Maximum Likelihood Estimates in Exponential Response Models

Haberman, Shelby J.

doi:10.1214/aos/1176343941

Cited by 248 publications

(158 citation statements)

References 8 publications

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“…However, their statements regarding these estimators are at odds with the literature. Specifically, JR state that "…the typical test has relatively few items…" and directly below that "…student ability [is] …estimated directly via maximum likelihood … [and] resulting estimate is (approximately) unbiased in most cases…" (p. 95) However, the maximum likelihood estimator (MLE) for the latent trait in IRT models is not unbiased (Kiefer and Wolfowitz 1956;Andersen 1972;Haberman 1977). The extent of the bias is directly related to the number of items, so that MLEs for tests with "relatively few items" will exhibit a more pronounced bias, as well as considerable noise.…”

Section: Theories and Models Of Measurementmentioning

confidence: 99%

The use of test scores from large-scale assessment surveys: psychometric and statistical considerations

Braun

Davier

2017

Large-scale Assess Educ

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Section: Theories and Models Of Measurementmentioning

confidence: 99%

The use of test scores from large-scale assessment surveys: psychometric and statistical considerations

Braun

Davier

2017

Large-scale Assess Educ

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“…In addition, visiting scholars made seminal contributions as well. Among these contributions were ones on testing the Rasch model as well as on bias in estimates (Andersen 1972(Andersen , 1973, ideas later generalized by scholars elsewhere (Haberman 1977).…”

Section: Psychometric and Statistical Methodologymentioning

confidence: 99%

Advancing Human Assessment: A Synthesis Over Seven Decades

Bennett

Davier

2017

Methodology of Educational Measurement and Assessment

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This book has documented the history of ETS's contributions to educational research and policy analysis, psychology, and psychometrics. We close the volume with a brief synthesis in which we try to make more general meaning from the diverse directions that characterized almost 70 years of work.Synthesizing the breadth and depth of the topics covered over that time period is not simple. One way to view the work is across time. Many of the book's chapters presented chronologies, allowing the reader to follow the path of a research stream over the years. Less evident from these separate chronologies was the extent to which multiple streams of work not only coexisted but sometimes interacted.From its inception, ETS was rooted in Henry Chauncey's vision of describing individuals through broad assessment of their capabilities, helping them to grow and society to benefit (Elliot 2014). Chauncey's conception of broad assessment of capability required a diverse research agenda.Following that vision, his research managers assembled an enormous range of staff expertise. Only through the assemblage of such expertise could one bring diverse perspectives and frameworks from many fields to a problem, leading to novel solutions.In the following sections, we summarize some of the key research streams evident in different time periods, where each period corresponds to roughly a decade. Whereas the segmentation of these time periods is arbitrary, it does give a general This work was conducted while M. von Davier was employed with Educational Testing Service.

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“…The fact that parameters are estimated consistently implies that the estimations can get arbitrarily close to the true values if the number of observations is increased (Andersen, 1980). The consistency follows from the condition as formulated by Haberman (1977) for consistent JML estimation.…”

Section: The Rasch Modelmentioning

confidence: 99%

Analyzing experimental data using the Rasch model

Verguts

Boeck

Storms

1998

Behavior Research Methods, Instruments, & Computers

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We present a method for studying experimental data based on a psychometric model, the "Rasch model" (Rasch, 1966;Thissen & Steinberg, 1986). Weillustrate the method with the use of a data set in the field of concept research. More specifically, we investigate whether a conjunctive concept can be seen as an additive combination of its constituents, High correlations between model and data are obtained, but a formal goodness-of-fit test indicates that the model does not completely account for the data. We then alter the Rasch model in such a way as to capture our idea of why the model deviates from the data. This results in higher correlations and a strong increase in goodness-of-fit. It is concluded that our ideas, as incorporated in the model, adequately summarize the data. More generally, this research illustrates that applying the Rasch model and altering it according to one's hypotheses is an excellent way to analyze experimental data. 501In the perception literature, considerable attention has been paid to thefuzzy logic model ofperception (FLMP; see, e.g., Massaro & Hary, 1986; Oden, 1977). Recently, Crowther, Batchelder, and Hu (1995) have established the formal equivalence between this model and a particular psychometric model-namely, the Rasch model (Rasch, 1966;Thissen & Steinberg, 1986). In this paper, we explore the consequences ofthis linkage and apply the Rasch model (or, equivalently, the FLMP) to data on conjunctive concepts (see, e.g., Hampton, 1987Hampton, , 1988Storms, De Boeck, Van Mechelen, & Geeraerts, 1993;Storms, De Boeck, Van Mechelen, & Ruts, 1996). We first present the FLMP model, followed by the (equivalent) Rasch model. We then apply the model to empirical data and discuss its analysis. In the example, both models lead to the same conclusions, although some extra information is provided in the Rasch formulation. THE FUZZY LOGIC MODEL OF PERCEPTIONSuppose we perform a letter recognition experiment (e.g., Oden, 1979) and ask participants whether a stimulus 0i should be classified as a G or as a Q. Furthermore, suppose that c l i indicates the degree to which aspectj is present in stimulus°i: If aspectj is present in the letter G, the evidence for G with respect to aspectj is equal to c l i ; otherwise, it is equal to I -Clio The same reasoning applies for the letter Q. For example, given that both G and Qare made up ofan oval and a line, the first aspect might be "oval is open on the right." The evidence in 0i for G with respect to this first aspect is Cli; for Q, it is I -Cli' Similarly, the second aspect might be "line is horizontal."The authors thank Iven Van Mechelen, Norman Verhelst, and Johan Wagemans for their useful comments. Correspondence should be addressed to T. Verguts, Department of Psychology, Tiensestraat 102, B-3000 Leuven, Belgium (e-mail: tom.verguts@psy.kuleuven.ac.be).The evidence for G and Qin stimulus°i is then c2i and 1 -c2i' respectively.To continue with our example: The FLMP predicts that the probability of stimulus 0i to be classified as G [formally, Pr (o,...

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Maximum Likelihood Estimates in Exponential Response Models

Cited by 248 publications

References 8 publications

The use of test scores from large-scale assessment surveys: psychometric and statistical considerations

The use of test scores from large-scale assessment surveys: psychometric and statistical considerations

Advancing Human Assessment: A Synthesis Over Seven Decades

Analyzing experimental data using the Rasch model

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