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1.
The primary purpose of this study is to investigate the mathematical characteristics of the test reliability coefficient ρ XX′ as a function of item response theory (IRT) parameters and present the lower and upper bounds of the coefficient. Another purpose is to examine relative performances of the IRT reliability statistics and two classical test theory (CTT) reliability statistics (Cronbach’s alpha and Feldt–Gilmer congeneric coefficients) under various testing conditions that result from manipulating large-scale real data. For the first purpose, two alternative ways of exactly quantifying ρ XX′ are compared in terms of computational efficiency and statistical usefulness. In addition, the lower and upper bounds for ρ XX′ are presented in line with the assumptions of essential tau-equivalence and congeneric similarity, respectively. Empirical studies conducted for the second purpose showed across all testing conditions that (1) the IRT reliability coefficient was higher than the CTT reliability statistics; (2) the IRT reliability coefficient was closer to the Feldt–Gilmer coefficient than to the Cronbach’s alpha coefficient; and (3) the alpha coefficient was close to the lower bound of IRT reliability. Some advantages of the IRT approach to estimating test-score reliability over the CTT approaches are discussed in the end.  相似文献   

2.
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   

3.
With known item response theory (IRT) item parameters, Lord and Wingersky provided a recursive algorithm for computing the conditional frequency distribution of number‐correct test scores, given proficiency. This article presents a generalized algorithm for computing the conditional distribution of summed test scores involving real‐number item scores. The generalized algorithm is distinct from the Lord‐Wingersky algorithm in that it explicitly incorporates the task of figuring out all possible unique real‐number test scores in each recursion. Some applications of the generalized recursive algorithm, such as IRT test score reliability estimation and IRT proficiency estimation based on summed test scores, are illustrated with a short test by varying scoring schemes for its items.  相似文献   

4.
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   

5.
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   

6.
A practical concern for many existing tests is that subscore test lengths are too short to provide reliable and meaningful measurement. A possible method of improving the subscale reliability and validity would be to make use of collateral information provided by items from other subscales of the same test. To this end, the purpose of this article is to compare two different formulations of an alternative Item Response Theory (IRT) model developed to parameterize unidimensional projections of multidimensional test items: Analytical and Empirical formulations. Two real data applications are provided to illustrate how the projection IRT model can be used in practice, as well as to further examine how ability estimates from the projection IRT model compare to external examinee measures. The results suggest that collateral information extracted by a projection IRT model can be used to improve reliability and validity of subscale scores, which in turn can be used to provide diagnostic information about strength and weaknesses of examinees helping stakeholders to link instruction or curriculum to assessment results.  相似文献   

7.
项目反应理论下的测验信度能够评价潜在特质估计的可靠性与稳定性,由于具有宏观性的特点,项目反应理论信度的作用并不能被测验信息函数所取代,是IRT测验的一个重要指标。本文参考国内外文献,首先介绍国内外学者关于IRT信度作用的观点,并介绍和评价了多种IRT信度估计方法,然后简要介绍IRT信度的影响因素,最后展望了IRT信度领域后续研究尚可着力之处。  相似文献   

8.
This article describes an ongoing project to develop a formative, inferential reading comprehension assessment of causal story comprehension. It has three features to enhance classroom use: equated scale scores for progress monitoring within and across grades, a scale score to distinguish among low‐scoring students based on patterns of mistakes, and a reading efficiency index. Instead of two response types for each multiple‐choice item, correct and incorrect, each item has three response types: correct and two incorrect response types. Prior results on reliability, convergent and discriminant validity, and predictive utility of mistake subscores are briefly described. The three‐response‐type structure of items required rethinking the item response theory (IRT) modeling. IRT‐modeling results are presented, and implications for formative assessments and instructional use are discussed.  相似文献   

9.
Single‐best answers to multiple‐choice items are commonly dichotomized into correct and incorrect responses, and modeled using either a dichotomous item response theory (IRT) model or a polytomous one if differences among all response options are to be retained. The current study presents an alternative IRT‐based modeling approach to multiple‐choice items administered with the procedure of elimination testing, which asks test‐takers to eliminate all the response options they consider to be incorrect. The partial credit model is derived for the obtained responses. By extracting more information pertaining to test‐takers’ partial knowledge on the items, the proposed approach has the advantage of providing more accurate estimation of the latent ability. In addition, it may shed some light on the possible answering processes of test‐takers on the items. As an illustration, the proposed approach is applied to a classroom examination of an undergraduate course in engineering science.  相似文献   

10.
Previous assessments of the reliability of test scores for testlet-composed tests have indicated that item-based estimation methods overestimate reliability. This study was designed to address issues related to the extent to which item-based estimation methods overestimate the reliability of test scores composed of testlets and to compare several estimation methods for different measurement models using simulation techniques. Three types of estimation approach were conceptualized for generalizability theory (GT) and item response theory (IRT): item score approach (ISA), testlet score approach (TSA), and item-nested-testlet approach (INTA). The magnitudes of overestimation when applying item-based methods ranged from 0.02 to 0.06 and were related to the degrees of dependence among within-testlet items. Reliability estimates from TSA were lower than those from INTA due to the loss of information with IRT approaches. However, this could not be applied in GT. Specified methods in IRT produced higher reliability estimates than those in GT using the same approach. Relatively smaller magnitudes of error in reliability estimates were observed for ISA and for methods in IRT. Thus, it seems reasonable to use TSA as well as INTA for both GT and IRT. However, if there is a relatively large dependence among within-testlet items, INTA should be considered for IRT due to nonnegligible loss of information.  相似文献   

11.
Examiners seeking guidance on multiple‐choice and true/false tests are likely to encounter various faulty or questionable ideas. Twelve of these are discussed in detail, having to do mainly with the effects on test reliability of test length, guessing and scoring method (i.e. number‐right scoring or negative marking). Some misunderstandings could be based on evidence from tests that were badly written or administered, while others may have arisen through the misinterpretation of reliability coefficients. The usefulness of item response theory in the analysis of academic test items is briefly dismissed.  相似文献   

12.
The posterior predictive model checking method is a flexible Bayesian model‐checking tool and has recently been used to assess fit of dichotomous IRT models. This paper extended previous research to polytomous IRT models. A simulation study was conducted to explore the performance of posterior predictive model checking in evaluating different aspects of fit for unidimensional graded response models. A variety of discrepancy measures (test‐level, item‐level, and pair‐wise measures) that reflected different threats to applications of graded IRT models to performance assessments were considered. Results showed that posterior predictive model checking exhibited adequate power in detecting different aspects of misfit for graded IRT models when appropriate discrepancy measures were used. Pair‐wise measures were found more powerful in detecting violations of the unidimensionality and local independence assumptions.  相似文献   

13.
Sometimes, test‐takers may not be able to attempt all items to the best of their ability (with full effort) due to personal factors (e.g., low motivation) or testing conditions (e.g., time limit), resulting in poor performances on certain items, especially those located toward the end of a test. Standard item response theory (IRT) models fail to consider such testing behaviors. In this study, a new class of mixture IRT models was developed to account for such testing behavior in dichotomous and polytomous items, by assuming test‐takers were composed of multiple latent classes and by adding a decrement parameter to each latent class to describe performance decline. Parameter recovery, effect of model misspecification, and robustness of the linearity assumption in performance decline were evaluated using simulations. It was found that the parameters in the new models were recovered fairly well by using the freeware WinBUGS; the failure to account for such behavior by fitting standard IRT models resulted in overestimation of difficulty parameters on items located toward the end of the test and overestimation of test reliability; and the linearity assumption in performance decline was rather robust. An empirical example is provided to illustrate the applications and the implications of the new class of models.  相似文献   

14.
Equivalent forms of a ten-item completion test were constructed. The same test items then were rewritten in matching format and in multiple-choice format, resulting in two forms (A and B) of each of three types of test. All tests were administered to 73 examinees, and parallel-forms reliability coefficients (correlation between scores on A and B) were calculated. These empirically obtained values were compared to the values of the reliability coefficient predicted from theoretically derived equations which indicate the influence of chance success due to guessing on test reliability. In accordance with theory it was found that the completion test was more reliable than the matching test and that the matching test was more reliable than the multiple-choice test. The empirically obtained reliability coefficients were very close to those predicted from the mathematically derived formulas.  相似文献   

15.
The equating performance of two internal anchor test structures—miditests and minitests—is studied for four IRT equating methods using simulated data. Originally proposed by Sinharay and Holland, miditests are anchors that have the same mean difficulty as the overall test but less variance in item difficulties. Four popular IRT equating methods were tested, and both the means and SDs of the true ability of the group to be equated were varied. We evaluate equating accuracy marginally and conditional on true ability. Our results suggest miditests perform about as well as traditional minitests for most conditions. Findings are discussed in terms of comparability to the typical minitest design and the trade‐off between accuracy and flexibility in test construction.  相似文献   

16.
In this article, linear item response theory (IRT) observed‐score equating is compared under a generalized kernel equating framework with Levine observed‐score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when using data from IRT models, linear IRT observed‐score equating is virtually identical to Levine observed‐score equating. This leads to the conclusion that poststratification equating based on true anchor scores can be viewed as the curvilinear Levine observed‐score equating.  相似文献   

17.
This article is a pedagogical piece on coefficient alpha (α) and its uses. The classical approach to test reliability is explained. Test‐retest, alternative‐forms, and internal‐consistency methods of approximating test reliability are described, equations are derived for each method, and α is shown to be a lower‐bound internal‐consistency approximation to test reliability. Emphasis is placed on the effects of violations of model assumptions on reliability estimation. The classical models are conceptualized as structural equation models and are displayed in path diagrams. Special emphasis is placed on the failure of α to meet certain basic criteria as an index of test homogeneity.  相似文献   

18.
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   

19.
Performance assessments, scenario‐based tasks, and other groups of items carry a risk of violating the local item independence assumption made by unidimensional item response theory (IRT) models. Previous studies have identified negative impacts of ignoring such violations, most notably inflated reliability estimates. Still, the influence of this violation on examinee ability estimates has been comparatively neglected. It is known that such item dependencies cause low‐ability examinees to have their scores overestimated and high‐ability examinees' scores underestimated. However, the impact of these biases on examinee classification decisions has been little examined. In addition, because the influence of these dependencies varies along the underlying ability continuum, whether or not the location of the cut‐point is important in regard to correct classifications remains unanswered. This simulation study demonstrates that the strength of item dependencies and the location of an examination systems’ cut‐points both influence the accuracy (i.e., the sensitivity and specificity) of examinee classifications. Practical implications of these results are discussed in terms of false positive and false negative classifications of test takers.  相似文献   

20.
Although reliability of subscale scores may be suspect, subscale scores are the most common type of diagnostic information included in student score reports. This research compared methods for augmenting the reliability of subscale scores for an 8th-grade mathematics assessment. Yen's Objective Performance Index, Wainer et al.'s augmented scores, and scores based on multidimensional item response theory (IRT) models were compared and found to improve the precision of the subscale scores. However, the augmented subscale scores were found to be more highly correlated and less variable than unaugmented scores. The meaningfulness of reporting such augmented scores as well as the implications for validity and test development are discussed.  相似文献   

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