A Proposed Number Correct Scoring Procedure Based on Classical True-Score Theory and Multidimensional Item Response Theory

A hybrid procedure for number correct scoring is proposed. The proposed scoring procedure is based on both classical true-score theory (CTT) and multidimensional item response theory (MIRT). Specifically, the hybrid scoring procedure uses test item weights based on MIRT and the total test scores are computed based on CTT. Thus, what makes the hybrid scoring method attractive is that this method accounts for the dimensionality of the test items while test scores remain easy to compute. Further, the hybrid scoring does not require large sample sizes once the item parameters are known. Monte Carlo techniques were used to compare and contrast the proposed hybrid scoring method with three other scoring procedures. Results indicated that all scoring methods in this study generated estimated and true scores that were highly correlated. However, the hybrid scoring procedure had significantly smaller error variances between the estimated and true scores relative to the other procedures.     

复杂决策规则下MIRT的分类准确性和分类一致性

介绍多维项目反应理论模型下分类准确性和分类一致性指标, 采用蒙特卡罗方法实现复杂决策规则下指标计算, 并从数学上证明分类准确性指标两类估计量在均匀先验和相同决策规则条件下依概率收敛于同一真值。研究结果表明：分类准确性指标可以比较准确地评价分类结果的准确性; 分类一致性指标可以较好地评价分类结果的重测一致性; 在一定条件下, 基于能力量尺的指标优于基于原始总分的指标; 纵使测验维度增加, 估计精度仍比较好; 随着测验长度和维度间相关增加, 分类准确性和分类一致性更高。指标可以用来评价标准参照测验或计算机分类测验的多种决策规则下分类信度和效度。     

Acquiescent Responding in Balanced Multidimensional Scales and Exploratory Factor Analysis

Personality tests often consist of a set of dichotomous or Likert items. These response formats are known to be susceptible to an agreeing-response bias called acquiescence. The common assumption in balanced scales is that the sum of appropriately reversed responses should be reasonably free of acquiescence. However, inter-item correlation (or covariance) matrices can still be affected by the presence of variance due to acquiescence. To analyse these correlation matrices, we propose a method that is based on an unrestricted factor analysis and can be applied to multidimensional scales. This method obtains a factor solution in which acquiescence response variance is isolated in an independent factor. It is therefore possible, without the potentially confounding effect of acquiescence, to: (a) examine the dominant factors related to content latent variables; and (b) estimate participants’ factor scores on content latent variables. This method, which is illustrated by two empirical data examples, has proved to be useful for improving the simplicity of the factor structure. This research was partially supported by a grant from the Spanish Ministry of Science and Technology (SEJ2005-09170-C04-04/PSIC), and a grant from the Catalan Ministry of Universities, the Research and Information Society (2005SGR00017). The authors are obliged to the team of reviewers for helpful comments on an earlier version of this paper.     

Latent variable selection in multidimensional item response theory models using the expectation model selection algorithm

The aim of latent variable selection in multidimensional item response theory (MIRT) models is to identify latent traits probed by test items of a multidimensional test. In this paper the expectation model selection (EMS) algorithm proposed by Jiang et al. (2015) is applied to minimize the Bayesian information criterion (BIC) for latent variable selection in MIRT models with a known number of latent traits. Under mild assumptions, we prove the numerical convergence of the EMS algorithm for model selection by minimizing the BIC of observed data in the presence of missing data. For the identification of MIRT models, we assume that the variances of all latent traits are unity and each latent trait has an item that is only related to it. Under this identifiability assumption, the convergence of the EMS algorithm for latent variable selection in the multidimensional two-parameter logistic (M2PL) models can be verified. We give an efficient implementation of the EMS for the M2PL models. Simulation studies show that the EMS outperforms the EM-based L₁ regularization in terms of correctly selected latent variables and computation time. The EMS algorithm is applied to a real data set related to the Eysenck Personality Questionnaire.     

反应风格的测量与统计控制

反应风格是共同方法偏差的主要来源之一。本文首先讨论反应风格的定义和类型,梳理其危害,认为反应风格能使测验分数出现偏差,影响测验信效度分析和变量关系分析,有必要控制其危害。然后介绍了常用的反应风格测量方法,包括计数法和模型法两大类,对测量方法的选择给出了建议,在此基础上,就如何结合反应风格的测量方法与残差回归法、偏相关法来控制反应风格危害给出建议。     

反应风格的测量与统计控制

反应风格是共同方法偏差的主要来源之一。本文首先讨论反应风格的定义和类型,梳理其危害,认为反应风格能使测验分数出现偏差,影响测验信效度分析和变量关系分析,有必要控制其危害。然后介绍了常用的反应风格测量方法,包括计数法和模型法两大类,对测量方法的选择给出了建议,在此基础上,就如何结合反应风格的测量方法与残差回归法、偏相关法来控制反应风格危害给出建议。     

多维项目反应理论：参数估计及其在心理测验中的应用

本研究介绍并引进了现代测量理论中的前沿技术—— 多维项目反应理论, 采用MCMC算法实现了其参数估计; 并将MIRT应用于瑞文高级推理测验, 以探讨MIRT在心理测验中的具体应用。研究结果表明：(1)本研究自主编制的MIRT参数估计程序基本可行, 其估计的精度与国外研究结论相当甚至更好。(2)在测验维度和样本容量两因素完全随机实验设计下(2×3), 随着被试和题目样本容量的增加, MIRT参数估计的精度越高且估计的稳定性越强; 但随着测验维度的增加, MIRT参数估计精度和稳定性均随之降低。(3)MIRT对心理测验的分析比UIRT能提供更为精确和细致的信息。它对心理测验的编制、开发及评价具有重要的指导和参考价值, 值得引进及借鉴。     

不同铆测验设计下多维IRT等值方法的比较

实际应用中测验往往具有多维结构, 如果仍采用单维IRT方法进行等值, 会得到不准确的结果。因此对于多维结构的测验, 需要使用多维IRT等值方法来实现参数的转换。基于共同题设计, 文章通过模拟研究的方法, 考察了不同铆测验设计下几种多维IRT等值方法的表现, 同时考虑了测验长度、两个维度题目数量的比例、铆测验长度、铆测验的选择策略、两个维度之间的相关和等值群体的能力水平差异六个因素的影响。所比较的多维IRT等值方法有：均值/均值(MM)方法, 均值/标准差(MS)方法, Stoking-Lord (SL)方法, Haebara (HB)方法, 最小平方(LS)方法。结果显示：(1) SL, HB和LS方法得到的等值误差均方根最小, 且在各条件下表现较为稳定。(2) MM和MS方法在非等组条件下呈现出很大的误差均方根。(3)铆测验设计对SL, HB和LS方法的等值结果没有显著影响。(4)在两个维度之间的相关较高, 测验长度和铆测验长度较长, 等值群体的能力水平没有差异的条件下, SL, HB和LS方法得到的等值误差均方根最小。     

随机截距因子分析模型在控制条目表述效应中的应用

本研究用中文修订版罗森博格自尊量表(RSES-R)考察随机截距因子分析模型在控制条目表述效应时的表现。用RSES-R和过分宣称问卷组成的量表调查621名中学生。结果表明,随机截距模型在建模时,拟合指数良好、因子方差与负荷合理,自尊因子分与RSES-R总分有极高相关,表明该模型能有效分离RSES-R得分的特质与表述效应。分离的表述效应因子分与受测者的自我提升水平具有显著但较弱的相关,表明表述效应与自受测者的社会赞许性有共同的成分。     

Differential responding to positive and negative items: the case of a negative item in a questionnaire for course and faculty evaluation

Previous factor-analytic studies of self-rating scales have yielded a factor on which negatively worded items loaded separately. The present study investigated the existence for such a factor in a questionnaire for course and teacher evaluation which included one negative item. The questionnaire was administered in 1,095 university classes. Two factors emerged, an exclusively positive-item factor and another factor on which the single negative item and one positive item loaded. It was suggested that both items of Factor 2 were ambiguous and may identify tendencies such as acquiescence, random responding, and response sets.     

A bias-corrected exploratory and confirmatory factor analysis of right-wing authoritarianism: Support for a three-factor structure

The factor structure of right-wing authoritarianism (RWA) remains a contentious issue. Although designed to measure three underlying attitude clusters, aggression, submission and conventionalism, many items are deliberately double- or triple-barrelled, to capture the covariation of the three clusters in a unidimensional scale. Additionally, although the scale is balanced, there is an item wording direction bias in the clusters; aggression items are pro-trait, and conventionalism items are con-trait. Sub-scale structure is therefore potentially confounded with acquiescence bias. Although RWA as a unitary construct has been an effective tool for exploring prejudice, it would be useful in many cases to measure its underlying components directly. Proposed solutions to this problem include creating short-form scales as subsets of the original scale, or modifying items to simplify and un-confound the structure. We present convergent evidence of an underlying factor structure by considering one-, two- and three-factor solutions to the uncorrected scale and then using an indirect method to correct for acquiescence bias. Before and after correction, factor analysis supported a three-factor solution. Confirmatory factor analyses also support a three-factor solution compared to a one-factor solution.     

Using multidimensional item response theory to evaluate how response styles impact measurement

Multidimensional item response theory (MIRT) models for response style (e.g., Bolt, Lu, & Kim, 2014, Psychological Methods, 19, 528; Falk & Cai, 2016, Psychological Methods, 21, 328) provide flexibility in accommodating various response styles, but often present difficulty in isolating the effects of response style(s) from the intended substantive trait(s). In the presence of such measurement limitations, we consider several ways in which MIRT models are nevertheless useful in lending insight into how response styles may interfere with measurement for a given test instrument. Such a study can also inform whether alternative design considerations (e.g., anchoring vignettes, self-report items of heterogeneous content) that seek to control for response style effects may be helpful. We illustrate several aspects of an MIRT approach using real and simulated analyses.     

测验理论的新发展:多维项目反应理论

多维项目反应理论是基于因子分析和单维项目反应理论两大背景下发展起来的一种新型测验理论。根据被试在完成一项任务时多种能力之间是如何相互作用的,多维项目反应模型可以分为补偿性模型和非补偿性模型两类。本文在系统介绍了当前普遍使用的补偿性模型的基础上,指出后续研究者应关注多维项目反应理论中多级评分和高维空间的多维模型、补偿性和非补偿性模型的融合、参数估计程序的开发和多维测验等值四个方面的研究。     

ESTIMATING CONTENT-ACQUIESCENCE CORRELATION BY COVARIANCE STRUCTURE ANALYSIS

A topic of continuing interest in the measurement area is response acquiescence. A recent study has demonstrated the feasibiliy of studying acquiescence or, more importantly, content/acquiescence correlation in the MMPI. Utilizing the components of variance approach, this study found that the variance due to acquiescence in scores on the Pt and Hg scales was small relative to content variance, but that the correlation between acquiescence and content may be substantial for the Pt scale. The present paper describes a general statistical procedure for investigating content variance, variance due to non-content characteristics of items, and the covariances of content and various item characteristics. The data from a previous paper are reanalyzed, using alternative covariance structure models. Maximum likelihood procedures which allow for a statistical test for parameters of interest are used. The results point to the significance of the content- acquiescence correlation in the Pt scale, but not in the Hy scale. The previous findings are verified statistically, and procedures which hold promise for other investigation into the properties of behavioral tests are described.     

Acquiescence as a source of bias and model and person misfit: A theoretical and empirical analysis

In personality and attitude measurement, the presence of acquiescent responding can have an impact on the whole process of item calibration and test scoring, and this can occur even when sensible procedures for controlling acquiescence are used. This paper considers a bidimensional (content acquiescence) factor‐analytic model to be the correct model, and assesses the effects of fitting unidimensional models to theoretically unidimensional scales when acquiescence is in fact operating. The analysis considers two types of scales: non‐balanced and fully balanced. The effects are analysed at both the calibration and the scoring stages, and are of two types: bias in the item/respondent parameter estimates and model/person misfit. The results obtained theoretically are checked and assessed by means of simulation. The results and predictions are then assessed in an empirical study based on two personality scales. The implications of the results for applied personality research are discussed.     

Is the acquiescent response style problem not so mythical after all? Some results from a successful balanced F scale

It is shown that Rorer's exoneration of the F scale from acquiescent response style contamination is dependent on the finding-that various acquiescence measures fail to intercorrelate. When acquiescence is measured as the total score on adequate balanced scales scored without reversals, significant internal reliability is found. It is found, in fact, even with scales that are not particularly ambiguous. It is concluded that some scales are not responded to meaningfully by some people and if these people are not to be confounded with real high scores, balancing against acquiescence is still needed.     

IRT与MIRT在测验垂直等值中的应用

测验垂直等值是指将测试同一心理特质的不同水平的测验转换到同一个分数量尺上的过程。IRT与MIRT是实现垂直等值的主要方法。IRT无需假设被试的能力分布, 参数估计不依赖于样本, 是构建垂直量表的有效方法, 但测验不满足单维假设时其应用受到限制。MIRT结合IRT和因素分析的特点对IRT进行了拓展, 可更有效估计多维测验的项目参数和被试能力参数, 在垂直等值中有重要应用。已有研究主要探讨IRT和MIRT在垂直等值应用中的适用性、标定方法和参数估计方法, 比较研究两种方法的特性。未来研究应纳入更多变量条件进行比较研究, 拓展方法的应用。     

Ipsative and Normative Scales in Adjectival Measurement of Personality: Problems of Bias and Discrepancy

887 respondents completed ipsative and normative versions of the PAL-TOPAS personality questionnaire. Data were analysed to test for (1) systematic bias in scores associated with the two response formats and (2) predictors of the magnitude of the discrepancy in the individual's ipsative and normative scores. Discrepancy was assessed for both item responses and scale scores. Sources of biases investigated included ipsative scaling artifact, extremeness of scores on the normative scales and response variability. Results showed that systematic bias in scale scores and magnitude of discrepancy were predicted by different factors. One source of systematic bias was associated with ipsative scaling artifact: the ipsative scales measure both the scale itself and rejection of other alternatives. A second source of systematic bias was acquiescence in response to normative items. A confirmatory factor analysis showed that a good but imperfect fit to the data may be obtained by constructing a structural model of the inter-relationship between normative and ipsative scores which accommodates both sources of bias. The strongest influence on discrepancy in scale scores was extremeness of normative scoring, associated with a bias towards either general acceptance or rejection of trait adjectives. It is concluded that both normative and ipsative response formats have limitations, and it may often be desirable to assess both.     

Patterns of extreme responses to items in self-esteem scales: Does conceptualisation and item content matter?

Self-esteem (SE) scales are particularly susceptible for various response-sets. Systematic response alterations, often mirroring self-presentational item characteristics, can be triggered differentially depending on the content of items in a scale. The present study examined extreme responding to items in the global SE scale (Rosenberg, 1965) and the basic SE scale (Forsman & Johnson, 1996). The results showed that global SE scores were determined to a higher extent by extreme responses, in particular rejecting negative item content, than basic self-esteem scores. The implications of self-presentation contra self-esteem for an asymmetry in response patterns between the two scales are discussed.     

Gaussian variational estimation for multidimensional item response theory

Multidimensional item response theory (MIRT) is widely used in assessment and evaluation of educational and psychological tests. It models the individual response patterns by specifying a functional relationship between individuals' multiple latent traits and their responses to test items. One major challenge in parameter estimation in MIRT is that the likelihood involves intractable multidimensional integrals due to the latent variable structure. Various methods have been proposed that involve either direct numerical approximations to the integrals or Monte Carlo simulations. However, these methods are known to be computationally demanding in high dimensions and rely on sampling data points from a posterior distribution. We propose a new Gaussian variational expectation--maximization (GVEM) algorithm which adopts variational inference to approximate the intractable marginal likelihood by a computationally feasible lower bound. In addition, the proposed algorithm can be applied to assess the dimensionality of the latent traits in an exploratory analysis. Simulation studies are conducted to demonstrate the computational efficiency and estimation precision of the new GVEM algorithm compared to the popular alternative Metropolis–Hastings Robbins–Monro algorithm. In addition, theoretical results are presented to establish the consistency of the estimator from the new GVEM algorithm.