Mastery Assessment with Latent Class and Quasi-Independence Models Representing Homogeneous Item Domains

“…In addition to the mastery models that are constrained forms of the ajf3J model, two other models have been presented in the literature (see Bergan, Cancelli, & Luiten, 1980;Knapp, 1977). Both of these models may be conceptualized as constrained forms of a &dquo;multi-state model&dquo; in which there are more than two mutually exclusive and exhaustive latent states defining mastery.…”

Section: Mnltt-state Mastery and Additional Latent State Modelsmentioning

confidence: 99%

“…The second multi-state mastery model, called the YJ3 model, which is also a constrained form of the a;(3;y,k model, was presented recently by Bergan, Cancelli, & Luiten (1980). This model (which is a special case of the &dquo;quasi-independence&dquo; model presented by Goodman, 1975) incorporates three latent states: nonmasters, (k=1); masters, (k=2); and &dquo;intrinsically unscalables,&dquo; (k=3).…”

Section: Mnltt-state Mastery and Additional Latent State Modelsmentioning

confidence: 99%

“…where A is an established loss ratio of false negative loss over false positive loss. Macready and and Bergan et al (1980) have developed similar optimizing decision rules, which in the generalized form presented here may be used with the a;(3, model, the apjy,,: model, or any of the models they subsume to minimize expected loss due to misclassification. However, this procedure implements mastery classification by separate assessment of each observed response pattern rather than by assessment of total scores.…”

Section: Implementation Of Mastery Classificationmentioning

confidence: 99%

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The Nature and Use of State Mastery Models

Macready

Dayton

1980

Applied Psychological Measurement

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This paper provides a review of a class of probabilistic models that has been developed for use in the assessment of trait or competency acquisition. Consideration is given to the relative merits and limitations of this class of state models, under which trait acquisition is conceived as being "all-ornone," as compared with those occurring under an alternative conceptual framework, in which trait acquisition is assumed to be gradual. In addition, some of the applications of these state models are presented, including the establishment of mastery classification decisions and the assessment of consistency with respect to items and classification. Finally, some extensions to the class of state models, which may be helpful in increasing the applicability of this class of models, are presented. An important element of the criterion-referenced approach to testing is the assessment of individuals in terms of absolute standards of attainment for traits or competencies of interest; and within this context, the concept of &dquo;mastery&dquo; has played a central role. To deal with this classification problem, a variety of strategies have been suggested (see Hambleton & Eignor, 1979). Meskauskas (1976) pointed out that most of these strategies can be grouped into two general classes based on the underlying conceptualization of the trait being assessed. Within the first class, called continuum models, trait acquisition is assumed to be gradual and mastery is viewed as an interval on a test score scale. Within the second class, called state models, trait acquisition is conceived of as an &dquo;all-or-none&dquo; process and mastery is viewed as the presence of trait acquisition. Limitatlons of Continuum Models From the perspective of continuum models, mastery of a trait is based on &dquo;sufficient&dquo; partial acquisition of that trait. Thus, mastery classification involves a judgmentally established point or set of points on the trait continuum. An integral part of procedures used to establish rules for mastery classification within the framework of continuum models, mentioned by both Linn (1978) and Glass (1978), is their fundamentally judgmental nature, resulting in rules for classification that are arbitrary. This arbitrariness presents a problem for effective implementation of the procedures; and as might be expected, consistency of mastery classifications both within and across procedures often is

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“…The various models employ decision rules to identify the cutoff score that minimizes expected loss due to classification errors (see, e.g., Bergan, Cancelli, & Luiten, 1980;Emrick, 1971;Macready & Dayton, 1977). These rules require judgment in designating the loss ratio.…”

Section: State Modelsmentioning

confidence: 99%

A Framework for Methodological Advances in Criterion-Referenced Testing

Berk

1980

Applied Psychological Measurement

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A vast body of methodological research on criterion-referenced testing has been amassed over the past decade. Much of that research is synthesized in the articles contained in this issue. The fact that this issue is devoted exclusively to criterion-referenced testing sets it apart as a quintessential journal publication on the topic. This paper is intended to provide a broad framework for understanding and evaluating the individual contributions in the context of the literature. The six articles appear to fall into four major categories: (1) test length; (2) validity; (3) standard setting; and (4) reliability. These categories correspond to most of the technical topics in the test development process (see, e.g., Berk, 1980b;Hambleton, 1980). Test LengthIf a teacher or curriculum specialist asked a psychometrician, 'How many items should be written for each objective?' or 'How many items should be sampled from the domain?' what answer could be given? Whether the test is norm referenced or criterion referenced, there is no available source that recommends a magical number of items. The guidelines offered in most measurement texts and technical papers on the topic are rather nonspecific; however, this perplexing issue cannot be dismissed or ignored, as are the properties of validity and reliability analyzed in subsequent sections of this paper. Every test maker, teacher through test publisher, must answer the test length question.The problem of determining test length can be approached from a practical perspective based on research evidence and/or from a purely technical perspective. The former has been explicated previously in terms of a multiplicity of factors, including importance and type of decision making, importance and emphases assigned to objectives, number of objectives, and practical constraints (Berk, 1980c); the latter constitutes the orientation of Wilcox's article.Wilcox has organized his review according to three achievement test conceptualizations based on three different types of true score: (1) the number of items a student would answer correctly if every item in the item domain was answered; (2) the proportion of skills among a domain of skills that a APPLIED

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Mastery Assessment with Latent Class and Quasi-Independence Models Representing Homogeneous Item Domains

Cited by 12 publications

References 0 publications

A Structural Approach to the Validation of Hierarchical Training Sequences

A Structural Approach to the Validation of Hierarchical Training Sequences

The Nature and Use of State Mastery Models

A Framework for Methodological Advances in Criterion-Referenced Testing

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