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1.
Patrick O. Monahan Won-Chan Lee Robert D. Ankenmann 《Journal of Educational Measurement》2007,44(3):211-225
A Monte Carlo simulation technique for generating dichotomous item scores is presented that implements (a) a psychometric model with different explicit assumptions than traditional parametric item response theory (IRT) models, and (b) item characteristic curves without restrictive assumptions concerning mathematical form. The four-parameter beta compound-binomial (4PBCB) strong true score model (with two-term approximation to the compound binomial) is used to estimate and generate the true score distribution. The nonparametric item-true score step functions are estimated by classical item difficulties conditional on proportion-correct total score. The technique performed very well in replicating inter-item correlations, item statistics (point-biserial correlation coefficients and item proportion-correct difficulties), first four moments of total score distribution, and coefficient alpha of three real data sets consisting of educational achievement test scores. The technique replicated real data (including subsamples of differing proficiency) as well as the three-parameter logistic (3PL) IRT model (and much better than the 1PL model) and is therefore a promising alternative simulation technique. This 4PBCB technique may be particularly useful as a more neutral simulation procedure for comparing methods that use different IRT models. 相似文献
2.
Detection of Differential Item Functioning with Nonlinear Regression: A Non‐IRT Approach Accounting for Guessing 
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下载免费PDF全文 In this article we present a general approach not relying on item response theory models (non‐IRT) to detect differential item functioning (DIF) in dichotomous items with presence of guessing. The proposed nonlinear regression (NLR) procedure for DIF detection is an extension of method based on logistic regression. As a non‐IRT approach, NLR can be seen as a proxy of detection based on the three‐parameter IRT model which is a standard tool in the study field. Hence, NLR fills a logical gap in DIF detection methodology and as such is important for educational purposes. Moreover, the advantages of the NLR procedure as well as comparison to other commonly used methods are demonstrated in a simulation study. A real data analysis is offered to demonstrate practical use of the method. 相似文献
3.
Scores estimated from multidimensional item response theory (IRT) models are not necessarily comparable across dimensions. In this article, the concept of aligned dimensions is formalized in the context of Rasch models, and two methods are described—delta dimensional alignment (DDA) and logistic regression alignment (LRA)—to transform estimated item parameters so that dimensions are aligned. Both the DDA and LRA methods are applied to real and simulated data, and it is demonstrated that both methods are broadly effective for achieving aligned scales. The routine use of scale alignment methods is recommended prior to comparing scores across dimensions. 相似文献
4.
Rob R. Meijer 《Journal of Educational Measurement》2004,41(2):119-136
Two new methods have been proposed to determine unexpected sum scores on sub-tests (testlets) both for paper-and-pencil tests and computer adaptive tests. A method based on a conservative bound using the hypergeometric distribution, denoted p, was compared with a method where the probability for each score combination was calculated using a highest density region (HDR). Furthermore, these methods were compared with the standardized log-likelihood statistic with and without a correction for the estimated latent trait value (denoted as l*z and lz , respectively). Data were simulated on the basis of the one-parameter logistic model, and both parametric and non-parametric logistic regression was used to obtain estimates of the latent trait. Results showed that it is important to take the trait level into account when comparing subtest scores. In a nonparametric item response theory (IRT) context, on adapted version of the HDR method was a powerful alterative to p. In a parametric IRT context, results showed that l*z had the highest power when the data were simulated conditionally on the estimated latent trait level. 相似文献
5.
Stefanie A. Wind 《Educational Measurement》2017,36(2):50-66
Mokken scale analysis (MSA) is a probabilistic‐nonparametric approach to item response theory (IRT) that can be used to evaluate fundamental measurement properties with less strict assumptions than parametric IRT models. This instructional module provides an introduction to MSA as a probabilistic‐nonparametric framework in which to explore measurement quality, with an emphasis on its application in the context of educational assessment. The module describes both dichotomous and polytomous formulations of the MSA model. Examples of the application of MSA to educational assessment are provided using data from a multiple‐choice physical science assessment and a rater‐mediated writing assessment. 相似文献
6.
When cut scores for classifications occur on the total score scale, popular methods for estimating classification accuracy (CA) and classification consistency (CC) require assumptions about a parametric form of the test scores or about a parametric response model, such as item response theory (IRT). This article develops an approach to estimate CA and CC nonparametrically by replacing the role of the parametric IRT model in Lee's classification indices with a modified version of Ramsay's kernel‐smoothed item response functions. The performance of the nonparametric CA and CC indices are tested in simulation studies in various conditions with different generating IRT models, test lengths, and ability distributions. The nonparametric approach to CA often outperforms Lee's method and Livingston and Lewis's method, showing robustness to nonnormality in the simulated ability. The nonparametric CC index performs similarly to Lee's method and outperforms Livingston and Lewis's method when the ability distributions are nonnormal. 相似文献
7.
Seock-Ho Kim Allan S. Cohen Cigdem Alagoz Sukwoo Kim 《Journal of Educational Measurement》2007,44(2):93-116
Data from a large-scale performance assessment ( N = 105,731) were analyzed with five differential item functioning (DIF) detection methods for polytomous items to examine the congruence among the DIF detection methods. Two different versions of the item response theory (IRT) model-based likelihood ratio test, the logistic regression likelihood ratio test, the Mantel test, and the generalized Mantel–Haenszel test were compared. Results indicated some agreement among the five DIF detection methods. Because statistical power is a function of the sample size, the DIF detection results from extremely large data sets are not practically useful. As alternatives to the DIF detection methods, four IRT model-based indices of standardized impact and four observed-score indices of standardized impact for polytomous items were obtained and compared with the R 2 measures of logistic regression. 相似文献
8.
Investigating the fit of a parametric model plays a vital role in validating an item response theory (IRT) model. An area that has received little attention is the assessment of multiple IRT models used in a mixed-format test. The present study extends the nonparametric approach, proposed by Douglas and Cohen (2001), to assess model fit of three IRT models (three- and two-parameter logistic model, and generalized partial credit model) used in a mixed-format test. The statistical properties of the proposed fit statistic were examined and compared to S-X2 and PARSCALE’s G2. Overall, RISE (Root Integrated Square Error) outperformed the other two fit statistics under the studied conditions in that the Type I error rate was not inflated and the power was acceptable. A further advantage of the nonparametric approach is that it provides a convenient graphical inspection of the misfit. 相似文献
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10.
An Extension of Four IRT Linking Methods for Mixed-Format Tests 总被引：1，自引：0，他引：1
Under item response theory (IRT), linking proficiency scales from separate calibrations of multiple forms of a test to achieve a common scale is required in many applications. Four IRT linking methods including the mean/mean, mean/sigma, Haebara, and Stocking-Lord methods have been presented for use with single-format tests. This study extends the four linking methods to a mixture of unidimensional IRT models for mixed-format tests. Each linking method extended is intended to handle mixed-format tests using any mixture of the following five IRT models: the three-parameter logistic, graded response, generalized partial credit, nominal response (NR), and multiple-choice (MC) models. A simulation study is conducted to investigate the performance of the four linking methods extended to mixed-format tests. Overall, the Haebara and Stocking-Lord methods yield more accurate linking results than the mean/mean and mean/sigma methods. When the NR model or the MC model is used to analyze data from mixed-format tests, limitations of the mean/mean, mean/sigma, and Stocking-Lord methods are described. 相似文献
11.
ABSTRACTCurrent procedures for equating number-correct scores using traditional item response theory (IRT) methods assume local independence. However, when tests are constructed using testlets, one concern is the violation of the local item independence assumption. The testlet response theory (TRT) model is one way to accommodate local item dependence. This study proposes methods to extend IRT true score and observed score equating methods to the dichotomous TRT model. We also examine the impact of local item dependence on equating number-correct scores when a traditional IRT model is applied. Results of the study indicate that when local item dependence is at a low level, using the three-parameter logistic model does not substantially affect number-correct equating. However, when local item dependence is at a moderate or high level, using the three-parameter logistic model generates larger equating bias and standard errors of equating compared to the TRT model. However, observed score equating is more robust to the violation of the local item independence assumption than is true score equating. 相似文献
12.
回顾国内外有关小样本情况下估计试题的Logistic IRT参数的研究,可以总结出六种参数估计方法,分别是:修改IRT模型法、提供先验信息法、人工神经网络法、非参数估计法、经典测验理论标准化法以及使用数据增强技术。后续研究应加强对已有参数估计方法的改进,使用包括标准误在内的多种误差指标,在250人以内的样本水平上,采用模拟数据与真实数据相结合的模拟实验法开展更加严谨的模拟研究。 相似文献
13.
The usefulness of item response theory (IRT) models depends, in large part, on the accuracy of item and person parameter estimates. For the standard 3 parameter logistic model, for example, these parameters include the item parameters of difficulty, discrimination, and pseudo-chance, as well as the person ability parameter. Several factors impact traditional marginal maximum likelihood (ML) estimation of IRT model parameters, including sample size, with smaller samples generally being associated with lower parameter estimation accuracy, and inflated standard errors for the estimates. Given this deleterious impact of small samples on IRT model performance, use of these techniques with low-incidence populations, where it might prove to be particularly useful, estimation becomes difficult, especially with more complex models. Recently, a Pairwise estimation method for Rasch model parameters has been suggested for use with missing data, and may also hold promise for parameter estimation with small samples. This simulation study compared item difficulty parameter estimation accuracy of ML with the Pairwise approach to ascertain the benefits of this latter method. The results support the use of the Pairwise method with small samples, particularly for obtaining item location estimates. 相似文献
14.
Given the relationships of item response theory (IRT) models to confirmatory factor analysis (CFA) models, IRT model misspecifications might be detectable through model fit indexes commonly used in categorical CFA. The purpose of this study is to investigate the sensitivity of weighted least squares with adjusted means and variance (WLSMV)-based root mean square error of approximation, comparative fit index, and Tucker–Lewis Index model fit indexes to IRT models that are misspecified due to local dependence (LD). It was found that WLSMV-based fit indexes have some functional relationships to parameter estimate bias in 2-parameter logistic models caused by violations of LD. Continued exploration into these functional relationships and development of LD-detection methods based on such relationships could hold much promise for providing IRT practitioners with global information on violations of local independence. 相似文献
15.
An item-preequating design and a random groups design were used to equate forms of the American College Testing (ACT) Assessment Mathematics Test. Equipercentile and 3-parameter logistic model item-response theory (IRT) procedures were used for both designs. Both pretest methods produced inadequate equating results, and the IRT item preequating method resulted in more equating error than had no equating been conducted. Although neither of the item preequating methods performed well, the results from the equipercentile preequating method were more consistent with those from the random groups method than were the results from the IRT item pretest method. Item context and position effects were likely responsible, at least in part, for the inadequate results for item preequating. Such effects need to be either controlled or modeled, and the design further researched before the item preequating design can be recommended for operational use. 相似文献
16.
Linear factor analysis (FA) models can be reliably tested using test statistics based on residual covariances. We show that the same statistics can be used to reliably test the fit of item response theory (IRT) models for ordinal data (under some conditions). Hence, the fit of an FA model and of an IRT model to the same data set can now be compared. When applied to a binary data set, our experience suggests that IRT and FA models yield similar fits. However, when the data are polytomous ordinal, IRT models yield a better fit because they involve a higher number of parameters. But when fit is assessed using the root mean square error of approximation (RMSEA), similar fits are obtained again. We explain why. These test statistics have little power to distinguish between FA and IRT models; they are unable to detect that linear FA is misspecified when applied to ordinal data generated under an IRT model. 相似文献
17.
Functional form misfit is frequently a concern in item response theory (IRT), although the practical implications of misfit are often difficult to evaluate. In this article, we illustrate how seemingly negligible amounts of functional form misfit, when systematic, can be associated with significant distortions of the score metric in vertical scaling contexts. Our analysis uses two‐ and three‐parameter versions of Samejima's logistic positive exponent model (LPE) as a data generating model. Consistent with prior work, we find LPEs generally provide a better comparative fit to real item response data than traditional IRT models (2PL, 3PL). Further, our simulation results illustrate how 2PL‐ or 3PL‐based vertical scaling in the presence of LPE‐induced misspecification leads to an artificial growth deceleration across grades, consistent with that commonly seen in vertical scaling studies. The results raise further concerns about the use of standard IRT models in measuring growth, even apart from the frequently cited concerns of construct shift/multidimensionality across grades. 相似文献
18.
Empirical studies demonstrated Type-I error (TIE) inflation (especially for highly discriminating easy items) of the Mantel-Haenszel chi-square test for differential item functioning (DIF), when data conformed to item response theory (IRT) models more complex than Rasch, and when IRT proficiency distributions differed only in means. However, no published study manipulated proficiency variance ratio (VR). Data were generated with the three-parameter logistic (3PL) IRT model. Proficiency VRs were 1, 2, 3, and 4. The present study suggests inflation may be greater, and may affect all highly discriminating items (low, moderate, and high difficulty), when IRT proficiency distributions of reference and focal groups differ also in variances. Inflation was greatest on the 21-item test (vs. 41) and 2,000 total sample size (vs. 1,000). Previous studies had not systematically examined sample size ratio. Sample size ratio of 1:1 produced greater TIE inflation than 3:1, but primarily for total sample size of 2,000. 相似文献
19.
Item response theory (IRT) methods are generally used to create score scales for large-scale tests. Research has shown that IRT scales are stable across groups and over time. Most studies have focused on items that are dichotomously scored. Now Rasch and other IRT models are used to create scales for tests that include polytomously scored items. When tests are equated across forms, researchers check for the stability of common items before including them in equating procedures. Stability is usually examined in relation to polytomous items' central “location” on the scale without taking into account the stability of the different item scores (step difficulties). We examined the stability of score scales over a 3–5-year period, considering both stability of location values and stability of step difficulties for common item equating. We also investigated possible changes in the scale measured by the tests and systematic scale drift that might not be evident in year-to-year equating. Results across grades and content areas suggest that equating results are comparable whether or not the stability of step difficulties is taken into account. Results also suggest that there may be systematic scale drift that is not visible using year-to-year common item equating. 相似文献
20.
Large-scale assessments often use a computer adaptive test (CAT) for selection of items and for scoring respondents. Such tests often assume a parametric form for the relationship between item responses and the underlying construct. Although semi- and nonparametric response functions could be used, there is scant research on their performance in a CAT. In this work, we compare parametric response functions versus those estimated using kernel smoothing and a logistic function of a monotonic polynomial. Monotonic polynomial items can be used with traditional CAT item selection algorithms that use analytical derivatives. We compared these approaches in CAT simulations with a variety of item selection algorithms. Our simulations also varied the features of the calibration and item pool: sample size, the presence of missing data, and the percentage of nonstandard items. In general, the results support the use of semi- and nonparametric item response functions in a CAT. 相似文献