测量估计研究:回顾与展望

测量估计是算术估计的一种常见形式,被看作个体数量能力早期获得的重要渠道,也可为物理测量教学提供一条有效途径。论文简要回顾了测量估计研究的发展历程,讨论了测量估计能力的发展及其影响因素,分析了个体常用的测量估计策略种类以及相关的教学训练方式,最后指出了现有研究的缺陷和今后的发展方向。     

青少年测量估计能力的发展状况及相关因素

测量估计(简称估测)是上世纪七十年代数学认知领域兴起的研究热点之一。采用自编的测验任务对747名青少年估测能力的发展状况及相关因素进行了考察。其中测验任务包括长度和面积估测两种类型,并且每种类型都采用了图形和实物两种题目形式。被试平均年龄为17.11岁。结果发现青少年的估测能力的发展表现出如下特点:(1)青少年的总体估测能力普遍较低;(2)青少年的估测能力在初中阶段会显著提高,但之后的发展相对缓慢;(3)青少年的估测成绩易受任务类型和题目形式的影响。对长度任务的估测成绩好于对面积的估测;对图形题目的估测成绩好于对实际物体的估测;(4)青少年的估测能力不存在明显性别差异。     

A comparison of three simple test theory models

In very simple test theory models such as the Rasch model, a single parameter is used to represent the ability of any examinee or the difficulty of any item. Simple models such as these provide very important points of departure for more detailed modeling when a substantial amount of data are available, and are themselves of real practical value for small or even medium samples. They can also serve a normative role in test design.As an alternative to the Rasch model, or the Rasch model with a correction for guessing, a simple model is introduced which characterizes strength of response in terms of the ratio of ability and difficulty parameters rather than their difference. This model provides a natural account of guessing, and has other useful things to contribute as well. It also offers an alternative to the Rasch model with the usual correction for guessing. The three models are compared in terms of statistical properties and fits to actual data. The goal of the paper is to widen the range of minimal models available to test analysts.This research was supported by grant AP320 from the Natural Sciences and Engineering Research Council of Canada. The author is grateful for discussions with M. Abrahamowicz, I. Molenaar, D. Thissen, and H. Wainer.     

数学困难儿童的数学估计能力

对数学困难儿童(简称数困)的数学估计进行探讨有助于理解数困的成因和寻找适当的干预措施。本文在简要回顾数困和估计的概念基础上, 重点对近年来国内外关于数困儿童数学估计(主要是估算和估数)的表现及影响因素、神经基础和相关的干预研究进行了回顾和梳理, 并强调未来对数困儿童的数学估计研究应注重从选取被试、扩展研究范围和加强干预方案设计等方面开展探讨。     

Estimation in the power law

Most psychophysicists neglect to consider how error should be characterized in applications of the power law. Failures of the power law to agree with certain theoretical predictions may be due to bias of parameter estimates. A power law with lognormal product structure is proposed and approximately unbiased parameter estimates are given for several common estimation situations.     

不同干扰刺激对成人数量估计的影响

研究采用自行设计的图形材料,考察了不同干扰刺激(纯靶刺激;干扰刺激与靶刺激数量相同;干扰刺激是靶刺激数量的2倍)对成人完成数量估计任务的影响.30名硕士生参加了本实验.行为数据和口头报告资料分析显示:1)反应时随数量估计任务难度的增加而不断增长;2)干扰刺激越多,任务越复杂,成人估计的误差率越高,准确性越低;3)成人存在多重数字表征形式,完成数量估计任务时主要采用线性表征,但随着干扰刺激物的增加,运用对数表征的趋势愈加明显.     

Iterative least squares estimates of communality: Initial estimate need not affect stabilized value

A common criticism of iterative least squares estimates of communality is that method of initial estimation may influence stabilized values. As little systematic research on this topic has been performed, the criticism appears to be based on cumulated experience with empirical data sets. In the present paper, two studies are reported in which four types of initial estimate (unities, squared multiple correlations, highestr, and zeroes) and four levels of convergence criterion were employed using four widely available computer packages (BMDP, SAS, SPSS, and SOUPAC). The results suggest that initial estimates have no effect on stabilized communality estimates when a stringent criterion for convergence is used, whereas initial estimates appear to affect stabilized values employing rather gross convergence criteria. There were no differences among the four computer packages for matrices without Heywood cases.     

An investigation of hierarchical Bayes procedures in item response theory

Hierarchical Bayes procedures for the two-parameter logistic item response model were compared for estimating item and ability parameters. Simulated data sets were analyzed via two joint and two marginal Bayesian estimation procedures. The marginal Bayesian estimation procedures yielded consistently smaller root mean square differences than the joint Bayesian estimation procedures for item and ability estimates. As the sample size and test length increased, the four Bayes procedures yielded essentially the same result.The authors wish to thank the Editor and anonymous reviewers for their insightful comments and suggestions.     

贝叶斯结构方程模型及其研究现状

在心理学研究中结构方程模型(Structural Equation Modeling, SEM)被广泛用于检验潜变量间的因果效应, 其估计方法有频率学方法(如, 极大似然估计)和贝叶斯方法两类。近年来由于贝叶斯统计的流行及其在结构方程建模中易于处理小样本、缺失数据及复杂模型等方面的优势, 贝叶斯结构方程模型发展迅速, 但其在国内心理学领域的应用不足。主要介绍了贝叶斯结构方程模型的方法基础和优良特性, 及几类常用的贝叶斯结构方程模型及其应用现状, 旨在为应用研究者介绍新的研究工具。     

Item Calibration Samples and the Stability of Achievement Estimates and System Rankings: Another Look at the PISA Model

Using an empirically-based simulation study, we show that typically used methods of choosing an item calibration sample have significant impacts on achievement bias and system rankings. We examine whether recent PISA accommodations, especially for lower performing participants, can mitigate some of this bias. Our findings indicate that standard operational methods, while not ideal, recover underlying proficiency reasonably well and generally outperform methods that more completely include all participants. Translating results onto the PISA scale, the calibration sample can induce bias of up to 12.49 points, which is important given that standard errors are around three points. Although ranking correlations are at least.95, we note the policy implications of slight ranking changes. Our findings indicate that limited accommodations targeted at low achieving educational systems do not outperform either of the other methods considered. Research that further explores accommodations for heterogeneous populations is recommended.     

六年级儿童的估算水平与策略

借鉴Lemaire与Siegler提出的儿童认知策略的一般概念框架,运用自编的估算题目对210名小学六年级儿童的估算能力进行了初步分析。结果表明;小学六年级儿童具有一定的估算能力,只是所给估算答案明显受到数字类型和运算规则的交互影响;他们会运用多种估算策略,但各种策略的使用频率、执行速度和准确性都存在明显差异。文章还对儿童估算策略的评估做了深入讨论。     

预期式时距估计年龄差异的初步研究

以5s、13s和26s为目标时距,采用产生法和复制法,探讨了预期式条件下时距估计的年龄差异。结果表明在单任务作业中。年老被试和年轻被试两个年龄组之间估计时距的平均值没有显著差异,但年老被试比年轻被试的估计时距具有更大的变异性。单一的内部时钟频率变化的假设并不能对单任务条件下时距估计的年龄差异做出合理的解释。时距估计的年龄差异可能是内部时钟频率变化和认知过程变化交互作用的结果。     

Cognitive distance of stairways: a multi-stairway investigation

The present study had two major purposes. First it sought to determine to what extent in an earlier study of distance estimation in stairways (Hanyu & Itsukushima, 1995) would generalize to other types of stairway. Second, it sought to examine which hypothesis, information storage or effort, better explain the earlier results, in which people overestimated distance and traversed time estimates. We obtained four distance and time measures: distance estimate, traversal time estimate, mental walking time and actual traversal time. To measure information, we had participants rate each stairway for complexity (simple-complex) and effort (effortless-effortful) before and after the distance and time measurement tasks. The results revealed that the earlier findings (Hanyu & Itsukushima, 1995) did not fully generalize. The results also did not support either the information storage or the effort hypothesis.     

疼痛条件下时间目标对时距估计的影响

本研究采用冷压任务引发疼痛,以健康大学生为被试,试图探讨在疼痛条件下时间目标对时距估计的影响。结果发现：疼痛条件下的时距估计值小于非疼痛条件下时距估计值,疼痛条件下具体时间目标的时距估计值显著大于无目标时距估计值。临床上给患者提供具体的时间目标或许有助于他们应对疼痛。     

Weighted likelihood estimation of ability in item response theory

Applications of item response theory, which depend upon its parameter invariance property, require that parameter estimates be unbiased. A new method, weighted likelihood estimation (WLE), is derived, and proved to be less biased than maximum likelihood estimation (MLE) with the same asymptotic variance and normal distribution. WLE removes the first order bias term from MLE. Two Monte Carlo studies compare WLE with MLE and Bayesian modal estimation (BME) of ability in conventional tests and tailored tests, assuming the item parameters are known constants. The Monte Carlo studies favor WLE over MLE and BME on several criteria over a wide range of the ability scale.     

Relating latent class membership to external variables: An overview

In this article we provide an overview of existing approaches for relating latent class membership to external variables of interest. We extend on the work of Nylund-Gibson et al. (Structural Equation Modeling: A Multidisciplinary Journal, 2019, 26, 967), who summarize models with distal outcomes by providing an overview of most recommended modeling options for models with covariates and larger models with multiple latent variables as well. We exemplify the modeling approaches using data from the General Social Survey for a model with a distal outcome where underlying model assumptions are violated, and a model with multiple latent variables. We discuss software availability and provide example syntax for the real data examples in Latent GOLD.     

学前儿童对时距的估计及其策略

该研究旨在探查学前儿童对时距的认识过程及其认识策略。使用2秒、4秒、6秒、8秒四种不同的时间间隔作为刺激物,在每次呈现之后要求儿童按键再现时距。5岁和6岁的学前儿童参加这一实验。主要结果表明:5、6岁儿童已能区分只有几秒钟差异的单一时距;在无声音参照条件下,他们对4秒钟的估计较为准确,而在有声音参照条件下,5岁儿童则对6秒钟的估计更趋准确。研究材料还证实了,儿童从5岁起初步能够使用时间标尺,开始把时间看成是可以计数的维量。     

Estimating an unobserved component of a serial response time model

A method is developed for estimating the response time distribution of an unobserved component in a two-component serial model, assuming the components are stochastically independent. The estimate of the component's density function is constrained only to be unimodal and non-negative. Numerical examples suggest that the method can yield reasonably accurate estimates with sample sizes of 300 and, in some cases, with sample sizes as small as 100.The author wishes to thank David Kohfeld, Jim Ramsay, Jim Townsend and two anonymous referees for a number of useful and stimulating comments on an earlier version of this paper.     

On the asymptotic standard error of a class of robust estimators of ability in dichotomous item response models

In item response theory, the classical estimators of ability are highly sensitive to response disturbances and can return strongly biased estimates of the true underlying ability level. Robust methods were introduced to lessen the impact of such aberrant responses on the estimation process. The computation of asymptotic (i.e., large‐sample) standard errors (ASE) for these robust estimators, however, has not yet been fully considered. This paper focuses on a broad class of robust ability estimators, defined by an appropriate selection of the weight function and the residual measure, for which the ASE is derived from the theory of estimating equations. The maximum likelihood (ML) and the robust estimators, together with their estimated ASEs, are then compared in a simulation study by generating random guessing disturbances. It is concluded that both the estimators and their ASE perform similarly in the absence of random guessing, while the robust estimator and its estimated ASE are less biased and outperform their ML counterparts in the presence of random guessing with large impact on the item response process.     

Dealing with Big Numbers: Representation and Understanding of Magnitudes Outside of Human Experience

Being able to estimate quantity is important in everyday life and for success in the STEM disciplines. However, people have difficulty reasoning about magnitudes outside of human perception (e.g., nanoseconds, geologic time). This study examines patterns of estimation errors across temporal and spatial magnitudes at large scales. We evaluated the effectiveness of hierarchical alignment in improving estimations, and transfer across dimensions. The activity was successful in increasing accuracy for temporal and spatial magnitudes, and learning transferred to the estimation of numeric magnitudes associated with events and objects. However, there were also a number of informative differences in performance on temporal, spatial, and numeric magnitude measures, suggesting that participants possess different categorical information for these scales. Educational implications are discussed.