Empirical underidentification in estimating random utility models: The role of choice sets and standardizations

A standard approach to distinguishing people’s risk preferences is to estimate a random utility model using a power utility function to characterize the preferences and a logit function to capture choice consistency. We demonstrate that with often-used choice situations, this model suffers from empirical underidentification, meaning that parameters cannot be estimated precisely. With simulations of estimation accuracy and Kullback–Leibler divergence measures we examined factors that potentially mitigate this problem. First, using a choice set that guarantees a switch in the utility order between two risky gambles in the range of plausible values leads to higher estimation accuracy than randomly created choice sets or the purpose-built choice sets common in the literature. Second, parameter estimates are regularly correlated, which contributes to empirical underidentification. Examining standardizations of the utility scale, we show that they mitigate this correlation and additionally improve the estimation accuracy for choice consistency. Yet, they can have detrimental effects on the estimation accuracy of risk preference. Finally, we also show how repeated versus distinct choice sets and an increase in observations affect estimation accuracy. Together, these results should help researchers make informed design choices to estimate parameters in the random utility model more precisely.     

Dysfunctional implications of narrow window theory: variability in the intuitive assessment of correlation

Narrow Window theory, suggested by Y. Kareev ten years ago, has so far focused on one central implication of the limited capacity of working memory on intuitive correlation estimation, namely, overestimation of the distal population correlation. This paper points to additional and perhaps more dramatic implications due to the large dispersion of intuitive estimates: (a) large estimation errors, possibly causing overestimation of negligible rhos, misses of strong rhos, and distorted hierarchies of the rhos between different pairs of variables; and (b) large interpersonal differences in the estimation of any given rho and highly incongruent hierarchies of estimated correlations between different pairs of variables. These implications impede both individuals' adaptation to the empirical world and communication among themselves.     

儿童数字估计的表征模式与发展

探讨中国儿童数字估计的表征模式与发展趋势。包括两个实验,均采用数字线估计任务,实验一以92名幼儿园、一年级及二年级儿童为被试,考察其在0~100范围的数字估计,结果显示,幼儿园儿童在数字估计更多地采用对数表征,而一二年级的儿童在数字估计中更多地采用线性表征;实验二以86名一、三、五年级儿童为被试,考察其在0~1000范围的数字估计,结果显示,一年级儿童有一半采用对数表征,另一半采用线性表征,而三五年级儿童大多采用线性表征。中国儿童的数字估计表现出与美国儿童相同的发展模式,都是由不精确的对数表征逐步向精确的线性表征发展;人的数表征有多种形式,即使在同一年龄阶段,也会因任务难度的不同而选择不同的表征模式。中国儿童精确数字估计能力的出现要早于美国儿童。     

时距估计任务中的间断期望效应

使用单任务研究程序,采用引入提示线索的方法,以产生时距作为反应指标对存在间断的时距估计任务中的间断期望效应和提示线索效应（注意效应）进行系统考察,并对间断时距的效应、产生时距与等待时距的关系问题作出进一步探讨。结果表明,间断位置（等待时距）因素是被试时间判断的主要线索,被试的产生时距随着等待时距的增加而延长。间断实验中表现出极其显著的提示线索效应,此效应既增加了时距估计的变异,又延长了被试的时距估计。无间断实验条件下,被试表现出显著的间断期望效应,被试对间断的期望有损于时间估计。     

Item difficulty parameter estimation using the idea of the graded response model and computerized adaptive testing

Abstract:  In test operations using IRT (item response theory), items are included in a test before being used to rate subjects and the response data is used to estimate their item parameters. However, this method of test operation may lead to item content leakage and an adequate test operation can become difficult. To address this problem, Ozaki and Toyoda (2005, 2006 ) developed item difficulty parameter estimation methods that use paired comparison data from the perspective of the difficulty of items as judged by raters familiar with the field. In the present paper, an improved method of item difficulty parameter estimation is developed. In this new method, an item for which the difficulty parameter is to be estimated is compared with multiple items simultaneously, from the perspective of their difficulty. This is not a one-to-one comparison but a one-to-many comparison. In the comparisons, raters are informed that items selected from an item pool are ordered according to difficulty. The order will provide insight to improve the accuracy of judgment.     

Quantity judgments of sequentially presented food items by capuchin monkeys (Cebus apella)

Recent assessments have shown that capuchin monkeys, like chimpanzees and other Old World primate species, are sensitive to quantitative differences between sets of visible stimuli. In the present study, we examined capuchins’ performance in a more sophisticated quantity judgment task that required the ability to form representations of food quantities while viewing the quantities only one piece at a time. In three experiments, we presented monkeys with the choice between two sets of discrete homogeneous food items and allowed the monkeys to consume the set of their choice. In Experiments 1 and 2, monkeys compared an entirely visible food set to a second set, presented item-by-item into an opaque container. All monkeys exhibited high accuracy in choosing the larger set, even when the entirely visible set was presented last, preventing the use of one-to-one item correspondence to compare quantities. In Experiment 3, monkeys compared two sets that were each presented item-by-item into opaque containers, but at different rates to control for temporal cues. Some monkeys performed well in this experiment, though others exhibited near-chance performance, suggesting that this species’ ability to form representations of food quantities may be limited compared to previously tested species such as chimpanzees. Overall, these findings support the analog magnitude model of quantity representation as an explanation for capuchin monkeys’ quantification of sequentially presented food items.

情绪体验影响估算策略运用的认知与脑机制

揭示情绪体验影响个体完成各种认知任务的认知神经机制是研究者关注的热点问题。以往研究主要采用问卷法和行为实验, 集中考察了焦虑对估算策略运用的影响, 但这种影响潜在的脑机制尚不清楚, 对焦虑以外的情绪体验与估算策略运用之间关系的研究也极其缺乏, 而情绪调节对估算策略运用影响方面的研究基本处于空白。本研究将采用面孔表情图片作为情绪刺激材料, 结合事件相关电位(event related potential, ERP)技术, 采用启动范式, 尝试从外显和内隐两个角度, 考察不同效价的情绪体验在估算策略运用过程中所起的作用, 进而揭示情绪调节影响估算策略执行的时间动态特征和大脑激活模式。这将有助于充分认识情绪体验影响估算策略运用的认知与脑机制, 为更好的优化估算策略运用效果提供实证依据。     

Bayes modal estimation in item response models

This article describes a Bayesian framework for estimation in item response models, with two-stage prior distributions on both item and examinee populations. Strategies for point and interval estimation are discussed, and a general procedure based on the EM algorithm is presented. Details are given for implementation under one-, two-, and three-parameter binary logistic IRT models. Novel features include minimally restrictive assumptions about examinee distributions and the exploitation of dependence among item parameters in a population of interest. Improved estimation in a moderately small sample is demonstrated with simulated data.This research was supported by a grant from the Spencer Foundation, Chicago, IL. Comments and suggestions on earlier drafts by Charles Lewis, Frederic Lord, Rosenbaum, James Ramsey, Hiroshi Watanabe, the editor, and two anonymous referees are gratefully acknowledged.     

On the robustness of maximum likelihood scaling for violations of the error model

A Monte Carlo study was conducted to investigate the robustness of the assumed error distribution in maximum likelihood estimation models for multidimensional scaling. Data sets generated according to the lognormal, the normal, and the rectangular distribution were analysed with the log-normal error model in Ramsay's MULTISCALE program package. The results show that violations of the assumed error distribution have virtually no effect on the estimated distance parameters. In a comparison among several dimensionality tests, the corrected version of thex ² test, as proposed by Ramsay, yielded the best results, and turned out to be quite robust against violations of the error model.     

Optimum examinee samples for item parameter estimation in item response theory: A multi-objective programming approach

This paper proposes a multi-objective programming method for determining samples of examinees needed for estimating the parameters of a group of items. In the numerical experiments, optimum samples are compared to uniformly and normally distributed samples. The results show that the samples usually recommended in the literature are well suited for estimating the difficulty parameters. Furthermore, they are also adequate for estimating the discrimination parameters in the three-parameter model, butnot for the guessing parameters.