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1.
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
2.
Various applications of item response theory often require linking to achieve a common scale for item parameter estimates obtained from different groups. This article used a simulation to examine the relative performance of four different item response theory (IRT) linking procedures in a random groups equating design: concurrent calibration with multiple groups, separate calibration with the Stocking-Lord method, separate calibration with the Haebara method, and proficiency transformation. The simulation conditions used in this article included three sampling designs, two levels of sample size, and two levels of the number of items. In general, the separate calibration procedures performed better than the concurrent calibration and proficiency transformation procedures, even though some inconsistent results were observed across different simulation conditions. Some advantages and disadvantages of the linking procedures are discussed. 相似文献
3.
Bjrn Andersson 《Journal of Educational Measurement》2016,53(4):459-477
In observed‐score equipercentile equating, the goal is to make scores on two scales or tests measuring the same construct comparable by matching the percentiles of the respective score distributions. If the tests consist of different items with multiple categories for each item, a suitable model for the responses is a polytomous item response theory (IRT) model. The parameters from such a model can be utilized to derive the score probabilities for the tests and these score probabilities may then be used in observed‐score equating. In this study, the asymptotic standard errors of observed‐score equating using score probability vectors from polytomous IRT models are derived using the delta method. The results are applied to the equivalent groups design and the nonequivalent groups design with either chain equating or poststratification equating within the framework of kernel equating. The derivations are presented in a general form and specific formulas for the graded response model and the generalized partial credit model are provided. The asymptotic standard errors are accurate under several simulation conditions relating to sample size, distributional misspecification and, for the nonequivalent groups design, anchor test length. 相似文献
4.
In practice, models always have misfit, and it is not well known in what situations methods that provide point estimates, standard errors (SEs), or confidence intervals (CIs) of standardized structural equation modeling (SEM) parameters are trustworthy. In this article we carried out simulations to evaluate the empirical performance of currently available methods. We studied maximum likelihood point estimates, as well as SE estimators based on the delta method, nonparametric bootstrap (NP-B), and semiparametric bootstrap (SP-B). For CIs we studied Wald CI based on delta, and percentile and BCa intervals based on NP-B and SP-B. We conducted simulation studies using both confirmatory factor analysis and SEM models. Depending on (a) whether point estimate, SE, or CI is of interest; (b) amount of model misfit; (c) sample size; and (d) model complexity, different methods can be the one that renders best performance. Based on the simulation results, we discuss how to choose proper methods in practice. 相似文献
5.
Christoph Knig Lale Khorramdel Kentaro Yamamoto Andreas Frey 《Educational Measurement》2021,40(1):17-27
Large‐scale assessments such as the Programme for International Student Assessment (PISA) have field trials where new survey features are tested for utility in the main survey. Because of resource constraints, there is a trade‐off between how much of the sample can be used to test new survey features and how much can be used for the initial item response theory (IRT) scaling. Utilizing real assessment data of the PISA 2015 Science assessment, this article demonstrates that using fixed item parameter calibration (FIPC) in the field trial yields stable item parameter estimates in the initial IRT scaling for samples as small as n = 250 per country. Moreover, the results indicate that for the recovery of the county‐specific latent trait distributions, the estimates of the trend items (i.e., the information introduced into the calibration) are crucial. Thus, concerning the country‐level sample size of n = 1,950 currently used in the PISA field trial, FIPC is useful for increasing the number of survey features that can be examined during the field trial without the need to increase the total sample size. This enables international large‐scale assessments such as PISA to keep up with state‐of‐the‐art developments regarding assessment frameworks, psychometric models, and delivery platform capabilities. 相似文献
6.
R. Philip Chalmers 《Journal of Educational Measurement》2015,52(2):200-222
A mixed‐effects item response theory (IRT) model is presented as a logical extension of the generalized linear mixed‐effects modeling approach to formulating explanatory IRT models. Fixed and random coefficients in the extended model are estimated using a Metropolis‐Hastings Robbins‐Monro (MH‐RM) stochastic imputation algorithm to accommodate for increased dimensionality due to modeling multiple design‐ and trait‐based random effects. As a consequence of using this algorithm, more flexible explanatory IRT models, such as the multidimensional four‐parameter logistic model, are easily organized and efficiently estimated for unidimensional and multidimensional tests. Rasch versions of the linear latent trait and latent regression model, along with their extensions, are presented and discussed, Monte Carlo simulations are conducted to determine the efficiency of parameter recovery of the MH‐RM algorithm, and an empirical example using the extended mixed‐effects IRT model is presented. 相似文献
7.
Nilufer Kahraman 《Journal of Educational Measurement》2013,50(2):227-246
This article considers potential problems that can arise in estimating a unidimensional item response theory (IRT) model when some test items are multidimensional (i.e., show a complex factorial structure). More specifically, this study examines (1) the consequences of model misfit on IRT item parameter estimates due to unintended minor item‐level multidimensionality, and (2) whether a Projection IRT model can provide a useful remedy. A real‐data example is used to illustrate the problem and also is used as a base model for a simulation study. The results suggest that ignoring item‐level multidimensionality might lead to inflated item discrimination parameter estimates when the proportion of multidimensional test items to unidimensional test items is as low as 1:5. The Projection IRT model appears to be a useful tool for updating unidimensional item parameter estimates of multidimensional test items for a purified unidimensional interpretation. 相似文献
8.
The analytically derived asymptotic standard errors (SEs) of maximum likelihood (ML) item estimates can be approximated by a mathematical function without examinees' responses to test items, and the empirically determined SEs of marginal maximum likelihood estimation (MMLE)/Bayesian item estimates can be obtained when the same set of items is repeatedly estimated from the simulation (or resampling) test data. The latter method will result in rather stable and accurate SE estimates as the number of replications increases, but requires cumbersome and time-consuming calculations. Instead of using the empirically determined method, the adequacy of using the analytical-based method in predicting the SEs for item parameter estimates was examined by comparing results produced from both approaches. The results indicated that the SEs yielded from both approaches were, in most cases, very similar, especially when they were applied to a generalized partial credit model. This finding encourages test practitioners and researchers to apply the analytically asymptotic SEs of item estimates to the context of item-linking studies, as well as to the method of quantifying the SEs of equating scores for the item response theory (IRT) true-score method. Three-dimensional graphical presentation for the analytical SEs of item estimates as the bivariate function of item difficulty together with item discrimination was also provided for a better understanding of several frequently used IRT models. 相似文献
9.
《Structural equation modeling》2013,20(3):353-377
Though the common default maximum likelihood estimator used in structural equation modeling is predicated on the assumption of multivariate normality, applied researchers often find themselves with data clearly violating this assumption and without sufficient sample size to utilize distribution-free estimation methods. Fortunately, promising alternatives are being integrated into popular software packages. Bootstrap resampling, which is offered in AMOS (Arbuckle, 1997), is one potential solution for estimating model test statistic p values and parameter standard errors under nonnormal data conditions. This study is an evaluation of the bootstrap method under varied conditions of nonnormality, sample size, model specification, and number of bootstrap samples drawn from the resampling space. Accuracy of the test statistic p values is evaluated in terms of model rejection rates, whereas accuracy of bootstrap standard error estimates takes the form of bias and variability of the standard error estimates themselves. 相似文献
10.
《教育实用测度》2013,26(2):125-141
Item parameter instability can threaten the validity of inferences about changes in student achievement when using Item Response Theory- (IRT) based test scores obtained on different occasions. This article illustrates a model-testing approach for evaluating the stability of IRT item parameter estimates in a pretest-posttest design. Stability of item parameter estimates was assessed for a random sample of pretest and posttest responses to a 19-item math test. Using MULTILOG (Thissen, 1986), IRT models were estimated in which item parameter estimates were constrained to be equal across samples (reflecting stability) and item parameter estimates were free to vary across samples (reflecting instability). These competing models were then compared statistically in order to test the invariance assumption. The results indicated a moderately high degree of stability in the item parameter estimates for a group of children assessed on two different occasions. 相似文献
11.
Christine E. DeMars 《Structural equation modeling》2013,20(4):610-632
In structural equation modeling software, either limited-information (bivariate proportions) or full-information item parameter estimation routines could be used for the 2-parameter item response theory (IRT) model. Limited-information methods assume the continuous variable underlying an item response is normally distributed. For skewed and platykurtic latent variable distributions, 3 methods were compared in Mplus: limited information, full information integrating over a normal distribution, and full information integrating over the known underlying distribution. Interfactor correlation estimates were similar for all 3 estimation methods. For the platykurtic distribution, estimation method made little difference for the item parameter estimates. When the latent variable was negatively skewed, for the most discriminating easy or difficult items, limited-information estimates of both parameters were considerably biased. Full-information estimates obtained by marginalizing over a normal distribution were somewhat biased. Full-information estimates obtained by integrating over the true latent distribution were essentially unbiased. For the a parameters, standard errors were larger for the limited-information estimates when the bias was positive but smaller when the bias was negative. For the d parameters, standard errors were larger for the limited-information estimates of the easiest, most discriminating items. Otherwise, they were generally similar for the limited- and full-information estimates. Sample size did not substantially impact the differences between the estimation methods; limited information did not gain an advantage for smaller samples. 相似文献
12.
R. Darrell Bock David Thissen Michele F. Zimowski 《Journal of Educational Measurement》1997,34(3):197-211
In classical test theory, a test is regarded as a sample of items from a domain defined by generating rules or by content, process, and format specifications, l f the items are a random sample of the domain, then the percent-correct score on the test estimates the domain score, that is, the expected percent correct for all items in the domain. When the domain is represented by a large set of calibrated items, as in item banking applications, item response theory (IRT) provides an alternative estimator of the domain score by transformation of the IRT scale score on the test. This estimator has the advantage of not requiring the test items to be a random sample of the domain, and of having a simple standard error. We present here resampling results in real data demonstrating for uni- and multidimensional models that the IRT estimator is also a more accurate predictor of the domain score than is the classical percent-correct score. These results have implications for reporting outcomes of educational qualification testing and assessment. 相似文献
13.
The focus of this article is on scale score transformations that can be used to stabilize conditional standard errors of measurement (CSEMs). Three transformations for stabilizing the estimated CSEMs are reviewed, including the traditional arcsine transformation, a recently developed general variance stabilization transformation, and a new method proposed in this article involving cubic transformations. Two examples are provided and the three scale score transformations are compared in terms of how well they stabilize CSEMs estimated from compound binomial and item response theory (IRT) models. Advantages of the cubic transformation are demonstrated with respect to CSEM stabilization and other scaling criteria (e.g., scale score distributions that are more symmetric). 相似文献
14.
Mark J. Gierl Dianne Henderson Michael Jodoin Don Klinger 《Journal of Experimental Education》2013,81(3):261-279
In test development, item response theory (IRT) is a method to determine the amount of information that each item (i.e., item information function) and combination of items (i.e., test information function) provide in the estimation of an examinee's ability. Studies investigating the effects of item parameter estimation errors over a range of ability have demonstrated an overestimation of information when the most discriminating items are selected (i.e., item selection based on maximum information). In the present study, the authors examined the influence of item parameter estimation errors across 3 item selection methods—maximum no target, maximum target, and theta maximum—using the 2- and 3-parameter logistic IRT models. Tests created with the maximum no target and maximum target item selection procedures consistently overestimated the test information function. Conversely, tests created using the theta maximum item selection procedure yielded more consistent estimates of the test information function and, at times, underestimated the test information function. Implications for test development are discussed. 相似文献
15.
16.
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
17.
IRT Equating Methods 总被引：1，自引：0，他引：1
The purpose of this instructional module is to provide the basis for understanding the process of score equating through the use of item response theory (IRT). A context is provided for addressing the merits of IRT equating methods. The mechanics of IRT equating and the need to place parameter estimates from separate calibration runs on the same scale are discussed. Some procedures for placing parameter estimates on a common scale are presented. In addition, IRT true-score equating is discussed in some detail. A discussion of the practical advantages derived from IRT equating is offered at the end of the module. 相似文献
18.
Many computerized testing algorithms require the fitting of some item response theory (IRT) model to examinees' responses to facilitate item selection, the determination of test stopping rules, and classification decisions. Some IRT models are thought to be particularly useful for small volume certification programs that wish to make the transition to computerized adaptive testing (CAT). The one-parameter logistic model (1-PLM) is usually assumed to require a smaller sample size than the three-parameter logistic model (3-PLM) for item parameter calibrations. This study examined the effects of model misspecification on the precision of the decisions made using the sequential probability ratio test (SPRT). For this comparison, the 1-PLM was used to estimate item parameters, even though the items' characteristics were represented by a 3-PLM. Results demonstrated that the 1-PLM produced considerably more decision errors under simulation conditions similar to a real testing environment, compared to the true model and to a fixed-form standard reference set of items. 相似文献
19.
Hong Jiao Akihito Kamata Shudong Wang Ying Jin 《Journal of Educational Measurement》2012,49(1):82-100
The applications of item response theory (IRT) models assume local item independence and that examinees are independent of each other. When a representative sample for psychometric analysis is selected using a cluster sampling method in a testlet‐based assessment, both local item dependence and local person dependence are likely to be induced. This study proposed a four‐level IRT model to simultaneously account for dual local dependence due to item clustering and person clustering. Model parameter estimation was explored using the Markov Chain Monte Carlo method. Model parameter recovery was evaluated in a simulation study in comparison with three other related models: the Rasch model, the Rasch testlet model, and the three‐level Rasch model for person clustering. In general, the proposed model recovered the item difficulty and person ability parameters with the least total error. The bias in both item and person parameter estimation was not affected but the standard error (SE) was affected. In some simulation conditions, the difference in classification accuracy between models could go up to 11%. The illustration using the real data generally supported model performance observed in the simulation study. 相似文献
20.
Holmes Finch 《Journal of Educational Measurement》2008,45(3):225-245
Missing data are a common problem in a variety of measurement settings, including responses to items on both cognitive and affective assessments. Researchers have shown that such missing data may create problems in the estimation of item difficulty parameters in the Item Response Theory (IRT) context, particularly if they are ignored. At the same time, a number of data imputation methods have been developed outside of the IRT framework and been shown to be effective tools for dealing with missing data. The current study takes several of these methods that have been found to be useful in other contexts and investigates their performance with IRT data that contain missing values. Through a simulation study, it is shown that these methods exhibit varying degrees of effectiveness in terms of imputing data that in turn produce accurate sample estimates of item difficulty and discrimination parameters. 相似文献