Univariate and Bivariate Loglinear Models for Discrete Test Score Distributions

Holland, Paul W.; Thayer, Dorothy T.

doi:10.2307/1165330

Cited by 57 publications

(96 citation statements)

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“… Population X, V bivariate score distributions for P and other population Y, V bivariate score distributions for Q were created as averages of the raw data (Tables 3 and 4) and representative, smooth loglinear models of the raw data (Holland & Thayer, 2000). The loglinear models’ bivariate distributions were smooth versions of the raw data, which matched the correlations, means, standard deviations, skewness, etc.…”

Section: Methodsmentioning

confidence: 99%

Comparison of the One‐ and Bi‐Direction Chained Equipercentile Equating

Moses

2012

J Educational Measurement

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This study investigated differences between two approaches to chained equipercentile (CE) equating (one-and bi-direction CE equating) in nearly equal groups and relatively unequal groups. In one-direction CE equating, the new form is linked to the anchor in one sample of examinees and the anchor is linked to the reference form in the other sample. In bi-direction CE equating, the anchor is linked to the new form in one sample of examinees and to the reference form in the other sample. The two approaches were evaluated in comparison to a criterion equating function (i.e., equivalent groups equating) using indexes such as root expected squared difference, bias, standard error of equating, root mean squared error, and number of gaps and bumps. The overall results across the equating situations suggested that the two CE equating approaches produced very similar results, whereas the bi-direction results were slightly less erratic, smoother (i.e., fewer gaps and bumps), usually closer to the criterion function, and also less variable.

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Section: Methodsmentioning

confidence: 99%

Comparison of the One‐ and Bi‐Direction Chained Equipercentile Equating

Moses

2012

J Educational Measurement

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“…To implement the PSE predictions we first used polynomial loglinear models (Holland & Thayer, 2000) to presmooth the bivariate distribution of ( X , A ) obtained from P and the bivariate distribution of ( Y , A ) from Q . These models are discussed briefly in the next section.…”

Section: The Predictions Of Pse and Ce For The Missing Datamentioning

confidence: 99%

“…First, to get an overall view of how well the predictions track the observed frequencies, we graph the observed and predicted frequencies together. To focus attention on the differences between the observed and predicted frequencies, we also graph their Freeman‐Tukey (FT) residuals (Holland & Thayer, 2000). The FT‐residuals have the form, where, n i denotes the observed frequencies and m i the predicted frequencies for either CE or PSE.…”

Section: The Predictions Of Pse and Ce For The Missing Datamentioning

confidence: 99%

“…Second, to get a more summary assessment of the agreement between the observed and predicted frequencies we use three standard goodness‐of‐fit measures—likelihood ratio chi‐square, Pearson chi‐square, and sum of squared FT‐residuals (Holland & Thayer, 2000; Read & Cressie, 1988). The following formulas define these measures: …”

Section: The Predictions Of Pse and Ce For The Missing Datamentioning

confidence: 99%

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An Approach to Evaluating the Missing Data Assumptions of the Chain and Post‐stratification Equating Methods for the NEAT Design

Holland¹,

Sinharay²,

Davier³

et al. 2008

J Educational Measurement

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Two important types of observed score equating (OSE) methods for the nonequivalent groups with Anchor Test (NEAT) design are chain equating (CE) and post-stratification equating (PSE). CE and PSE reflect two distinctly different ways of using the information provided by the anchor test for computing OSE functions. Both types of methods include linear and nonlinear equating functions. In practical situations, it is known that the PSE and CE methods will give different results when the two groups of examinees differ on the anchor test. However, given that both types of methods are justified as OSE methods by making different assumptions about the missing data in the NEAT design, it is difficult to conclude which, if either, of the two is more correct in a particular situation. This study compares the predictions of the PSE and CE assumptions for the missing data using a special data set for which the usually missing data are available. Our results indicate that in an equating setting where the linking function is decidedly non-linear and CE and PSE ought to be different, both sets of predictions are quite similar but those for CE are slightly more accurate.

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“…subgroups. An algorithm using Newton's Method to estimate the β i s is available in Holland and Thayer (2000).…”

Section: Log-linear Smoothing Modificationmentioning

confidence: 99%

Differential item functioning procedures for polytomous items when examinee sample sizes are small

Wood¹

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As part of test score validity, differential item functioning (DIF) is a quantitative characteristic used to evaluate potential item bias. In applications where a small number of examinees take a test, statistical power of DIF detection methods may be affected.Researchers have proposed modifications to DIF detection methods to account for small focal group examinee sizes for the case when items are dichotomously scored. These methods, however, have not been applied to polytomously scored items.Simulated polytomous item response strings were used to study the Type I error rates and statistical power of three popular DIF detection methods (Mantel test/Cox's β, Liu-Agresti statistic, HW3) and three modifications proposed for contingency tables (empirical Bayesian, randomization, log-linear smoothing). The simulation considered two small sample size conditions, the case with 40 reference group and 40 focal group examinees and the case with 400 reference group and 40 focal group examinees.In order to compare statistical power rates, it was necessary to calculate the Type I error rates for the DIF detection methods and their modifications. Under most simulation conditions, the unmodified, randomization-based, and log-linear smoothingbased Mantel and Liu-Agresti tests yielded Type I error rates around 5%. The HW3 statistic was found to yield higher Type I error rates than expected for the 40 reference group examinees case, rendering power calculations for these cases meaningless. Results from the simulation suggested that the unmodified Mantel and Liu-Agresti tests yielded the highest statistical power rates for the pervasive-constant and pervasive-convergent patterns of DIF, as compared to other DIF method alternatives. Power rates improved by several percentage points if log-linear smoothing methods were applied to the contingency tables prior to using the Mantel or Liu-Agresti tests. Power rates did not improve if Bayesian methods or randomization tests were applied to the contingency tables prior to using the Mantel or Liu-Agresti tests. ANOVA tests showed that 2011 All Rights Reserved Graduate College

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Univariate and Bivariate Loglinear Models for Discrete Test Score Distributions

Cited by 57 publications

References 0 publications

Comparison of the One‐ and Bi‐Direction Chained Equipercentile Equating

Comparison of the One‐ and Bi‐Direction Chained Equipercentile Equating

An Approach to Evaluating the Missing Data Assumptions of the Chain and Post‐stratification Equating Methods for the NEAT Design

Differential item functioning procedures for polytomous items when examinee sample sizes are small

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