混合IRT潜在模型及其应用轨迹

项目反应理论是测量被试潜在特质的现代测量理论, 潜在类别分析是基于模型的潜在特质分类技术。混合项目反应理论将项目反应理论与潜在类别分析相结合, 能够同时对被试分类并量化其潜在特质。在阐述混合项目反应理论概念、原理的基础上, 介绍了MRM、mNRM和mPCM等几种常见混合模型及其参数估计方法, 并从心理与行为特征分类、项目功能差异检测、测验效度评价等方面评述了其在心理测验中的应用发展轨迹。     

General mixture item response models with different item response structures: Exposition with an application to Likert scales

This article proposes a general mixture item response theory (IRT) framework that allows for classes of persons to differ with respect to the type of processes underlying the item responses. Through the use of mixture models, nonnested IRT models with different structures can be estimated for different classes, and class membership can be estimated for each person in the sample. If researchers are able to provide competing measurement models, this mixture IRT framework may help them deal with some violations of measurement invariance. To illustrate this approach, we consider a two-class mixture model, where a person’s responses to Likert-scale items containing a neutral middle category are either modeled using a generalized partial credit model, or through an IRTree model. In the first model, the middle category (“neither agree nor disagree”) is taken to be qualitatively similar to the other categories, and is taken to provide information about the person’s endorsement. In the second model, the middle category is taken to be qualitatively different and to reflect a nonresponse choice, which is modeled using an additional latent variable that captures a person’s willingness to respond. The mixture model is studied using simulation studies and is applied to an empirical example.     

Investigating latent constructs with item response models: A MATLAB IRTm toolbox

Item response theory (IRT) models are the central tools in modern measurement and advanced psychometrics. We offer a MATLAB IRT modeling (IRTm) toolbox that is freely available and that follows an explicit design matrix approach, giving the end user control and flexibility in building a model that goes beyond standard models, such as the Rasch model (Rasch, 1960) and the two-parameter logistic model. As such, IRTm allows for a large variety of unidimensional IRT models for binary responses, the incorporation of additional person and item information, and deviations from common model assumptions. An exclusive key feature of the toolbox is the inclusion of copula IRT models to handle local item dependencies. Two appendixes for this report, containing example code and information on the general copula IRT in IRTm, may be downloaded from brm.psychonomic-journals.org/content/supplemental.     

An IRT Model with a Parameter-Driven Process for Change

An IRT model with a parameter-driven process for change is proposed. Quantitative differences between persons are taken into account by a continuous latent variable, as in common IRT models. In addition, qualitative interindividual differences and autodependencies are accounted for by assuming within-subject variability with respect to the parameters of the IRT model. In particular, the parameters of the IRT model are governed by an unobserved or “hidden'” homogeneous Markov process. The model includes the mixture linear logistic test model (Mislevy & Verhelst, 1990), the mixture Rasch model (Rost, 1990), and the Saltus model (Wilson, 1989) as specific instances. The model is applied to a longitudinal experiment on discontinuity in conservation acquisition (van der Maas, 1993). Frank Rijmen was supported by the Fund for Scientific Research Flanders (FWO), the GOA/2000/02 granted by the Katholieke Universiteit Leuven to Paul De Boeck and Iven Van Mechelen, and the PDM/02/067 granted by the Katholieke Universiteit Leuven to Paul De Boeck.     

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.     

Analyzing Longitudinal Item Response Data via the Pairwise Fitting Method

Multidimensional item response theory (MIRT) models can be applied to longitudinal educational surveys where a group of individuals are administered different tests over time with some common items. However, computational problems typically arise as the dimension of the latent variables increases. This is especially true when the latent variable distribution cannot be integrated out analytically, as with MIRT models for binary data. In this article, based on the pseudolikelihood theory, we propose a pairwise modeling strategy to estimate item and population parameters in longitudinal studies. Our pairwise method effectively reduces the dimensionality of the problem and hence is applicable to longitudinal IRT data with high-dimensional latent variables, which are challenging for classical methods. And in the low-dimensional case, our simulation study shows that it performs comparably with the classical methods. We further illustrate the implementation of the pairwise method using a development study of mathematics levels of junior high school students in which the response data are collected from 65 classes of 8 schools from 4 different school districts in China.     

Testing Differential Item Functioning in Small Samples

Abstract

Differential item functioning (DIF) is a pernicious statistical issue that can mask true group differences on a target latent construct. A considerable amount of research has focused on evaluating methods for testing DIF, such as using likelihood ratio tests in item response theory (IRT). Most of this research has focused on the asymptotic properties of DIF testing, in part because many latent variable methods require large samples to obtain stable parameter estimates. Much less research has evaluated these methods in small sample sizes despite the fact that many social and behavioral scientists frequently encounter small samples in practice. In this article, we examine the extent to which model complexity—the number of model parameters estimated simultaneously—affects the recovery of DIF in small samples. We compare three models that vary in complexity: logistic regression with sum scores, the 1-parameter logistic IRT model, and the 2-parameter logistic IRT model. We expected that logistic regression with sum scores and the 1-parameter logistic IRT model would more accurately estimate DIF because these models yielded more stable estimates despite being misspecified. Indeed, a simulation study and empirical example of adolescent substance use show that, even when data are generated from / assumed to be a 2-parameter logistic IRT, using parsimonious models in small samples leads to more powerful tests of DIF while adequately controlling for Type I error. We also provide evidence for minimum sample sizes needed to detect DIF, and we evaluate whether applying corrections for multiple testing is advisable. Finally, we provide recommendations for applied researchers who conduct DIF analyses in small samples.     

Robust Measurement via A Fused Latent and Graphical Item Response Theory Model

Item response theory (IRT) plays an important role in psychological and educational measurement. Unlike the classical testing theory, IRT models aggregate the item level information, yielding more accurate measurements. Most IRT models assume local independence, an assumption not likely to be satisfied in practice, especially when the number of items is large. Results in the literature and simulation studies in this paper reveal that misspecifying the local independence assumption may result in inaccurate measurements and differential item functioning. To provide more robust measurements, we propose an integrated approach by adding a graphical component to a multidimensional IRT model that can offset the effect of unknown local dependence. The new model contains a confirmatory latent variable component, which measures the targeted latent traits, and a graphical component, which captures the local dependence. An efficient proximal algorithm is proposed for the parameter estimation and structure learning of the local dependence. This approach can substantially improve the measurement, given no prior information on the local dependence structure. The model can be applied to measure both a unidimensional latent trait and multidimensional latent traits.     

Unidimensionality and bandwidth in the Center for Epidemiologic Studies Depression (CES-D) Scale

In this study, we compared classical test theory (CTT) and item response theory (IRT) approaches in analyzing the Center for Epidemiological Studies Depression (CES-D) Scale (Radloff, 1977). Standard item analyses, as well as Rasch (1960) analyses, both revealed item departures from unidimensionality in a sample of 2,455 older persons responding to the CES-D. Positive affect items in the scale performed poorly overall, their removal reducing the scale's bandwidth only slightly. Modeling depression scores derived from Rasch measures and raw totals showed subtle but important differences for statistical inference. The assessment of depressive risk was slightly enhanced by using 16-item scale measures obtained from the results of the Rasch analysis as the dependent variable. Confirmatory factor analysis and parallel analysis verified the advantages of removing positively worded items. IRT and CTT techniques proved to be complementary in this study and can be usefully combined to improve measuring depression.     

Constant latent odds-ratios models and the mantel-haenszel null hypothesis

In the present paper, a new family of item response theory (IRT) models for dichotomous item scores is proposed. Two basic assumptions define the most general model of this family. The first assumption is local independence of the item scores given a unidimensional latent trait. The second assumption is that the odds-ratios for all item-pairs are constant functions of the latent trait. Since the latter assumption is characteristic of the whole family, the models are called constant latent odds-ratios (CLORs) models. One nonparametric special case and three parametric special cases of the general CLORs model are shown to be generalizations of the one-parameter logistic Rasch model. For all CLORs models, the total score (the unweighted sum of the item scores) is shown to be a sufficient statistic for the latent trait. In addition, conditions under the general CLORs model are studied for the investigation of differential item functioning (DIF) by means of the Mantel-Haenszel procedure. This research was supported by the Dutch Organization for Scientific Research (NWO), grant number 400-20-026.     

Detecting differential item functioning with confirmatory factor analysis and item response theory: toward a unified strategy

In this article, the authors developed a common strategy for identifying differential item functioning (DIF) items that can be implemented in both the mean and covariance structures method (MACS) and item response theory (IRT). They proposed examining the loadings (discrimination) and the intercept (location) parameters simultaneously using the likelihood ratio test with a free-baseline model and Bonferroni corrected critical p values. They compared the relative efficacy of this approach with alternative implementations for various types and amounts of DIF, sample sizes, numbers of response categories, and amounts of impact (latent mean differences). Results indicated that the proposed strategy was considerably more effective than an alternative approach involving a constrained-baseline model. Both MACS and IRT performed similarly well in the majority of experimental conditions. As expected, MACS performed slightly worse in dichotomous conditions but better than IRT in polytomous cases where sample sizes were small. Also, contrary to popular belief, MACS performed well in conditions where DIF was simulated on item thresholds (item means), and its accuracy was not affected by impact.     

多水平项目反应理论模型在测验发展中的应用

作者简要介绍了多水平项目反应模型,对多水平项目反应理论与通常项目反应理论之间的关系进行了探讨,得到了多水平项目反应模型参数与通常项目反应模型参数之间的关系,并讨论了多水平项目反应模型的推广模型。通过一个实际例子,用多水平项目反应模型对测验中项目的特征进行分析;检验个体水平和组水平预测变量对能力参数的影响;对项目功能差异进行分析。最后文章就多水平项目反应理论模型的优势与不足进行了讨论     

Cognitive psychology meets psychometric theory: on the relation between process models for decision making and latent variable models for individual differences

This article analyzes latent variable models from a cognitive psychology perspective. We start by discussing work by Tuerlinckx and De Boeck (2005), who proved that a diffusion model for 2-choice response processes entails a 2-parameter logistic item response theory (IRT) model for individual differences in the response data. Following this line of reasoning, we discuss the appropriateness of IRT for measuring abilities and bipolar traits, such as pro versus contra attitudes. Surprisingly, if a diffusion model underlies the response processes, IRT models are appropriate for bipolar traits but not for ability tests. A reconsideration of the concept of ability that is appropriate for such situations leads to a new item response model for accuracy and speed based on the idea that ability has a natural zero point. The model implies fundamentally new ways to think about guessing, response speed, and person fit in IRT. We discuss the relation between this model and existing models as well as implications for psychology and psychometrics.     

协单参数单维度Rasch模型的优势与意义

相比多参数多维度IRT模型通过增加参数的方式来提升模型拟合度和解释度，Rasch模型流派强调“理论驱动研究”和“数据符合模型”，推崇单参数单维度的测量模型能最大限度地减少额外因素对真实测量目的的影响和干扰，从而保证测量的客观性和准确性。Rasch模型关注测量目标与测量工具的对应关系，它的“简单”特性有助于研究者更准确地评估和解释被测目标与测量工具间的适配性，且在将非线性数据转化为等距数据时具有天然的优势。     

An introduction to mixture item response theory models

Mixture item response theory (IRT) allows one to address situations that involve a mixture of latent subpopulations that are qualitatively different but within which a measurement model based on a continuous latent variable holds. In this modeling framework, one can characterize students by both their location on a continuous latent variable as well as by their latent class membership. For example, in a study of risky youth behavior this approach would make it possible to estimate an individual's propensity to engage in risky youth behavior (i.e., on a continuous scale) and to use these estimates to identify youth who might be at the greatest risk given their class membership. Mixture IRT can be used with binary response data (e.g., true/false, agree/disagree, endorsement/not endorsement, correct/incorrect, presence/absence of a behavior), Likert response scales, partial correct scoring, nominal scales, or rating scales. In the following, we present mixture IRT modeling and two examples of its use. Data needed to reproduce analyses in this article are available as supplemental online materials at http://dx.doi.org/10.1016/j.jsp.2016.01.002.     

Diagnosing item score patterns on a test using item response theory-based person-fit statistics

Person-fit statistics have been proposed to investigate the fit of an item score pattern to an item response theory (IRT) model. The author investigated how these statistics can be used to detect different types of misfit. Intelligence test data were analyzed using person-fit statistics in the context of the G. Rasch (1960) model and R. J. Mokken's (1971, 1997) IRT models. The effect of the choice of an IRT model to detect misfitting item score patterns and the usefulness of person-fit statisticsfor diagnosis of misfit are discussed. Results showed that different types of person-fit statistics can be used to detect different kinds of person misfit. Parametric person-fit statistics had more power than nonparametric person-fit statistics.     

Random Item IRT Models

It is common practice in IRT to consider items as fixed and persons as random. Both, continuous and categorical person parameters are most often random variables, whereas for items only continuous parameters are used and they are commonly of the fixed type, although exceptions occur. It is shown in the present article that random item parameters make sense theoretically, and that in practice the random item approach is promising to handle several issues, such as the measurement of persons, the explanation of item difficulties, and trouble shooting with respect to DIF. In correspondence with these issues, three parts are included. All three rely on the Rasch model as the simplest model to study, and the same data set is used for all applications. First, it is shown that the Rasch model with fixed persons and random items is an interesting measurement model, both, in theory, and for its goodness of fit. Second, the linear logistic test model with an error term is introduced, so that the explanation of the item difficulties based on the item properties does not need to be perfect. Finally, two more models are presented: the random item profile model (RIP) and the random item mixture model (RIM). In the RIP, DIF is not considered a discrete phenomenon, and when a robust regression approach based on the RIP difficulties is applied, quite good DIF identification results are obtained. In the RIM, no prior anchor sets are defined, but instead a latent DIF class of items is used, so that posterior anchoring is realized (anchoring based on the item mixture). It is shown that both approaches are promising for the identification of DIF.     

Bayesian estimation and model selection in ordered latent class models for polytomous items

In a latent class IRT model in which the latent classes are ordered on one dimension, the class specific response probabilities are subject to inequality constraints. The number of these inequality constraints increase dramatically with the number of response categories per item, if assumptions like monotonicity or double monotonicity of the cumulative category response functions are postulated. A Markov chain Monte Carlo method, the Gibbs sampler, can sample from the multivariate posterior distribution of the parameters under the constraints. Bayesian model selection can be done by posterior predictive checks and Bayes factors. A simulation study is done to evaluate results of the application of these methods to ordered latent class models in three realistic situations. Also, an example of the presented methods is given for existing data with polytomous items. It can be concluded that the Bayesian estimation procedure can handle the inequality constraints on the parameters very well. However, the application of Bayesian model selection methods requires more research.     

Comparing Latent Structures of the Grade of Membership,Rasch, and Latent Class Models

This paper focuses on model interpretation issues and employs a geometric approach to compare the potential value of using the Grade of Membership (GoM) model in representing population heterogeneity. We consider population heterogeneity manifolds generated by letting subject specific parameters vary over their natural range, while keeping other population parameters fixed, in the marginal space (based on marginal probabilities) and in the full parameter space (based on cell probabilities). The case of a 2 × 2 contingency table is discussed in detail, and a generalization to 2^J tables with J ≥ 3 is sketched. Our approach highlights the main distinction between the GoM model and the probabilistic mixture of classes by demonstrating geometrically the difference between the concepts of partial and probabilistic memberships. By using the geometric approach we show that, in special cases, the GoM model can be thought of as being similar to an item response theory (IRT) model in representing population heterogeneity. Finally, we show that the GoM item parameters can provide quantities analogous to more general logistic IRT item parameters. As a latent structure model, the GoM model might be considered a useful alternative for a data analysis when both classes of extreme responses, and additional heterogeneity that cannot be captured by those latent classes, are expected in the population. This work was supported by Award #1R03 AG18986-01 from the National Institute on Aging and NIH grant #1R01 CA94212-01. The presentation of the ideas in this paper owes much to discussions with Stephen Fienberg and Brian Junker, Carnegie Mellon University. The author thanks Jim Ramsay and two anonymous reviewers for their valuable comments on earlier drafts of this paper.     

Psychometric examination of the short version of the learning climate questionnaire using item response theory

Self-determination theory proposes that autonomy support in the classroom is critical for students’ optimal motivation and performance. However, the literature has not adequately demonstrated the psychometric qualities of the most popular measurement for autonomy-supportive classrooms, the Learning Climate Questionnaire (LCQ) and its short version. Using the graded response model in item response theory (IRT), the current study evaluates the short version of the LCQ with a large sample (N?=?13570). IRT and classic psychometric analyses show that the scale is generally satisfactory in measuring latent learning climate, with the exceptions that Item 4 appears to be inadequate and that the scale is relatively weak in distinguishing highly autonomy-supportive classrooms. We provide suggestions for future studies, such as dropping Item 4 and including more items that tap into instructional practices located on the higher end of the latent autonomy support spectrum. Implications of the current findings for the conceptualization of autonomy support are also discussed.