Linking Item Response Model Parameters

With a few exceptions, the problem of linking item response model parameters from different item calibrations has been conceptualized as an instance of the problem of test equating scores on different test forms. This paper argues, however, that the use of item response models does not require any test score equating. Instead, it involves the necessity of parameter linking due to a fundamental problem inherent in the formal nature of these models—their general lack of identifiability. More specifically, item response model parameters need to be linked to adjust for the different effects of the identifiability restrictions used in separate item calibrations. Our main theorems characterize the formal nature of these linking functions for monotone, continuous response models, derive their specific shapes for different parameterizations of the 3PL model, and show how to identify them from the parameter values of the common items or persons in different linking designs.     

Improvement in Detection of Differential Item Functioning Using a Mixture Item Response Theory Model

Usually, methods for detection of differential item functioning (DIF) compare the functioning of items across manifest groups. However, the manifest groups with respect to which the items function differentially may not necessarily coincide with the true source of the bias. It is expected that DIF detection under a model that includes a latent DIF variable is more sensitive to this source of bias. In a simulation study, it is shown that a mixture item response theory model, which includes a latent grouping variable, performs better in identifying DIF items than DIF detection methods using manifest variables only. The difference between manifest and latent DIF detection increases as the correlation between the manifest variable and the true source of the DIF becomes smaller. Different sample sizes, relative group sizes, and significance levels are studied. Finally, an empirical example demonstrates the detection of heterogeneity in a minority sample using a latent grouping variable. Manifest and latent DIF detection methods are applied to a Vocabulary test of the General Aptitude Test Battery (GATB).     

Specifying Ability Growth Models Using a Multidimensional Item Response Model for Repeated Measures Categorical Ordinal Item Response Data

When categorical ordinal item response data are collected over multiple timepoints from a repeated measures design, an item response theory (IRT) modeling approach whose unit of analysis is an item response is suitable. This study proposes a few longitudinal IRT models and illustrates how a popular compensatory multidimensional IRT model can be utilized to formulate such longitudinal IRT models, which permits an investigation of ability growth at both individual and population levels. The equivalence of an existing multidimensional IRT model and those longitudinal IRT models is also elaborated so that one can make use of an existing multidimensional IRT model to implement the longitudinal IRT models.     

A Truncated-Probit Item Response Model for Estimating Psychophysical Thresholds

Human abilities in perceptual domains have conventionally been described with reference to a threshold that may be defined as the maximum amount of stimulation which leads to baseline performance. Traditional psychometric links, such as the probit, logit, and t, are incompatible with a threshold as there are no true scores corresponding to baseline performance. We introduce a truncated probit link for modeling thresholds and develop a two-parameter IRT model based on this link. The model is Bayesian and analysis is performed with MCMC sampling. Through simulation, we show that the model provides for accurate measurement of performance with thresholds. The model is applied to a digit-classification experiment in which digits are briefly flashed and then subsequently masked. Using parameter estimates from the model, individuals’ thresholds for flashed-digit discrimination is estimated.     

人格测验的项目反应过程与展开模型研究述评

一些研究者提出了人格测验的项目反应理想点过程假设, 并在此基础上开发了拓广等级展开模型(GGUM)用于现有人格测验的数据分析和新量表的建构, 显示出了较优势模型更优良的一些性质。不过, 现有项目反应过程的研究结果来自于大样本的调查, 缺乏实验证据的支持, GGUM也存在不适用于分析多类别人格测验数据的局限性。未来需要对GGUM进行拓展, 剔除其主观反应类别阈限对称的限定。此外, 还要重视配对格式人格测验数据分析模型的研究和开发。     

The generalized Logit-Linear Item Response Model for Binary-Designed Items

This paper introduces the generalized logit-linear item response model (GLLIRM), which represents the item-solving process as a series of dichotomous operations or steps. The GLLIRM assumes that the probability function of the item response is a logistic function of a linear composite of basic parameters which describe the operations, and the coefficients depend on three design matrices X, Y and Z. The GLLIRM provides a tool for testing hypotheses on the item-solving process and generalizes existing models. An empirical application is included, in which the model is applied to evaluate sources of difficulty and pairwise item interactions in a logical analysis test. This research was supported by the Comunidad de Madrid grant CCG06-UAM/ESP-0043.     

A Speeded Item Response Model with Gradual Process Change

An item response theory model for dealing with test speededness is proposed. The model consists of two random processes, a problem solving process and a random guessing process, with the random guessing gradually taking over from the problem solving process. The involved change point and change rate are considered random parameters in order to model examinee differences in both respects. The proposed model is evaluated on simulated data and in a case study. The research reported in this paper was supported by IAP P5/24 and GOA/2005/04, both awarded to Paul De Boeck and Iven Van Mechelen, and by IAP P6/03, awarded to Iven Van Mechelen. Yuri Goegebeur’s research was supported by a grant of the Danish Natural Science Research Council.     

项目反应时间的对数偏正态模型

近年来,项目反应时间数据的建模是心理和教育测量领域的热门方向之一。针对反应时间的对数正态模型和Box-Cox正态模型的不足,本文在van der Linden的分层模型框架下基于偏正态分布建立一个反应时间的对数线性模型,并成功给出模型参数估计的马尔科夫链蒙特卡罗（Markov Chain Monte Carlo, MCMC）算法。模拟研究和实例分析的结果均表明,与对数正态模型和Box-Cox正态模型相比,对数偏正态模型表现出更加优良的拟合效果,具有更强的灵活性和适用性。     

Assessing Item Fit for Unidimensional Item Response Theory Models Using Residuals from Estimated Item Response Functions

Residual analysis (e.g. Hambleton & Swaminathan, Item response theory: principles and applications, Kluwer Academic, Boston, 1985; Hambleton, Swaminathan, & Rogers, Fundamentals of item response theory, Sage, Newbury Park, 1991) is a popular method to assess fit of item response theory (IRT) models. We suggest a form of residual analysis that may be applied to assess item fit for unidimensional IRT models. The residual analysis consists of a comparison of the maximum-likelihood estimate of the item characteristic curve with an alternative ratio estimate of the item characteristic curve. The large sample distribution of the residual is proved to be standardized normal when the IRT model fits the data. We compare the performance of our suggested residual to the standardized residual of Hambleton et al. (Fundamentals of item response theory, Sage, Newbury Park, 1991) in a detailed simulation study. We then calculate our suggested residuals using data from an operational test. The residuals appear to be useful in assessing the item fit for unidimensional IRT models.     

Using Deterministic, Gated Item Response Theory Model to Detect Test Cheating due to Item Compromise

The Deterministic, Gated Item Response Theory Model (DGM, Shu, Unpublished Dissertation. The University of North Carolina at Greensboro, 2010) is proposed to identify cheaters who obtain significant score gain on tests due to item exposure/compromise by conditioning on the item status (exposed or unexposed items). A “gated” function is introduced to decompose the observed examinees’ performance into two distributions (the true ability distribution determined by examinees’ true ability and the cheating distribution determined by examinees’ cheating ability). Test cheaters who have score gain due to item exposure are identified through the comparison of the two distributions. Hierarchical Markov Chain Monte Carlo is used as the model’s estimation framework. Finally, the model is applied in a real data set to illustrate how the model can be used to identify examinees having pre-knowledge on the exposed items.     

On Identification and Non-normal Simulation in Ordinal Covariance and Item Response Models

Psychometrika - A standard approach for handling ordinal data in covariance analysis such as structural equation modeling is to assume that the data were produced by discretizing a multivariate...     

A Speeded Item Response Model: Leave the Harder till Later

A speeded item response model is proposed. We consider the situation where examinees may retain the harder items to a later test period in a time limit test. With such a strategy, examinees may not finish answering some of the harder items within the allocated time. In the proposed model, we try to describe such a mechanism by incorporating a speeded-effect term into the two-parameter logistic item response model. A Bayesian estimation procedure of the current model using Markov chain Monte Carlo is presented, and its performance over the two-parameter logistic item response model in a speeded test is demonstrated through simulations. The methodology is applied to physics examination data of the Department Required Test for college entrance in Taiwan for illustration.     

Model Selection of Nested and Non-Nested Item Response Models Using Vuong Tests

Abstract

In this paper, we apply Vuong’s general approach of model selection to the comparison of nested and non-nested unidimensional and multidimensional item response theory (IRT) models. Vuong’s approach of model selection is useful because it allows for formal statistical tests of both nested and non-nested models. However, only the test of non-nested models has been applied in the context of IRT models to date. After summarizing the statistical theory underlying the tests, we investigate the performance of all three distinct Vuong tests in the context of IRT models using simulation studies and real data. In the non-nested case we observed that the tests can reliably distinguish between the graded response model and the generalized partial credit model. In the nested case, we observed that the tests typically perform as well as or sometimes better than the traditional likelihood ratio test. Based on these results, we argue that Vuong’s approach provides a useful set of tools for researchers and practitioners to effectively compare competing nested and non-nested IRT models.     

等级反应模型下计算机化自适应测验选题策略

计算机化自适应测验(CAT)中的选题策略,一直是国内外相关学者关注的问题。然而对多级评分的CAT的选题策略的研究却很少报导。本研究采用计算机模拟程序对等级反应模型(Graded Response Model)下CAT的四种选题策略进行研究。研究表明：等级难度值与当前能力估计值匹配选题策略的综合评价最高;在选题策略中增设 “影子题库”可以明显提高项目调用的均匀性;并且不同的项目参数分布或不同的能力估计方法都对CAT评价指标有影响     

Revisiting the 4-Parameter Item Response Model: Bayesian Estimation and Application

There has been renewed interest in Barton and Lord’s (An upper asymptote for the three-parameter logistic item response model (Tech. Rep. No. 80-20). Educational Testing Service, 1981) four-parameter item response model. This paper presents a Bayesian formulation that extends Béguin and Glas (MCMC estimation and some model fit analysis of multidimensional IRT models. Psychometrika, 66 (4):541–561, 2001) and proposes a model for the four-parameter normal ogive (4PNO) model. Monte Carlo evidence is presented concerning the accuracy of parameter recovery. The simulation results support the use of less informative uniform priors for the lower and upper asymptotes, which is an advantage to prior research. Monte Carlo results provide some support for using the deviance information criterion and \(\chi ^{2}\) index to choose among models with two, three, and four parameters. The 4PNO is applied to 7491 adolescents’ responses to a bullying scale collected under the 2005–2006 Health Behavior in School-Aged Children study. The results support the value of the 4PNO to estimate lower and upper asymptotes in large-scale surveys.     

A Doubly Latent Space Joint Model for Local Item and Person Dependence in the Analysis of Item Response Data

Item response theory (IRT) is one of the most widely utilized tools for item response analysis; however, local item and person independence, which is a critical assumption for IRT, is often violated in real testing situations. In this article, we propose a new type of analytical approach for item response data that does not require standard local independence assumptions. By adapting a latent space joint modeling approach, our proposed model can estimate pairwise distances to represent the item and person dependence structures, from which item and person clusters in latent spaces can be identified. We provide an empirical data analysis to illustrate an application of the proposed method. A simulation study is provided to evaluate the performance of the proposed method in comparison with existing methods.