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Browsing by Author "Zeng, Lingjia"

Now showing 1 - 5 of 5
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    An alternative approach for IRT observed-score equating of number-correct scores
    (1995) Zeng, Lingjia; Kolen, Michael J.
    An alternative approach for item response theory observed-score equating is described. The number-correct score distributions needed in equating are found by numerical integration over the theoretical or empirical distributions of examinees’ traits. The item response theory true-score equating method and the observed-score equating method described by Lord, in which the number-correct score distributions are summed over a sample of trait estimates, are compared in a real test example. In a computer simulation, the observed-score equating methods based on numerical integration and summation were compared using data generated from standard normal and skewed populations. The method based on numerical integration was found to be less biased, especially at the two ends of the score distribution. This method can be implemented without the need to estimate trait level for individual examinees, and it is less computationally intensive than the method based on summation. Index terms: equating, item response theory, numerical integration, observed-score equating.
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    A numerical approach for computing standard errors of linear equating
    (1993) Zeng, Lingjia
    A numerical approach for computing standard errors (SEs) of a linear equating is described. In the proposed approach, the first partial derivatives of the equating function needed to compute the SEs are derived numerically. Thus, the difficulty of deriving the analytical formulas of the partial derivatives for a complicated equating method is avoided. The numerical and analytical approaches were compared using the Tucker equating method. The SEs derived numerically were found to be indistinguishable from the SEs derived analytically. In a computer simulation of the numerical approach using the Levine equating method, the SEs based on the normality assumption were found to be less accurate than those derived without the normality assumption when the score distributions were skewed. Index terms: common-item design, Levine equating method, linear equating, standard error of equating, Tucker equating method.
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    The optimal degree of smoothing in equipercentile equating with postsmoothing
    (1995) Zeng, Lingjia
    The effects of different degrees of smoothing on the results of equipercentile equating in the random groups design using a postsmoothing method based on cubic splines were investigated. A computer-based procedure was introduced for selecting a desirable degree of smoothing. The procedure was based on two criteria: (1) that the equating function is reasonably smooth, as evaluated by the second derivatives of the cubic spline functions, and (2) that the equated score distributions are close to that of the old form. The equating functions obtained from smoothing the equipercentile equivalents by a fixed smoothing degree and a degree selected by the computer-based procedure were evaluated in computer simulations for four tests. The results suggest that no particular fixed degree of smoothing always led to an optimal degree of smoothing. The degrees of smoothing selected by the computer-based procedure were better than the best fixed degrees of smoothing for two of the four tests studied; for one of the other two tests, the degrees selected by the computer procedure performed better or nearly as well as the best fixed degrees. Index terms: computer simulation, cubic spline, equating, equipercentile equating, smoothing.
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    Standard errors of a chain of linear equatings
    (1994) Zeng, Lingjia; Hanson, Bradley A.; Kolen, Michael J.
    A general delta method is described for computing the standard error (SE) of a chain of linear equatings. The general delta method derives the SEs directly from the moments of the score distributions obtained in the equating chain. The partial derivatives of the chain equating function needed for computing the SEs are derived numerically. The method can be applied to equatings using the common-items nonequivalent populations design. Computer simulations were conducted to evaluate the SEs of a chain of two equatings using the Levine and Tucker methods. The general delta method was more accurate than a method that assumes the equating processes in the chain are statistically independent. Index terms: chain equating, delta method, equating, linear equating, standard error of equating.
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    Standard errors of Levine linear equating
    (1993) Hanson, Bradley A.; Zeng, Lingjia; Kolen, Michael J.
    The delta method was used to derive standard errors (SEs) of the Levine observed score and Levine true score linear equating methods. SEs with a normality assumption as well as without a normality assumption were derived. Data from two forms of a test were used as an example to evaluate the derived SEs of equating. Bootstrap SEs also were computed for the purpose of comparison. The SEs derived without the normality assumption and the bootstrap SEs were very close. For the skewed score distributions, the SEs derived with the normality assumption differed from the SEs derived without the normality assumption and the bootstrap SEs. Index terms: equating, delta method, linear equating, score equating, standard errors of equating.