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1.
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   

2.
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   

3.
Standard 3.9 of the Standards for Educational and Psychological Testing ( 1999 ) demands evidence of model fit when item response theory (IRT) models are employed to data from tests. Hambleton and Han ( 2005 ) and Sinharay ( 2005 ) recommended the assessment of practical significance of misfit of IRT models, but few examples of such assessment can be found in the literature concerning IRT model fit. In this article, practical significance of misfit of IRT models was assessed using data from several tests that employ IRT models to report scores. The IRT model did not fit any data set considered in this article. However, the extent of practical significance of misfit varied over the data sets.  相似文献   

4.
This article presents a new method for multiple-group confirmatory factor analysis (CFA), referred to as the alignment method. The alignment method can be used to estimate group-specific factor means and variances without requiring exact measurement invariance. A strength of the method is the ability to conveniently estimate models for many groups. The method is a valuable alternative to the currently used multiple-group CFA methods for studying measurement invariance that require multiple manual model adjustments guided by modification indexes. Multiple-group CFA is not practical with many groups due to poor model fit of the scalar model and too many large modification indexes. In contrast, the alignment method is based on the configural model and essentially automates and greatly simplifies measurement invariance analysis. The method also provides a detailed account of parameter invariance for every model parameter in every group.  相似文献   

5.
Drawing valid inferences from item response theory (IRT) models is contingent upon a good fit of the data to the model. Violations of model‐data fit have numerous consequences, limiting the usefulness and applicability of the model. This instructional module provides an overview of methods used for evaluating the fit of IRT models. Upon completing this module, the reader will have an understanding of traditional and Bayesian approaches for evaluating model‐data fit of IRT models, the relative advantages of each approach, and the software available to implement each method.  相似文献   

6.
The effects of levels of aggregation on measures of goodness of fit and higher order parameter estimates obtained from confirmatory factor analysis (CFA) were investigated. For a higher order model of academic self‐concept, 3 levels of aggregation were considered—disaggregated, partially disaggregated, and partially aggregated. In the disaggregated model, measured variables represented individual items. In the partially disaggregated model, testlets (groups of 4 items) represented measured variables. In the partially aggregated model, subscale scores represented measured variables. Three indexes of fit were employed: the Tucker‐Lewis Index (TLI), the Comparative Fit Index (CFI), and chi‐square. Solutions for the disaggregated models consistently evidenced poor fit. TLI and CFI values for partially disaggregated and partially aggregated solutions were satisfactory. Standardized parameter estimates were similar across all solutions. Implications of these findings are discussed with consideration of other research on model complexity in CFA.  相似文献   

7.
One of the major assumptions of item response theory (IRT)models is that performance on a set of items is unidimensional, that is, the probability of successful performance by examinees on a set of items can be modeled by a mathematical model that has only one ability parameter. In practice, this strong assumption is likely to be violated. An important pragmatic question to consider is: What are the consequences of these violations? In this research, evidence is provided of violations of unidimensionality on the verbal scale of the GRE Aptitude Test, and the impact of these violations on IRT equating is examined. Previous factor analytic research on the GRE Aptitude Test suggested that two verbal dimensions, discrete verbal (analogies, antonyms, and sentence completions)and reading comprehension, existed. Consequently, the present research involved two separate calibrations (homogeneous) of discrete verbal items and reading comprehension items as well as a single calibration (heterogeneous) of all verbal item types. Thus, each verbal item was calibrated twice and each examinee obtained three ability estimates: reading comprehension, discrete verbal, and all verbal. The comparability of ability estimates based on homogeneous calibrations (reading comprehension or discrete verbal) to each other and to the all-verbal ability estimates was examined. The effects of homogeneity of item calibration pool on estimates of item discrimination were also examined. Then the comparability of IRT equatings based on homogeneous and heterogeneous calibrations was assessed. The effects of calibration homogeneity on ability parameter estimates and discrimination parameter estimates are consistent with the existence of two highly correlated verbal dimensions. IRT equating results indicate that although violations of unidimensionality may have an impact on equating, the effect may not be substantial.  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   

9.
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   

10.
Methods are presented for comparing grades obtained in a situation where students can choose between different subjects. It must be expected that the comparison between the grades is complicated by the interaction between the students' pattern and level of proficiency on one hand, and the choice of the subjects on the other hand. Three methods based on item response theory (IRT) for the estimation of proficiency measures that are comparable over students and subjects are discussed: a method based on a model with a unidimensional representation of proficiency, a method based on a model with a multidimensional representation of proficiency, and a method based on a multidimensional representation of proficiency where the stochastic nature of the choice of examination subjects is explicitly modeled. The methods are compared using the data from the Central Examinations in Secondary Education in the Netherlands. The results show that the unidimensional IRT model produces unrealistic results, which do not appear when using the two multidimensional IRT models. Further, it is shown that both the multidimensional models produce acceptable model fit. However, the model that explicitly takes the choice process into account produces the best model fit.  相似文献   

11.
A Monte Carlo simulation study was conducted to investigate the effects on structural equation modeling (SEM) fit indexes of sample size, estimation method, and model specification. Based on a balanced experimental design, samples were generated from a prespecified population covariance matrix and fitted to structural equation models with different degrees of model misspecification. Ten SEM fit indexes were studied. Two primary conclusions were suggested: (a) some fit indexes appear to be noncomparable in terms of the information they provide about model fit for misspecified models and (b) estimation method strongly influenced almost all the fit indexes examined, especially for misspecified models. These 2 issues do not seem to have drawn enough attention from SEM practitioners. Future research should study not only different models vis‐à‐vis model complexity, but a wider range of model specification conditions, including correctly specified models and models specified incorrectly to varying degrees.  相似文献   

12.
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13.
As low-stakes testing contexts increase, low test-taking effort may serve as a serious validity threat. One common solution to this problem is to identify noneffortful responses and treat them as missing during parameter estimation via the effort-moderated item response theory (EM-IRT) model. Although this model has been shown to outperform traditional IRT models (e.g., two-parameter logistic [2PL]) in parameter estimation under simulated conditions, prior research has failed to examine its performance under violations to the model’s assumptions. Therefore, the objective of this simulation study was to examine item and mean ability parameter recovery when violating the assumptions that noneffortful responding occurs randomly (Assumption 1) and is unrelated to the underlying ability of examinees (Assumption 2). Results demonstrated that, across conditions, the EM-IRT model provided robust item parameter estimates to violations of Assumption 1. However, bias values greater than 0.20 SDs were observed for the EM-IRT model when violating Assumption 2; nonetheless, these values were still lower than the 2PL model. In terms of mean ability estimates, model results indicated equal performance between the EM-IRT and 2PL models across conditions. Across both models, mean ability estimates were found to be biased by more than 0.25 SDs when violating Assumption 2. However, our accompanying empirical study suggested that this biasing occurred under extreme conditions that may not be present in some operational settings. Overall, these results suggest that the EM-IRT model provides superior item and equal mean ability parameter estimates in the presence of model violations under realistic conditions when compared with the 2PL model.  相似文献   

14.
Even though Bayesian estimation has recently become quite popular in item response theory (IRT), there is a lack of works on model checking from a Bayesian perspective. This paper applies the posterior predictive model checking (PPMC) method ( Guttman, 1967 ; Rubin, 1984 ), a popular Bayesian model checking tool, to a number of real applications of unidimensional IRT models. The applications demonstrate how to exploit the flexibility of the posterior predictive checks to meet the need of the researcher. This paper also examines practical consequences of misfit, an area often ignored in educational measurement literature while assessing model fit.  相似文献   

15.
Using a New Statistical Model for Testlets to Score TOEFL   总被引：1，自引：0，他引：1  
Standard item response theory (IRT) models fit to examination responses ignore the fact that sets of items (testlets) often are matched with a single common stimulus (e.g., a reading comprehension passage). In this setting, all items given to an examinee are unlikely to be conditionally independent (given examinee proficiency). Models that assume conditional independence will overestimate the precision with which examinee proficiency is measured. Overstatement of precision may lead to inaccurate inferences as well as prematurely ended examinations in which the stopping rule is based on the estimated standard error of examinee proficiency (e.g., an adaptive test). The standard three parameter IRT model was modified to include an additional random effect for items nested within the same testlet (Wainer, Bradlow, & Du, 2000). This parameter, γ characterizes the amount of local dependence in a testlet.
We fit 86 TOEFL testlets (50 reading comprehension and 36 listening comprehension) with the new model, and obtained a value for the variance of γ for each testlet. We compared the standard parameters (discrimination (a), difficulty (b) and guessing (c)) with what is obtained through traditional modeling. We found that difficulties were well estimated either way, but estimates of both a and c were biased if conditional independence is incorrectly assumed. Of greater import, we found that test information was substantially over-estimated when conditional independence was incorrectly assumed.  相似文献   

16.
A 30-item survey was devised to determine Chinese TEFL (Teaching English as a Foreign Language) academics’ potential for conducting research. A five-part Likert scale was used to gather data from 182 academics on four factors: (1) perceptions on teaching–research nexus, (2) personal perspectives for conducting research, (3) predispositions for conducting research and (4) workplace contexts for conducting research. Data were subjected to confirmatory factor analysis (CFA) for structural equation modelling using various fit indices. The independence model was rejected. Accordingly, the CFA model proposed that the four factors covaried and were associated with each indicated item. The hypothesized CFA model demonstrated an acceptable model fit. After statistical analysis, a revised CFA model presented more reliable fit measures, which required a reduction in survey item numbers. This instrument will require further testing but may be used to draw comparisons between past and present data and determine areas for enhancing research productivity.  相似文献   

17.
Data collected from questionnaires are often in ordinal scale. Unweighted least squares (ULS), diagonally weighted least squares (DWLS) and normal-theory maximum likelihood (ML) are commonly used methods to fit structural equation models. Consistency of these estimators demands no structural misspecification. In this article, we conduct a simulation study to compare the equation-by-equation polychoric instrumental variable (PIV) estimation with ULS, DWLS, and ML. Accuracy of PIV for the correctly specified model and robustness of PIV for misspecified models are investigated through a confirmatory factor analysis (CFA) model and a structural equation model with ordinal indicators. The effects of sample size and nonnormality of the underlying continuous variables are also examined. The simulation results show that PIV produces robust factor loading estimates in the CFA model and in structural equation models. PIV also produces robust path coefficient estimates in the model where valid instruments are used. However, robustness highly depends on the validity of instruments.  相似文献   

18.
The motivated strategies for learning questionnaire (MSLQ) is widely used as a self-report instrument to assess students’ motivation and self-regulation. This study utilized the MSLQ Junior High to examine the motivational beliefs and self-regulation of secondary school students (Grades 8 and 9) from Singapore. The instrument was slightly modified and administered to students (N?=?610) in mathematics and science classes. In the first sample, 314 students completed the MSLQ Junior High while a second sample of 296 students completed the revised MSLQ Junior High. Using a congeneric approach of confirmatory factor analysis (CFA), the five-factor measurement model was determined with the first sample. This measurement model was further supported using a second sample and its goodness-of-fit indices were compared with other CFA models. Statistical findings showed that the five-factor structure of the revised MSLQ Junior High had a good model fit. The present study contributes a novel methodological approach by investigating the parsimony confirmatory factor structure of the revised MSLQ Junior High in local academic contexts.  相似文献   

19.
ABSTRACT

Based on concerns about the item response theory (IRT) linking approach used in the Programme for International Student Assessment (PISA) until 2012 as well as the desire to include new, more complex, interactive items with the introduction of computer-based assessments, alternative IRT linking methods were implemented in the 2015 PISA round. The new linking method represents a concurrent calibration using all available data, enabling us to find item parameters that maximize fit across all groups and allowing us to investigate measurement invariance across groups. Apart from the Rasch model that historically has been used in PISA operational analyses, we compared our method against more general IRT models that can incorporate item-by-country interactions. The results suggest that our proposed method holds promise not only to provide a strong linkage across countries and cycles but also to serve as a tool for investigating measurement invariance.  相似文献   

20.
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   

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