Missing data imputation and corrected statistics for large-scale behavioral databases

This article presents a new methodology for solving problems resulting from missing data in large-scale item performance behavioral databases. Useful statistics corrected for missing data are described, and a new method of imputation for missing data is proposed. This methodology is applied to the Dutch Lexicon Project database recently published by Keuleers, Diependaele, and Brysbaert (Frontiers in Psychology, 1, 174, 2010), which allows us to conclude that this database fulfills the conditions of use of the method recently proposed by Courrieu, Brand-D’Abrescia, Peereman, Spieler, and Rey (2011) for testing item performance models. Two application programs in MATLAB code are provided for the imputation of missing data in databases and for the computation of corrected statistics to test models.     

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.

     

A simplified version of the maximum information per time unit method in computerized adaptive testing

In this article, we propose a simplified version of the maximum information per time unit method (MIT; Fan, Wang, Chang, & Douglas, Journal of Educational and Behavioral Statistics 37: 655–670, 2012), or MIT-S, for computerized adaptive testing. Unlike the original MIT method, the proposed MIT-S method does not require fitting a response time model to the individual-level response time data. It is also computationally efficient. The performance of the MIT-S method was compared against that of the maximum information (MI) method in terms of measurement precision, testing time saving, and item pool usage under various item response theory (IRT) models. The results indicated that when the underlying IRT model is the two- or three-parameter logistic model, the MIT-S method maintains measurement precision and saves testing time. It performs similarly to the MI method in exposure control; both result in highly skewed item exposure distributions, due to heavy reliance on the highly discriminating items. If the underlying model is the one-parameter logistic (1PL) model, the MIT-S method maintains the measurement precision and saves a considerable amount of testing time. However, its heavy reliance on time-saving items leads to a highly skewed item exposure distribution. This weakness can be ameliorated by using randomesque exposure control, which successfully balances the item pool usage. Overall, the MIT-S method with randomesque exposure control is recommended for achieving better testing efficiency while maintaining measurement precision and balanced item pool usage when the underlying IRT model is 1PL.     

A general Bayesian multilevel multidimensional IRT model for locally dependent data

Many item response theory (IRT) models take a multidimensional perspective to deal with sources that induce local item dependence (LID), with these models often making an orthogonal assumption about the dimensional structure of the data. One reason for this assumption is because of the indeterminacy issue in estimating the correlations among the dimensions in structures often specified to deal with sources of LID (e.g., bifactor and two-tier structures), and the assumption usually goes untested. Unfortunately, the mere fact that assessing these correlations is a challenge for some estimation methods does not mean that data seen in practice support such orthogonal structure. In this paper, a Bayesian multilevel multidimensional IRT model for locally dependent data is presented. This model can test whether item response data violate the orthogonal assumption that many IRT models make about the dimensional structure of the data when addressing sources of LID, and this test is carried out at the dimensional level while accounting for sampling clusters. Simulations show that the model presented is effective at carrying out this task. The utility of the model is also illustrated on an empirical data set.     

应征公民计算机自适应化拼图测验的编制

在文献回顾和参考外军有关资料的基础上,根据项目反应理论和空间能力测验的有关理论编制试题库。首先采用纸笔测验的形式进行预实验,探讨采用IRT理论编制CAT拼图测验的可行性。然后,在预实验的基础上对试题进行修订并扩充试题数量,编制计算机辅助测验。选择三参数Logistic模型,采用铆题等值设计,分7份不同的试卷在全国征兵心理检测的过程中对55777名应征公民进行施测。根据测试结果,对题目进行分析,选择高质量的题目构成CAT试题库,采用a系数分层抽样的方法控制曝光率,并采用不同的测验终止策略编制CAT拼图测验。最后用WAIS智力测验积木分测验和三门功课的考试成绩为效标,通过72名被试对CAT拼图测验进行效度验证。结果显示该测验符合项目反应理论三参数Logistic模型的假设,各题目参数比较理想,所编制的测验具有较好的信度和效度,可用于应征公民心理选拔的实践     

Normative Scoring of Multidimensional Pairwise Preference Personality Scales Using IRT: Empirical Comparisons With Other Formats

In this article, we offer some suggestions as to why tetrads and pentads have become the dominant formats for administering multidimensional forced choice (MFC) items but, in turn, raise questions regarding the underlying psychometric model and means of addressing item quality and scoring accuracy. We then focus our attention on multidimensional pairwise preference (MDPP) items and present an item response theory–based approach to constructing and modeling MDPP responses directly, assessing information at the item and scale levels, and a way of computing standard errors for trait scores and estimating scale reliability. To demonstrate the viability of this method for applied use, we show that the correspondence between MDPP scores derived from direct modeling with those obtained using single statement and unidimensional pairwise preference measures administered in a laboratory setting. Trait score correlations and criterion related validities are compared across testing formats and rating sources (i.e., self and other), and the usefulness of our model-based approach is further demonstrated by some illustrative results involving computerized adaptive tests (CAT).     

四种新的基于属性平衡的CD-CAT选题策略开发研究

基于属性平衡的CD-CAT选题策略能够保证每个认知属性被相当数量的题目测量,从而提高被试属性判准率,传统的基于属性平衡的选题策略包括MMGDI法和MGCDI法。本文针对传统的基于属性测量次数平衡选题策略进行改进,提出4种新的基于属性平衡的选题策略：RMGDI、RMCDI、SE-RMGDI、SE-RMCDI,前两种为基于属性测量次数平衡,后两种为基于属性测量精度平衡的选题策略。模拟研究表明：（1）定长CD-CAT条件下,短测验中,MMGDI表现最好,而长测验中,SE-RMGDI和SE-RMCDI的表现优于传统的属性平衡选题策略。（2）不定长CD-CAT条件下,RMGDI在判准率指标上表现优于传统的属性平衡选题策略,4种新的属性平衡策略在测量效率和综合指标上的表现均优于传统的选题策略。     

Exact person fit indexes for the rasch model for arbitrary alternatives

A new algorithm for obtaining exact person fit indexes for the Rasch model is introduced which realizes most powerful tests for a very general family of alternative hypotheses, including tests concerning DIF as well as model-deviating item correlations. The method is also used as a goodness-of-fit test for whole data sets where the item parameters are assumed to be known. For tests with 30 items at most, exact values are obtained, for longer tests a Monte Carlo-algorithm is proposed. Simulated examples and an empirical investigation demonstrate test power and applicability to item elimination.The author wishes to thank Elisabeth Ponocny-Seliger and the reviewers for many helpful comments. All exact goodness-of-fit tests proposed in this article are implemented in the menu-driven program T-Rasch 1.0 by Ponocny and Ponocny-Seliger (1999) which can be obtained from ProGAMMA (WWW: http://www.gamma.rug.nl) and also performs nonparametric tests.     

CD-CAT初始阶段项目选取方法

CD-CAT是CDA同CAT的相结合的产物,适用于课堂教学,是教师补救教学、学生自我学习的重要工具。作为CD-CAT重要组成部分的初始阶段项目选取方法是影响测验判准率的重要因素。本文基于现有研究和CDA的项目区分度提出了四种新的初始阶段项目选取方法:CTTID法、CDI法、CTTIDR*法和CDIR*法。通过模拟研究发现,在定长的CD-CAT下,题库质量是HD-HV下,初始阶段结束时,CTTIDR*法的PCCR比现有的T阵法高了.2999,比PWKL高了.1707,其它题库下趋势相同。整个测验结束时CTTIDR*法的判准率仍然是最高的。在变长的CD-CAT下,最大后验概率大于.7、.8、.9下,CTTIDR*法的被试平均测验长度比T阵法分别缩短了2.6170、2.2347、1.7470道题。     

Modeling and Testing Differential Item Functioning in Unidimensional Binary Item Response Models with a Single Continuous Covariate: A Functional Data Analysis Approach

Differential item functioning (DIF), referring to between-group variation in item characteristics above and beyond the group-level disparity in the latent variable of interest, has long been regarded as an important item-level diagnostic. The presence of DIF impairs the fit of the single-group item response model being used, and calls for either model modification or item deletion in practice, depending on the mode of analysis. Methods for testing DIF with continuous covariates, rather than categorical grouping variables, have been developed; however, they are restrictive in parametric forms, and thus are not sufficiently flexible to describe complex interaction among latent variables and covariates. In the current study, we formulate the probability of endorsing each test item as a general bivariate function of a unidimensional latent trait and a single covariate, which is then approximated by a two-dimensional smoothing spline. The accuracy and precision of the proposed procedure is evaluated via Monte Carlo simulations. If anchor items are available, we proposed an extended model that simultaneously estimates item characteristic functions (ICFs) for anchor items, ICFs conditional on the covariate for non-anchor items, and the latent variable density conditional on the covariate—all using regression splines. A permutation DIF test is developed, and its performance is compared to the conventional parametric approach in a simulation study. We also illustrate the proposed semiparametric DIF testing procedure with an empirical example.     

A mixture hierarchical model for response times and response accuracy

In real testing, examinees may manifest different types of test‐taking behaviours. In this paper we focus on two types that appear to be among the more frequently occurring behaviours – solution behaviour and rapid guessing behaviour. Rapid guessing usually happens in high‐stakes tests when there is insufficient time, and in low‐stakes tests when there is lack of effort. These two qualitatively different test‐taking behaviours, if ignored, will lead to violation of the local independence assumption and, as a result, yield biased item/person parameter estimation. We propose a mixture hierarchical model to account for differences among item responses and response time patterns arising from these two behaviours. The model is also able to identify the specific behaviour an examinee engages in when answering an item. A Monte Carlo expectation maximization algorithm is proposed for model calibration. A simulation study shows that the new model yields more accurate item and person parameter estimates than a non‐mixture model when the data indeed come from two types of behaviour. The model also fits real, high‐stakes test data better than a non‐mixture model, and therefore the new model can better identify the underlying test‐taking behaviour an examinee engages in on a certain item.     

2PLM下缺失数据处理方法及其比较

项目反应理论(IRT)是用于客观测量的现代教育与心理测量理论之一,广泛用于缺失数据十分常见的大尺度测验分析。IRT中两参数逻辑斯蒂克模型(2PLM)下仅有完全随机缺失机制下缺失反应和缺失能力处理的EM算法。本研究推导2PLM下缺失反应忽略的EM 算法,并提出随机缺失机制下缺失反应和缺失能力处理的EM算法和考虑能力估计和作答反应不确定性的多重借补法。研究显示：在各种缺失机制、缺失比例和测验设计下,缺失反应忽略的EM算法和多重借补法表现理想。     

Latent class models for testing monotonicity and invariant item ordering for polytomous items

Two assumptions that are relevant to many applications using item response theory are the assumptions of monotonicity (M) and invariant item ordering (IIO). A latent class model is proposed for ordinal items with inequality constraints on the class-specific item means. This model is used as a tool for testing for violations of M and IIO. A Gibbs sampling scheme is used for estimating the model parameters. It is shown that the deviance information criterion can be used as an overall test of M and IIO, while posterior predictive checks can be used to test these assumptions at the item level. A real data application illustrates a model-fitting strategy for detecting items that violate M and IIO.     

The linear transformation model with frailties for the analysis of item response times

The item response times (RTs) collected from computerized testing represent an underutilized source of information about items and examinees. In addition to knowing the examinees’ responses to each item, we can investigate the amount of time examinees spend on each item. In this paper, we propose a semi‐parametric model for RTs, the linear transformation model with a latent speed covariate, which combines the flexibility of non‐parametric modelling and the brevity as well as interpretability of parametric modelling. In this new model, the RTs, after some non‐parametric monotone transformation, become a linear model with latent speed as covariate plus an error term. The distribution of the error term implicitly defines the relationship between the RT and examinees’ latent speeds; whereas the non‐parametric transformation is able to describe various shapes of RT distributions. The linear transformation model represents a rich family of models that includes the Cox proportional hazards model, the Box–Cox normal model, and many other models as special cases. This new model is embedded in a hierarchical framework so that both RTs and responses are modelled simultaneously. A two‐stage estimation method is proposed. In the first stage, the Markov chain Monte Carlo method is employed to estimate the parametric part of the model. In the second stage, an estimating equation method with a recursive algorithm is adopted to estimate the non‐parametric transformation. Applicability of the new model is demonstrated with a simulation study and a real data application. Finally, methods to evaluate the model fit are suggested.     

CAT中结合贝叶斯方法与序贯监测程序的题库质量监控技术

Zhang(2013)提出了序贯监测程序(SMP)用以检测CAT中的题目在作答过程中是否发生泄漏。然而,该方法会出现虚报且未关注在题目泄漏后,对能力估计精度产生的影响。本研究在SMP基础上引入个人拟合指标,提出SMP_PFI方法,拟在给定的置信度上核实被SMP标记的题目是否真正泄漏,并探查SMP_PFI方法对能力估计精度与被封存题目数量关系的影响。实验结果表明：新方法能够有效降低SMP单独运行时的一类错误。通过控制CPFI值能够平衡能力估计精度与被封存题目数量之间的关系。     

Nonparametric IRT: Testing the bi-isotonicity of isotonic probabilistic models (ISOP)

Nonparametric tests for testing the validity of polytomous ISOP-models (unidimensional ordinal probabilistic polytomous IRT-models) are presented. Since the ISOP-model is a very general nonparametric unidimensional rating scale model the test statistics apply to a great multitude of latent trait models. A test for the comonotonicity of item sets of two or more items is suggested. Procedures for testing the comonotonicity of two item sets and for item selection are developed. The tests are based on Goodman-Kruskal's gamma index of ordinal association and are generalizations thereof. It is an essential advantage of polytomous ISOP-models within probabilistic IRT-models that the tests of validity of the model can be performed before and without the model being fitted to the data. The new test statistics have the further advantage that no prior order of items or subjects needs to be known.     

Marginal likelihood inference for a model for item responses and response times

Marginal maximum‐likelihood procedures for parameter estimation and testing the fit of a hierarchical model for speed and accuracy on test items are presented. The model is a composition of two first‐level models for dichotomous responses and response times along with multivariate normal models for their item and person parameters. It is shown how the item parameters can easily be estimated using Fisher's identity. To test the fit of the model, Lagrange multiplier tests of the assumptions of subpopulation invariance of the item parameters (i.e., no differential item functioning), the shape of the response functions, and three different types of conditional independence were derived. Simulation studies were used to show the feasibility of the estimation and testing procedures and to estimate the power and Type I error rate of the latter. In addition, the procedures were applied to an empirical data set from a computerized adaptive test of language comprehension.     

High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature

Although the Bock–Aitkin likelihood-based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations, a serious limitation of the method is its reliance on fixed-point Gauss-Hermite (G-H) quadrature in the solution of the likelihood equations and likelihood-ratio tests. When the number of latent dimensions is large, computational considerations require that the number of quadrature points per dimension be few. But with large numbers of items, the dispersion of the likelihood, given the response pattern, becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space. In this paper, we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data. In particular, we show that adaptive G-H quadrature, combined with mean and covariance adjustments at each iteration of an EM algorithm, produces an accurate fast-converging solution with as few as two points per dimension. Evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions. Unlike an earlier application of adaptive Gibbs sampling to this problem by Meng and Schilling, the simulations also confirm the validity of the present method in calculating likelihood-ratio chi-square statistics for determining the number of factors required in the model. Finally, we apply the method to a sample of real data from a test of teacher qualifications.     

可以兼顾策略、认知状态和能力的CD-CAT选题方法

当CD-CAT测验需要同时诊断被试的解题策略、认知状态并评估被试的宏观能力时,就需要在选题过程中兼顾这三个测量目标。用两种不同方式将多策略香农熵(MSSHE)指标与Fisher信息量相结合,提出多策略情境中的DWI指标MSDWI)选题法与“先用MSSHE后用Fisher信息量”的两步选题法。基于多策略RRUM模型(MS-RRUM),将这两种方法与随机选题法在不同属性数量条件下进行模拟比较,结果表明：当属性数量为4个或6个时,两步选题法在策略判准率、认知状态判准率和能力估计三个方面都有最佳的效果。     

A Two Factor ANOVA-like Test for Correlated Correlations: CORANOVA

Testing homogeneity of correlations with Fisher's Z is inappropriate when correlations are themselves correlated. Suppose measurements of brain activation and performance are taken before and during a verbal memory task. Of interest are changes in activity gradients in specific regions, R₁, R₂, R₃, and performance, V. The "correlated correlations" of interest ρ_V,R1 , ρ_V,R2 , and ρ_V,R3 , have a single variable, V, in common. We wish to compare these correlations between males and females, across regions, and to assess an interaction of the correlation. Fisher's Z can compare pairs of correlations, and Olkin and Finn's (1990) method can test homogeneity of correlated correlations across a single within factor (based on asymptotic normality), but no current procedure can test a region by gender (within by between) interaction of correlations. We propose a nonparametric method for testing this interaction and both main effects. The procedure is analogous to two-way ANOVA, but hypotheses test homogeneity of correlations, not means. The null distributions are estimated with permutations, avoiding asymptotic distributional assumptions and enhancing applicability to smaller samples and non-normal data. Simulations demonstrated maintenance of correct level (power = alpha level under the null) for normal and non-normal data and small samples. The Olkin-Finn test had inflated level for non-normal data or small samples. The Fisher's Z had inflated level for non-normal data, but not for small samples. Our method had better efficiency across contrasts and data types and sizes. Applied to correlations between regional laterality of blood flow and verbal memory performance, the method showed sensitivity to a biologically meaningful sex by region interaction in these correlations. A SAS macro for CORANOVA is available.