A Bayesian Semiparametric Item Response Model with Dirichlet Process Priors

In Item Response Theory (IRT), item characteristic curves (ICCs) are illustrated through logistic models or normal ogive models, and the probability that examinees give the correct answer is usually a monotonically increasing function of their ability parameters. However, since only limited patterns of shapes can be obtained from logistic models or normal ogive models, there is a possibility that the model applied does not fit the data. As a result, the existing method can be rejected because it cannot deal with various item response patterns. To overcome these problems, we propose a new semiparametric IRT model using a Dirichlet process mixture logistic distribution. Our method does not rely on assumptions but only requires that the ICCs be a monotonically nondecreasing function; that is, our method can deal with more types of item response patterns than the existing methods, such as the one-parameter normal ogive models or the two- or three-parameter logistic models.     

High-dimensional Exploratory Item Factor Analysis by A Metropolis–Hastings Robbins–Monro Algorithm

A Metropolis–Hastings Robbins–Monro (MH-RM) algorithm for high-dimensional maximum marginal likelihood exploratory item factor analysis is proposed. The sequence of estimates from the MH-RM algorithm converges with probability one to the maximum likelihood solution. Details on the computer implementation of this algorithm are provided. The accuracy of the proposed algorithm is demonstrated with simulations. As an illustration, the proposed algorithm is applied to explore the factor structure underlying a new quality of life scale for children. It is shown that when the dimensionality is high, MH-RM has advantages over existing methods such as numerical quadrature based EM algorithm. Extensions of the algorithm to other modeling frameworks are discussed.     

Multidimensional Adaptive Testing with Optimal Design Criteria for Item Selection

Several criteria from the optimal design literature are examined for use with item selection in multidimensional adaptive testing. In particular, it is examined what criteria are appropriate for adaptive testing in which all abilities are intentional, some should be considered as a nuisance, or the interest is in the testing of a composite of the abilities. Both the theoretical analyses and the studies of simulated data in this paper suggest that the criteria of A-optimality and D-optimality lead to the most accurate estimates when all abilities are intentional, with the former slightly outperforming the latter. The criterion of E-optimality showed occasional erratic behavior for this case of adaptive testing, and its use is not recommended. If some of the abilities are nuisances, application of the criterion of A _s -optimality (or D _s -optimality), which focuses on the subset of intentional abilities is recommended. For the measurement of a linear combination of abilities, the criterion of c-optimality yielded the best results. The preferences of each of these criteria for items with specific patterns of parameter values was also assessed. It was found that the criteria differed mainly in their preferences of items with different patterns of values for their discrimination parameters. The first author is now at the Department of Methodology and Statistics, Statistics, Faculty of Social Sciences, Utrecht University, Heidelberglaan 1, 3854 Utrecht, The Netherlands. The second author is now at Research Department, CTB/McGraw-Hill, Monterey, CA, USA.     

A Social Desirability Item Response Theory Model: Retrieve–Deceive–Transfer

Psychometrika - In this study, a new item response theory model is developed to account for situations in which respondents overreport or underreport their actual opinions on a positive or negative...     

Taxicab Correspondence Analysis of Contingency Tables with One Heavyweight Column

The aim of this paper is to study the analysis of contingency tables with one heavyweight column or one heavyweight entry by taxicab correspondence analysis (TCA). Given that the mathematics of TCA is simpler than the mathematics of correspondence analysis (CA), the influence of one heavyweight column on the outputs of TCA is studied explicitly without recourse to asymptotics as done by Benzécri (Les Cahiers de L’Analyse des Données 4:413–16, 1979). A reweighting of the heavyweight column is proposed, which can also be applied to CA. A real data set is analyzed. This research is financed by NSERC of Canada. The author is grateful to the Editor, Professor B. Junker, to an Associate Editor and to three referees for their constructive comments.     

Measuring Growth in a Longitudinal Large-Scale Assessment with a General Latent Variable Model

The aim of the research presented here is the use of extensions of longitudinal item response theory (IRT) models in the analysis and comparison of group-specific growth in large-scale assessments of educational outcomes.     

Is Clinical Anxiety a Risk or a Protective Factor for Executive Functioning in Youth with ADHD? A Meta-regression Analysis

Comorbidity rates between ADHD and anxiety disorders (AD) are high, but little is known about the nature of this co-occurrence. A dominant idea is that AD may intensify some (i.e., attention and working memory) and attenuate other (i.e., inhibition) ADHD symptoms. Results are mixed, potentially because of between-study differences. To investigate this further we performed a meta-regression analysis on 11 studies (n ‘ADHD-only’ = 695; n ‘ADHD + AD’ = 608), containing 35 effect sizes on attention, inhibition and working memory. Main results were: (1) no evidence of a negative effect of AD on attention and working memory; (2) better response inhibition in children with ADHD with AD than those with only ADHD (medium ES g = ? .40); (3) medication moderated this association: the effect seemed limited to studies that included medication-naïve participants; (4) the difference between the two groups increased with age for attention and with proportion of boys for working memory ability. There was no effect of comorbid disruptive behavior disorder. In conclusion, AD seems to be a protective factor for inhibition problems as assessed with laboratory tasks in ADHD, especially in children who are medication naïve. Further, AD may have a protective function for attention in older children, and for working memory in boys with ADHD. It is therefore important to screen for AD when diagnosing ADHD, and to educate those with comorbid AD about the possible positive function of feeling anxious. Potential negative effects of ADHD medication on inhibition in children with comorbid AD should be considered.     

A Note on Stochastic Ordering of the Latent Trait Using the Sum of Polytomous Item Scores

In contrast to dichotomous item response theory (IRT) models, most well-known polytomous IRT models do not imply stochastic ordering of the latent trait by the total test score (SOL). This has been thought to make the ordering of respondents on the latent trait using the total test score questionable and throws doubt on the justifiability of using nonparametric polytomous IRT models for ordinal measurement. We show that a broad class of polytomous IRT models has a weaker form of SOL, denoted weak SOL, and argue that weak SOL justifies ordering respondents on the latent trait using the total test score and, therefore, the use of nonparametric polytomous IRT models for ordinal measurement.     

Evaluating Exploratory Factor Analysis Which Initial-Extraction Techniques Provide the Best Factor Fidelity?

Attacks by communication scholars on exploratory factor analysis (EFA) have cast doubt on prior findings based on the technique. The present study is one in a series of studies performed to test the ability of EFA to produce results that replicate known dimensions in a data set. It was designed to determine which of 7 initial extraction techniques produce the highest factor fidelity across 5 item distribution shapes and 3 sample sizes. Monte-Carlo-created data sets with known factors, known item distribution shapes, and a 30% error rate were submitted to EFA. Results from an analysis of variance (ANOH) indicate that image analysis reaches perfect factor fidelity with a smaller number of cases regardless of item distribution shape. This and other results reported in this study suggest that3ndings based on EFA should be viewed with cautious optimism and be evaluated according to the findings from this and similar studies.     

Model Evaluation and Multiple Strategies in Cognitive Diagnosis: An Analysis of Fraction Subtraction Data

This paper studies three models for cognitive diagnosis, each illustrated with an application to fraction subtraction data. The objective of each of these models is to classify examinees according to their mastery of skills assumed to be required for fraction subtraction. We consider the DINA model, the NIDA model, and a new model that extends the DINA model to allow for multiple strategies of problem solving. For each of these models the joint distribution of the indicators of skill mastery is modeled using a single continuous higher-order latent trait, to explain the dependence in the mastery of distinct skills. This approach stems from viewing the skills as the specific states of knowledge required for exam performance, and viewing these skills as arising from a broadly defined latent trait resembling the θ of item response models. We discuss several techniques for comparing models and assessing goodness of fit. We then implement these methods using the fraction subtraction data with the aim of selecting the best of the three models for this application. We employ Markov chain Monte Carlo algorithms to fit the models, and we present simulation results to examine the performance of these algorithms. The work reported here was performed under the auspices of the External Diagnostic Research Team funded by Educational Testing Service. Views expressed in this paper does not necessarily represent the views of Educational Testing Service.     

Investigating the Impact of Uncertainty About Item Parameters on Ability Estimation

Asymptotic expansions of the maximum likelihood estimator (MLE) and weighted likelihood estimator (WLE) of an examinee’s ability are derived while item parameter estimators are treated as covariates measured with error. The asymptotic formulae present the amount of bias of the ability estimators due to the uncertainty of item parameter estimators. A numerical example is presented to illustrate how to apply the formulae to evaluate the impact of uncertainty about item parameters on ability estimation and the appropriateness of estimating ability using the regular MLE or WLE method.     

A Latent Class Multidimensional Scaling Model for Two-Way One-Mode Continuous Rating Dissimilarity Data

In this paper, we propose a cluster-MDS model for two-way one-mode continuous rating dissimilarity data. The model aims at partitioning the objects into classes and simultaneously representing the cluster centers in a low-dimensional space. Under the normal distribution assumption, a latent class model is developed in terms of the set of dissimilarities in a maximum likelihood framework. In each iteration, the probability that a dissimilarity belongs to each of the blocks conforming to a partition of the original dissimilarity matrix, and the rest of parameters, are estimated in a simulated annealing based algorithm. A model selection strategy is used to test the number of latent classes and the dimensionality of the problem. Both simulated and classical dissimilarity data are analyzed to illustrate the model.     

Confirmatory Factor Analysis of Arnold et al.’s Parenting Scale Across Race, Age, and Sex

We used confirmatory factor analysis (CFA) to investigate the factor structure of several models of Arnold et al.’s Parenting Scale [Arnold et al. (1993). Psychological Assessment, 5, 137–144] across children from various age groups and races. Participants were parents of children (ages 2–16 years) presenting to four community-based pediatric practices for routine care. Parents completed questionnaires pertaining to various aspects of parenting and child behavior problems. Results indicated that a two-factor revision proposed by Reitman et al. [(2001). Journal of Clinical Child Psychology, 30, 514–524] represented the data well and better than the original three-factor structure and other two-factor models. Results from multigroup CFA analyses indicated that this factor structure did not vary across child sex, child age, and parental race. Results of validity analyses indicated that scores on both factors were related to reports of children’s behavior and parental affect and cognitions. This study was the first to use multigroup CFA procedures to demonstrate that relationships between individual items and factors of the Parenting Scale are similar for parents of children across various age groups.     

Discrete Choice Models for Ordinal Response Variables: A Generalization of the Stereotype Model

In this paper I present a class of discrete choice models for ordinal response variables based on a generalization of the stereotype model. The stereotype model can be derived and generalized as a random utility model for ordered alternatives. Random utility models can be specified to account for heteroscedastic and correlated utilities. In the case of the generalized stereotype model this includes category-specific random effects due to individual differences in response style. But unlike standard random utility models the generalized stereotype model is better suited for ordinal response variables and can be interpreted as a kind of unidimensional unfolding model. This paper discusses the specification, interpretation, identification, and estimation of generalized stereotype models. Two applications are provided for illustration. This paper benefited significantly from the comments and suggestions of the editor, associate editor, and three anonymous reviewers. It is dedicated to my late colleague, peer, and friend Bradley D. Crouch.     

College Women��s Feminist Identity: A Multidimensional Analysis with Implications for Coping with Sexism

This study examined components of women's feminist identity and possible relations to their reported coping responses to sexism. A sample of 169 undergraduate women (M?=?19.4?y, SD?=?1.2) from diverse ethnic backgrounds completed surveys assessing their experiences and gender-related views. The first set of analyses revealed that women's social gender identity, exposure to feminism, and gender-egalitarian attitudes independently contributed to feminist identification; moreover, non-stereotyping of feminists further predicted feminist self-identification. A second set of analyses tested the relative contribution of feminist identity components to women's cognitive appraisals of coping responses to sexual harassment. Seeking social support was predicted by self-identification as a feminist (for White European American women only). Confronting was predicted by social gender identity, non-stereotyping of feminists, and public identification as a feminist. Findings highlight possible components of women's feminist identity and their possible impact on coping responses to sexism.     

A Psychometric Analysis of the Trait Emotional Intelligence Questionnaire–Short Form (TEIQue–SF) Using Item Response Theory

Trait emotional intelligence refers to a constellation of emotional self-perceptions located at the lower levels of personality hierarchies. In 2 studies, we sought to examine the psychometric properties of the Trait Emotional Intelligence Questionnaire–Short Form (TEIQue–SF; Petrides, 2009) using item response theory (IRT). Study 1 (N= 1,119, 455 men) showed that most items had good discrimination and threshold parameters and high item information values. At the global level, the TEIQue–SF showed very good precision across most of the latent trait range. Study 2 (N= 866, 432 men) used similar IRT techniques in a new sample based on the latest version of the TEIQue–SF (version 1.50). Results replicated Study 1, with the instrument showing good psychometric properties at the item and global level. Overall, the 2 studies suggest the TEIQue-SF can be recommended when a rapid assessment of trait emotional intelligence is required.     

A Note on Comparing the Estimates of Models for Cluster-Correlated or Longitudinal Data with Binary or Ordinal Outcomes

When using linear models for cluster-correlated or longitudinal data, a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps. New predictors might be added to the model, or a more complex covariance structure might be specified for the observations. When fitting models for binary or ordered-categorical outcomes, however, comparisons between such models are impeded by the implicit rescaling of the model estimates that takes place with the inclusion of new predictors and/or random effects. This paper presents an approach for putting the estimates on a common scale to facilitate relative comparisons between models fit to binary or ordinal outcomes. The approach is developed for both population-average and unit-specific models.     

A Robust Bayesian Approach for Structural Equation Models with Missing Data

In this paper, normal/independent distributions, including but not limited to the multivariate t distribution, the multivariate contaminated distribution, and the multivariate slash distribution, are used to develop a robust Bayesian approach for analyzing structural equation models with complete or missing data. In the context of a nonlinear structural equation model with fixed covariates, robust Bayesian methods are developed for estimation and model comparison. Results from simulation studies are reported to reveal the characteristics of estimation. The methods are illustrated by using a real data set obtained from diabetes patients.