ILLINOIS UNIV AT URBANA Dept. of STATISTICS
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Works:  11 works in 11 publications in 1 language and 11 library holdings 

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ILLINOIS UNIV AT URBANA Dept. of STATISTICS
Instrumentation for Computational Statistical Research(
Book
)
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
This is the final report of a grant issued under the University Research Instrumentation Program. Computing equipment was purchased to establish a network of 14 Sun workstations. This network made a variety of research efforts in the area of design and analysis of computational experiments. This report details purchases and related publications. Keywords: Probability density function estimation; Monte Carlo method; Statistical tests; Bibliographics. (KR)
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
This is the final report of a grant issued under the University Research Instrumentation Program. Computing equipment was purchased to establish a network of 14 Sun workstations. This network made a variety of research efforts in the area of design and analysis of computational experiments. This report details purchases and related publications. Keywords: Probability density function estimation; Monte Carlo method; Statistical tests; Bibliographics. (KR)
A Procedure to Detect Item Bias Present Simultaneously in Several Items(
Book
)
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
This paper presents a statistical procedure (denoted by SIB) designed to test for undirectional test bias existing simultaneously in several items of an ability test. It was argued in Shealy and Stout (1991) that in order to model such bias with an IRT model, a multidimensional model is necessary. The proposed procedure, based on this multidimensional IRT modeling approach, statistically tests for bias in one or more items at a time and is corrected for the inflation (or deflation) of the test statistic due to target ability difference, a valid group difference that is conceptually independent of psychological test bias. The correction plays the same role as the practice of including the single studied item in the matching criterion score in the MantelHaenszel (MH) procedure adapted for test responses by Holland and Thayer (1988). It is shown through the initial portion of an extensive simulation study underway (Shealy (1991)) that, with the correction in place, the procedure performs as well as the MH procedure in many cases when there is a single biased item, and performs well in the case of multiple item test bias
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
This paper presents a statistical procedure (denoted by SIB) designed to test for undirectional test bias existing simultaneously in several items of an ability test. It was argued in Shealy and Stout (1991) that in order to model such bias with an IRT model, a multidimensional model is necessary. The proposed procedure, based on this multidimensional IRT modeling approach, statistically tests for bias in one or more items at a time and is corrected for the inflation (or deflation) of the test statistic due to target ability difference, a valid group difference that is conceptually independent of psychological test bias. The correction plays the same role as the practice of including the single studied item in the matching criterion score in the MantelHaenszel (MH) procedure adapted for test responses by Holland and Thayer (1988). It is shown through the initial portion of an extensive simulation study underway (Shealy (1991)) that, with the correction in place, the procedure performs as well as the MH procedure in many cases when there is a single biased item, and performs well in the case of multiple item test bias
Simultaneous DIF Amplification and Cancellation: ShealyStout's Test for DIF by
Ratna Nandakumar(
Book
)
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
The present study investigates the phenomena of simultaneous DIF amplification and cancellation and SIBTEST's role in detecting such. A variety of simulated test data were generated for this purpose. In addition, real test data from various sources were used. The results from both simulated as well as real test data, as Shealy and Stout's theory suggests, show that the SIBTEST is effective in assessing the DIF amplification and cancellation (partially or fully) at the test score level. Finally, methodological and substantive implications of DIF amplification and cancellation are discussed. SIBTEST, DIF, Item bias, Test bias, Bias amplification, Bias cancellation
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
The present study investigates the phenomena of simultaneous DIF amplification and cancellation and SIBTEST's role in detecting such. A variety of simulated test data were generated for this purpose. In addition, real test data from various sources were used. The results from both simulated as well as real test data, as Shealy and Stout's theory suggests, show that the SIBTEST is effective in assessing the DIF amplification and cancellation (partially or fully) at the test score level. Finally, methodological and substantive implications of DIF amplification and cancellation are discussed. SIBTEST, DIF, Item bias, Test bias, Bias amplification, Bias cancellation
Tuning Complex Computer Code to Data(
Book
)
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
The problem of estimating parameters in a complex computer simulator of a nuclear fusion reactor from an experimental database is treated. Practical limitations do not permit a standard statistical analysis using nonlinear regression methodology. The assumption that the function giving the true theoretical predictions is a realization of a Gaussian stochastic process provides a statistical method for combining information from relatively few computer runs with information from the experimental database and making inferences on the parameters
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
The problem of estimating parameters in a complex computer simulator of a nuclear fusion reactor from an experimental database is treated. Practical limitations do not permit a standard statistical analysis using nonlinear regression methodology. The assumption that the function giving the true theoretical predictions is a realization of a Gaussian stochastic process provides a statistical method for combining information from relatively few computer runs with information from the experimental database and making inferences on the parameters
Progress in characterizing strictly unidimensional IRT representations by
Brian W Junker(
)
1 edition published in 1990 in English and held by 0 WorldCat member libraries worldwide
Item response theory, IRT, is a modern attempt to modeland statistically analyzeexaminee responses on standardized achievement or aptitude tests. IRT modeling and analysis, which occurs at the level of individual test questionsitemis greatly facilitated by the assumption of unidimensionality, i. e. that the latent trait driving the item responses is a onedimensional, typically realvalued, random variable. Birnbaum (1968) and Lord (1980) provide complete accounts of traditional unidimensional IRT. In this paper we are concerned with general characterization of (the distributions of) item response data for which traditional unidimensional IRT representations exist. For our purposes, a test is simply a vector of J items, or equivalently J binary (0/1) item response variables representing the correctness of responses of a randomly chosen examinee to the J test items
1 edition published in 1990 in English and held by 0 WorldCat member libraries worldwide
Item response theory, IRT, is a modern attempt to modeland statistically analyzeexaminee responses on standardized achievement or aptitude tests. IRT modeling and analysis, which occurs at the level of individual test questionsitemis greatly facilitated by the assumption of unidimensionality, i. e. that the latent trait driving the item responses is a onedimensional, typically realvalued, random variable. Birnbaum (1968) and Lord (1980) provide complete accounts of traditional unidimensional IRT. In this paper we are concerned with general characterization of (the distributions of) item response data for which traditional unidimensional IRT representations exist. For our purposes, a test is simply a vector of J items, or equivalently J binary (0/1) item response variables representing the correctness of responses of a randomly chosen examinee to the J test items
Assessing Essential Dimensionality of Real Data by
Ratna Nandakumar(
)
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
The purpose of this article is to validate the capability of DIMTEST to assess essential dimensionality of the model underlying the item responses of real test as opposed to simulated tests. A variety of real test data from different sources are used to assess essential dimensionality. Based on DIMTEST results, some test data are assessed as fitting an essential unidimensional model while others are not. Essential unidimensional test data, as assessed by DIMTEST, are then combined to form twodimensional test data. The power of Stout's statistic T is examined for these twodimensional data. It is shown that the results of DIMTEST on real tests replicate findings from simulated tests in that the statistic T discriminates well between essential unidimensional and multidimensional tests. It is also highly sensitive to major abilities while being insensitive to relatively minor abilities influencing item responses
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
The purpose of this article is to validate the capability of DIMTEST to assess essential dimensionality of the model underlying the item responses of real test as opposed to simulated tests. A variety of real test data from different sources are used to assess essential dimensionality. Based on DIMTEST results, some test data are assessed as fitting an essential unidimensional model while others are not. Essential unidimensional test data, as assessed by DIMTEST, are then combined to form twodimensional test data. The power of Stout's statistic T is examined for these twodimensional data. It is shown that the results of DIMTEST on real tests replicate findings from simulated tests in that the statistic T discriminates well between essential unidimensional and multidimensional tests. It is also highly sensitive to major abilities while being insensitive to relatively minor abilities influencing item responses
The Asymptotic Posterior Normality of the Latent Trait in an IRT Model(
)
1 edition published in 1991 in English and held by 0 WorldCat member libraries worldwide
It has long been part of the Item Response Theory (IRT) folklore that under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test. Under very general non parametric assumptions, we make this claim rigorous for a broad class of latent models
1 edition published in 1991 in English and held by 0 WorldCat member libraries worldwide
It has long been part of the Item Response Theory (IRT) folklore that under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test. Under very general non parametric assumptions, we make this claim rigorous for a broad class of latent models
Essential Independence and LikelihoodBased Ability Estimation for Polytomous Items(
)
1 edition published in 1991 in English and held by 0 WorldCat member libraries worldwide
A definition of essential independence is proposed for sequences of polytomous items. For items satisfying the reasonable assumption that the expected amount of credit awarded increases with examinee ability, we develop a theory of essential unidimensionality which closely parallels that of Stout. Essentially unidimensional item sequences can be shown to have a unique (up to changeofscale) dominant underlying trait, which can be consistently estimated by a monotone transformation of the sum of the item scores. In more general polytomousresponse latent trait models (with or without ordered responses), an Mestimator based upon maximum likelihood may be shown to be consistent for theta under essentially unidimensional violations of local independence and a variety of monotonicity/identifiability conditions. A rigorous proof of this fact is given, and the standard error of the estimator is explored. These results suggest that ability estimation methods that rely on the summation form of the log likelihood under local independence should generally be robust under essential independence, but standard errors may vary greatly from what is usually expected, depending on the degree of departure from local independence. An index of departure from local independence is also proposed
1 edition published in 1991 in English and held by 0 WorldCat member libraries worldwide
A definition of essential independence is proposed for sequences of polytomous items. For items satisfying the reasonable assumption that the expected amount of credit awarded increases with examinee ability, we develop a theory of essential unidimensionality which closely parallels that of Stout. Essentially unidimensional item sequences can be shown to have a unique (up to changeofscale) dominant underlying trait, which can be consistently estimated by a monotone transformation of the sum of the item scores. In more general polytomousresponse latent trait models (with or without ordered responses), an Mestimator based upon maximum likelihood may be shown to be consistent for theta under essentially unidimensional violations of local independence and a variety of monotonicity/identifiability conditions. A rigorous proof of this fact is given, and the standard error of the estimator is explored. These results suggest that ability estimation methods that rely on the summation form of the log likelihood under local independence should generally be robust under essential independence, but standard errors may vary greatly from what is usually expected, depending on the degree of departure from local independence. An index of departure from local independence is also proposed
Assessing Dimensionality of a Set of Items Comparison of Different Approaches by
Ratna Nandakumar(
)
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
This study examines the performance of the following four methodologies for assessing unidimensionality: DIMTEST, Holland and Rosenbaum's approach, linear factor analysis, and nonlinear factor analysis. Each method is examined and compared with other methods on simulated data sets and on real data sets. Seven data sets, all with 2000 examinees, were generated: three unidimensional, and four twodimensional data sets. Two levels of correlation between abilities were considered: p=.3 and p=.7. Eight different real data sets were used: four of them were expected to be unidimensional, and the other four were expected to be twodimensional. Findings suggest that, while the linear factor analysis often overestimated the number of underlying dimensions, the other three methods correctly confirmed unidimensionality but differed in their ability to detect lack of unidimensionality. DIMTEST showed excellent power in detecting lack of unidimensionality; Holland and Rosenbaum's and nonlinear factor analysis approaches showed good power, provided the correlation between abilities was low
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
This study examines the performance of the following four methodologies for assessing unidimensionality: DIMTEST, Holland and Rosenbaum's approach, linear factor analysis, and nonlinear factor analysis. Each method is examined and compared with other methods on simulated data sets and on real data sets. Seven data sets, all with 2000 examinees, were generated: three unidimensional, and four twodimensional data sets. Two levels of correlation between abilities were considered: p=.3 and p=.7. Eight different real data sets were used: four of them were expected to be unidimensional, and the other four were expected to be twodimensional. Findings suggest that, while the linear factor analysis often overestimated the number of underlying dimensions, the other three methods correctly confirmed unidimensionality but differed in their ability to detect lack of unidimensionality. DIMTEST showed excellent power in detecting lack of unidimensionality; Holland and Rosenbaum's and nonlinear factor analysis approaches showed good power, provided the correlation between abilities was low
Refinements of Stout's Procedure for Assessing Latent Trait Unidimensionality by
Ratna Nandakumar(
)
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
This paper provides a detailed investigation of Stout's statistical procedure (the computer program DIMTEST) for testing the hypothesis that an essentially unidimensional latent trait model fits observed binary item response data from a psychological test. One finding was that DIMTEST may fail to perform as desired in the presence of guessing when coupled with many highdiscriminating items. A revision of DIMTEST is proposed to overcome this limitation. Also, an automatic approach is devised to determine the size of the assessment subtests. Further, an adjustment is made on the estimated standard error of the statistic on which DIMTEST depends. These three refinements have led to an improved procedure that is shown in simulation studies to adhere closely to the nominal level of significance while achieving considerably greater power. Finally, DIMTEST is validated on a selection of real data sets
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
This paper provides a detailed investigation of Stout's statistical procedure (the computer program DIMTEST) for testing the hypothesis that an essentially unidimensional latent trait model fits observed binary item response data from a psychological test. One finding was that DIMTEST may fail to perform as desired in the presence of guessing when coupled with many highdiscriminating items. A revision of DIMTEST is proposed to overcome this limitation. Also, an automatic approach is devised to determine the size of the assessment subtests. Further, an adjustment is made on the estimated standard error of the statistic on which DIMTEST depends. These three refinements have led to an improved procedure that is shown in simulation studies to adhere closely to the nominal level of significance while achieving considerably greater power. Finally, DIMTEST is validated on a selection of real data sets
An Item Response Theory Model for Test Bias(
)
1 edition published in 1991 in English and held by 0 WorldCat member libraries worldwide
A multidimensional nonparametric IRT model of test bias is presented, providing an explanation of how individuallybiased items can combine through a test score to produce test bias. The claim is thus that bias, though expressed at the item level, should be studied at the test level. The model postulates an intendedtobemeasured target ability and nuisance determinants whose differing ability distributions across examinee group cause bias. Multiple nuisance determinants can produce item bias cancellation, resulting in little or no test bias. Detection of test bias requires a valid subtest, whose items measure only target ability. A longtest viewpoint of bias is also developed
1 edition published in 1991 in English and held by 0 WorldCat member libraries worldwide
A multidimensional nonparametric IRT model of test bias is presented, providing an explanation of how individuallybiased items can combine through a test score to produce test bias. The claim is thus that bias, though expressed at the item level, should be studied at the test level. The model postulates an intendedtobemeasured target ability and nuisance determinants whose differing ability distributions across examinee group cause bias. Multiple nuisance determinants can produce item bias cancellation, resulting in little or no test bias. Detection of test bias requires a valid subtest, whose items measure only target ability. A longtest viewpoint of bias is also developed
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