A nonparametric approach for assessing latent trait unidimensionality

Assuming a nonparametric family of item response theory models, a theory-based procedure for testing the hypothesis of unidimensionality of the latent space is proposed. The asymptotic distribution of the test statistic is derived assuming unidimensionality, thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait. Based upon a new notion of dimensionality, the test is shown to have asymptotic power 1. A 6300 trial Monte Carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice.The referees' comments were remarkably detailed and greatly enhanced the writeup and sensitized the author to certain pertinent issues. Discussions with Fritz Drasgow, Lloyd Humphreys, Dennis Jennings, Brian Junker, Robert Linn, Ratna Nandakumar, and Robin Shealy were also very useful.This research was supported by the Office of Naval Research under grant N00014-84-K-0186; NR 150-533, and by the National Science Foundation under grant DMS 85-03321.     

A taxonomy of item response models

A number of models for categorical item response data have been proposed in recent years. The models appear to be quite different. However, they may usefully be organized as members of only three distinct classes, within which the models are distinguished only by assumptions and constraints on their parameters. “Difference models” are appropriate for ordered responses, “divide-by-total” models may be used for either ordered or nominal responses, and “left-side added” models are used for multiple-choice responses with guessing. The details of the taxonomy and the models are described in this paper. The present study was supported in part by two postdoctoral fellowships awarded to Lynne Steinberg: an Educational Testing Service Postdoctoral Fellowship at ETS, Princeton, NJ and an NIMH Individual National Research Service Award at Stanford University, Stanford, CA. Helpful comments by the editor and three anonymous reviewers are gratefully acknowledged.     

The comparison problem for approximating epistemic ideals

Some epistemologists think that the Bayesian ideals matter because we can approximate them. That is, our attitudes can be more or less close to the ones of our ideal Bayesian counterpart. In this paper, I raise a worry for this justification of epistemic ideals. The worry is this: In order to correctly compare agents to their ideal counterparts, we need to imagine idealized agents who have the same relevant information, knowledge, or evidence. However, there are cases in which one's ideal counterpart cannot have one's information, knowledge, or evidence. In these situations, agents cannot compare themselves to their ideal counterpart.     

The influence of mindset abstraction on preference for mixed versus extreme approaches to multigoal pursuits

Facing multiple conflicting goals, consumers may attempt to simultaneously pursue multiple goals by choosing mixed vice–virtue bundles in each consumption episode (mixed approach). Alternatively, they may maximize their pursuit of one goal at a time and sequentially manage multiple goals by alternating between pure-virtue and pure-vice bundles across consumption episodes (extreme approach). The current research proposes that consumer preferences between the two approaches depend on mindset abstraction. Across four experimental studies in the domains of food and financial decision-making, we demonstrate that, relative to an abstract mindset, a concrete mindset increases preference for the extreme approach over the mixed approach. Furthermore, by observing actual food choices over a seven-day period, this research provides a comprehensive picture of how a chronic mindset relates to multigoal management in long-term consumption patterns. The findings have both theoretical implications for the goal literature and managerial implications for marketers and policymakers.     

Premature conclusions about the signal-to-noise ratio in structural equation modeling research: A commentary on Yuan and Fang (2023)

In a recent article published in this journal, Yuan and Fang (British Journal of Mathematical and Statistical Psychology, 2023) suggest comparing structural equation modeling (SEM), also known as covariance-based SEM (CB-SEM), estimated by normal-distribution-based maximum likelihood (NML), to regression analysis with (weighted) composites estimated by least squares (LS) in terms of their signal-to-noise ratio (SNR). They summarize their findings in the statement that “[c]ontrary to the common belief that CB-SEM is the preferred method for the analysis of observational data, this article shows that regression analysis via weighted composites yields parameter estimates with much smaller standard errors, and thus corresponds to greater values of the [SNR].” In our commentary, we show that Yuan and Fang have made several incorrect assumptions and claims. Consequently, we recommend that empirical researchers not base their methodological choice regarding CB-SEM and regression analysis with composites on the findings of Yuan and Fang as these findings are premature and require further research.     

“均”与“寡”阶段性变动下中国居民公平感的变迁

利用中国综合社会调查和中国社会状况综合调查重复截面数据,通过年龄-时期-队列模型对居民公平感的时代变化进行分析。研究发现公平感在年龄上呈“J”型趋势;从时期效应看, 2008年公平感较高, 2010～2013年在低谷徘徊,2015年以后又开始回升;从队列视角看,建国前出生队列公平感偏低,建国后初期的队列相对较高,“50”后有所下滑,从“60”后开始公平感持续走低,到“80”后跌入低谷,但“90”后又开始升高。从1949年前后“寡且不均”到建国初期阶段的“寡且均”,再到改革开放40年快速经济增长下“不寡但不均”的社会变迁过程影响了居民的公平感。     

“‘WE' AND ‘THEY'”: WHY MUST WE ENGAGE IN CROSS-CULTURAL CONVERSATION?

This article contains the principal ideas that I presented in four different sessions at the IRAS 2022 conference, on the theme “‘We' and ‘They’: Cross-Cultural Conversation on Identity.” Focusing on the central topic, the article begins with (i) the contents of my opening lecture; followed by (ii) a broad outline of the concerns discussed in my book, Cross-Cultural Conversation: A New Way of Learning, intertwined with glimpses of the intellectual journey that led me to CCC, delivered in the Book-discussion session; (iii) a summary of the main ideas about the importance of meeting of religions today, which formed the background for the CCC Panel discussion on religion, where I was in conversation with spokespersons of five world religions; and (iv) my comments on how science–religion dialogue can help promote a sense for human solidarity by combining knowledge with wisdom, in the concluding session.     

The asymptotic posterior normality of the latent trait in an IRT model

It has long been part of the item response theory (IRT) folklore that under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test. Under very general and nonrestrictive nonparametric assumptions, we make this claim rigorous for a broad class of latent models.This research was partially supported by Office of Naval Research Cognitive and Neural Sciences Grant N0014-J-90-1940, 442-1548, National Science Foundation Mathematics Grant NSF-DMS-91-01436, and the National Center for Supercomputing Applications. We wish to thank Kumar Joag-dev and Zhiliang Ying for enlightening suggestions concerning the proof of the basic result.The authors wish to thank Kumar Joag-Dev, Brian Junker, Bert Green, Paul Holland, Robert Mislevy, and especially Zhiliang Ying for their useful comments and discussions.     

Modeling item responses when different subjects employ different solution strategies

A model is presented for item responses when different subjects employ different strategies, but only responses, not choice of strategy, can be observed. Using substantive theory to differentiate the likelihoods of response vectors under a fixed set of strategies, we model response probabilities in terms of item parameters for each strategy, proportions of subjects employing each strategy, and distributions of subject proficiency within strategies. The probabilities that an individual subject employed the various strategies can then be obtained, along with a conditional estimate of proficiency under each. A conceptual example discusses response strategies for spatial rotation tasks, and a numerican example resolves a population of subjects into subpopulations of valid responders and random guessers.The first author's work was supported by Contract No. N00014-85-K-0683, project designation NR 150-539, from the Cognitive Science Program, Cognitive and Neural Sciences Division, Office of Naval Research. We are grateful to Murray Aitkin, Isaac Bejar, Neil Dorans, Frederiksen, and Marklyn Wingersky for their comments and suggestions, and to Alison Gooding, Maxine Kingston, Donna Lembeck, Joling Liang, and Kentaro Yamamoto for their assistance with Example 2.     

A marginalization model for the multidimensional unfolding analysis of ranking data

A marginalization model for the multidimensional unfolding analysis of ranking data is presented. A subject samples one of a number of random points that are multivariate normally distributed. The subject perceives the distances from the point to all the stimulus points fixed in the same multidimensional space. The distances are error perturbed in this perception process. He/she produces a ranking dependent on these error-perturbed distances. The marginal probability of a ranking is obtained according to this ranking model and by integrating out the subject (ideal point) parameters, assuming the above distribution. One advantage of the model is that the individual differences are captured using the posterior probabilities of subject points. Three sets of ranking data are analyzed by the model.