Developments in the Design of Experiments, Correspondent Paper

Atkinson, Anthony C.

doi:10.2307/1402599

Cited by 86 publications

(34 citation statements)

References 80 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several other optimality criteria-defined as a function of the asymptotic variance-covariance matrix of ML estimators-have been proposed in the literature for optimal designs. One review of these criteria is given by Atkinson (1982). Each of these measures has advantages in specific situations and may be more or less sensitive to different scale restrictions of the parameters.…”

Section: Discussionmentioning

confidence: 99%

On the Efficiency of IRT Models When Applied to Different Sampling Designs

Berger

1991

Applied Psychological Measurement

View full text Add to dashboard Cite

The problem of obtaining designs that result in the greatest precision of the parameter estimates is encountered in at least two situations in which item response theory (IRT) (1976). Although this result has been used to stress the importance of multiple-matrix sampling designs, the question still remains whether these designs are also efficient to estimate IRT parameters.As the sampling concept from survey analysis gained currency in educational measurement, the interest in alternative sampling designs increased. In large-scale assessment studies, it would save considerable classroom administration time if only a subset of items instead of a whole test is administered to the examinees. Whether such a selection of items would influence the efficiency of the item parameter estimates will depend on the assumed IRT model.The efficiency of designs is considered here in terms of a generalized variance criterion connected with IRT parameters, and this criterion is used to compare the efficiencies of designs for the one-,

show abstract

Section: Discussionmentioning

confidence: 99%

On the Efficiency of IRT Models When Applied to Different Sampling Designs

Berger

1991

Applied Psychological Measurement

View full text Add to dashboard Cite

show abstract

“…The deterninant or D-optimality criterion is then the (weighted) product of the diagonal elements. Of course, alternative criteria belonging to the family ~(~), such as the E-optimality and the A-optimality criteria (see Atkinson, 1982), or the MAXIMIN-optimality criterion (Van der Linden & Boekkooi-Timminga, 1989), also can be applied. A review of these alternative criteria is given by Berger & van der Linden (1992) and Berger & Veerkamp (in press Berger (1992aBerger ( , 1992bBerger ( , 1994 In adaptive testing, the Os are re-estimated after each step; therefore, elk) in Equation 7 is replaced by its estimate and will generally not be the same in each step because of the stepwise updating of 0.…”

Section: ~®T~tion and Assumptionsmentioning

confidence: 99%

A General Approach to Algorithmic Design of Fixed-Form Tests, Adaptive Tests, and Testlets

Berger

1994

Applied Psychological Measurement

View full text Add to dashboard Cite

The selection of items from a calibrated item bank for fixed-form tests is an optimal test design problem; this problem has been handled in the literature by mathematical (1971, 1980) and Weiss (1976, 1978) The purpose of administering achievement tests is to obtain an efficient estimate of the trait levels of a sample of examinees. The trait estimates obtained from different test types, however, may differ in efficiency. The purpose of the present study was to stress the similarities in designing fixed-form tests, adaptive tests, and testlets using optimal design theory. Reviews of optimal design theory are given by Silvey (1980) and Ford, Kitsos, & Titterington (1989).

show abstract

“…Nowadays, optimum design is a respected field of statistical research with numerous theoretical results and applications. Reviews of the literature on optimum design can be found in Atkinson (1982), Silvey (1980), and Steinburg and Hunter (1984). Though the original interest was in linear models, remarkable results have been derived for nonlinear models too.…”

Section: Optimum Design In Irt: Applications To Test Assembly and Itementioning

confidence: 99%

Optimum Design in Item Response Theory: Test Assembly and Item Calibration

Linden

1994

Recent Research in Psychology

View full text Add to dashboard Cite

The idea of optimizing experimental design to give estimators maximal efficiency has been around in the statistical literature for several decades, but its applicability to sampling problems in item response theory (IRT) has not been widely noticed. It is the purpose of this paper to show how optimum design principles C&ll be used to improve item &lid examinee sampling in IRT-based test assembly and item calibration. For both applications a result based on the maximin principle is given. The maximin principle fits these applications naturally, because IRT models are nonlinear and involve criteria of optimality that are dependent on the unknown parameters. Optimum Design in IRT: Applications to Test Assembly and Item CalibrationThe main topics addressed in statistics are parameter estimation and hypothesis testing. For both topics the literature has produced fruitful methods of finding estimators and test statistics as well as important criteria to evaluate their performances. Most statistical theory is based on the assumption of simple random sampling, and it seems safe to assert that the majority of the statisticians have hardly any interest in sampling beyond this assumption. Two exceptions to this practice are known, though. One is the interest in more complicated sampling procedures than simple random sampling, notably in the domain of survey research (Kalton, 1983; Sarndal, Swensson, and Wretman, 1992). Another exception began with the pioneering work on optimum design of statistical experiments by R. A. Fisher, who, ironically, can also be considered the founder of mainstream statistics. Fisher's work originated in the domain of linear models. Linear models have the important aspect that they focus on the outcomes of statistical experiments in which the statistician may have control over some of the variables, and hence is able to design an experiment in which sampling with respect to estimation of the parameters is optimal. An example is the experiment underlying the estimation of the parameters in a bivariate linear regression model in which the predictor is a fixed variable and the statistician can select the levels of this predictor. Likewise, if the predictor is a random variable, the statistician may have control of the probabilities with which the levels of the lUniversity of Twente,

show abstract

Developments in the Design of Experiments, Correspondent Paper

Cited by 86 publications

References 80 publications

On the Efficiency of IRT Models When Applied to Different Sampling Designs

On the Efficiency of IRT Models When Applied to Different Sampling Designs

A General Approach to Algorithmic Design of Fixed-Form Tests, Adaptive Tests, and Testlets

Optimum Design in Item Response Theory: Test Assembly and Item Calibration

Contact Info

Product

Resources

About