have recently been studied by Gross and Su (1975), Huynh (1976Huynh ( , 1977, Novick and Petersen (1976), Lindley (1978, 1979), Petersen (1976), Petersen and Novick (1976) and Van der Linden and In a mastery decision, there are two categories, mastery (selection) and nonmastery (nonselection). It is reasonable to assume that the utility for granting mastery status is a nondecreasing function of a person 1 s ability, and the utility for denying mastery status is nonincreasing.…”

Section: Introductionmentioning

confidence: 99%

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Theory and Practice for the use of Cut-Scores for Personnel Decisions

Chuang

Chen

Novick

1981

Journal of Educational Statistics

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Cut-scores are commonly used in industrial personnel selection, academic selection, minimum competence certification testing, and professional licensing, using simple and multiple-person/multiple-job category decision paradigms. Previous approaches have proposed cut-score solutions in a variety of applications using threshold, normal ogive, linear and discrete utility functions. This paper considers these results by investigating conditions on the posterior, likelihood and utility functions required for setting a cut-score in a Bayesian decision approach. Generalizing and extending results of Lehmann, Karlin, Ferguson and others, it is shown that cut-scores are appropriate in a wide range of applications, but they are less than universally appropriate. Following this, a general paradigm and computational algorithm for cut-score solutions is developed under the assumption that the conditions for a cut-score have been satisfied.at Bibliothekssystem der Universitaet Giessen on June 15, 2015 http://jebs.aera.net Downloaded from 130 Chuang, Ckw and Hoviak Mellenbergh (1977). There are two fundamental elements in all Bayesian decision-theoretic models: probabilities and utilities (or losses). The probabilities express the decision maker's uncertainty about the possible outcome of an action that may be taken and the utilities express the relative values associated with possible outcomes. The optimal procedure prescribed by Bayesian decision theory is to take that action that maximizes expected utility.Consider a situation in which there are several categories and a group of applicants. Given the utility function of each category and the individual outcome, a classification problem is to assign each applicant to one and only one category so that the decision maximizes (total) expected utilities. Karlin and Rubin (1956), Karlin (1957aKarlin ( , 1957b showed that if the difference of two utilities is monotonic and the probability distribution has monotone likelihood ratio then the decision rule is monotonic (Ferguson, 1967).

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Section: Cut-scores In Regression Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Theory and Practice for the use of Cut-Scores for Personnel Decisions

Chuang

Chen

Novick

1981

Journal of Educational Statistics

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“…Hambleton and Novick (1973), Gross and Su (1975), Huynh (1976a), Petersen (1976), and Mellenbergh, Koppelaar, and van der Linden (1977) used threshold loss functions. For a cutting score c on the observed score X and a cutting score d on the variable Z, the threshold loss function is Petersen (1976) has pointed out that the threshold loss function is rather unrealistic. For example, in the threshold loss function it is supposed that for all accepted, not suitable subjects the amount of loss is equal.…”

Section: Optimality Versus Consistencymentioning

confidence: 99%

The Internal and External Optimality of Decisions Based on Tests

Mellenbergh

Linden

1979

Applied Psychological Measurement

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In applied measurement, test scores are usually transformed to decisions. Analogous to classical test theory, the reliability of decisions has been defined as the consistency of decisions on a test and a retest or on two parallel tests. Coefficient kappa (Cohen, 1960) is used for assessing the consistency of decisions. This coefficient has been developed for assessing agreement between nominal scales. It is argued that the coefficient is not suited for assessing consistency of decisions. Moreover, it is argued that the concept consistency of decisions is not appropriate for assessing the quality of a decision procedure. It is proposed that the concept consistency of decisions be replaced by the concept optimality of the decision procedure. Two types of optimality are distinguished. The internal optimality is the risk of the decision procedure with respect to the true score the test is measuring. The external optimality is the risk of the decision procedure with respect to an external criterion. For assessing the optimality of a decision procedure, coefficient delta (van der Linden & Mellenbergh, 1978), which can be considered a standardization of the Bayes risk or expected loss, can be used. Two loss functions are dealt with: the threshold and the linear loss functions. Assuming psychometric theory, coefficient delta for internal optimality can be computed from empirical data for both the threshold and the linear loss functions. The computation of coefficient delta for external optimality needs no assumption of psychometric theory. For six tests coefficient delta as an index for internal optimality is computed for both loss functions; the results are compared with coefficient kappa for assessing the consistency of decisions with the same tests.

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“…Following Gross and Su (1975) and Petersen (1974) assume that the applicants to an institution can be separated into two subpopulations referred to as the disadvantaged population (ir ) and the advantaged population (TO .…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…We shall deal only with a single predictor variable. The multi-predictor case is treated by Petersen (1974).…”

Section: Posterior Predictive Distributionmentioning

confidence: 99%

An Expected Utility Model for “Optimal” Selection

Petersen

1976

Journal of Educational Statistics

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The Threshold Utility Model for culture-fair selection introduced by Gross and Su (1975) and by Petersen (1974) is defined here for both quota-free and for restricted selection. In addition, a full Bayesian solution based on posterior predictive distributions is provided. By providing a mechanism for coherently combining probabilities and utilities, this model makes it possible to determine an optimal selection strategy in all situations in which a threshold utility function is applicable. This paper studies the mathematical properties of the solution in detail in the case of quota-free selection. In the more complex restricted selection case, the study lacks some detail but is more complete than that given by Gross and Su and should be adequate for most practical purposes. Several data analyses highlight the strengths and weaknesses of the model.

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An Expected Utility Model for "Optimal" Selection

Cited by 23 publications

References 0 publications

Theory and Practice for the use of Cut-Scores for Personnel Decisions

Theory and Practice for the use of Cut-Scores for Personnel Decisions

The Internal and External Optimality of Decisions Based on Tests

An Expected Utility Model for “Optimal” Selection

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