Power of the likelihood ratio test in covariance structure analysis

A procedure for computing the power of the likelihood ratio test used in the context of covariance structure analysis is derived. The procedure uses statistics associated with the standard output of the computer programs commonly used and assumes that a specific alternative value of the parameter vector is specified. Using the noncentral Chi-square distribution, the power of the test is approximated by the asymptotic one for a sequence of local alternatives. The procedure is illustrated by an example. A Monte Carlo experiment also shows how good the approximation is for a specific case.This research was made possible by a grant from the Dutch Organization for Advancement of Pure Research (ZWO). The authors also like to acknowledge the helpful comments and suggestions from the editor and anonymous reviewers.     

时间知觉与估计的认知理论综述

本文回顾时间知觉与估计的实验研究 ,总结该领域的国内外研究结果 ,对该领域的各主要认知模型作了较全面的考察和评述 ,并进一步探讨了时间认知领域研究的今后发展 ,尤其是时间知觉与估计研究的脑电研究思路。     

A Bayesian Approach to More Stable Estimates of Group-Level Effects in Contextual Studies

Multilevel analyses are often used to estimate the effects of group-level constructs. However, when using aggregated individual data (e.g., student ratings) to assess a group-level construct (e.g., classroom climate), the observed group mean might not provide a reliable measure of the unobserved latent group mean. In the present article, we propose a Bayesian approach that can be used to estimate a multilevel latent covariate model, which corrects for the unreliable assessment of the latent group mean when estimating the group-level effect. A simulation study was conducted to evaluate the choice of different priors for the group-level variance of the predictor variable and to compare the Bayesian approach with the maximum likelihood approach implemented in the software Mplus. Results showed that, under problematic conditions (i.e., small number of groups, predictor variable with a small ICC), the Bayesian approach produced more accurate estimates of the group-level effect than the maximum likelihood approach did.     

Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models

Using the theory of pseudo maximum likelihood estimation the asymptotic covariance matrix of maximum likelihood estimates for mean and covariance structure models is given for the case where the variables are not multivariate normal. This asymptotic covariance matrix is consistently estimated without the computation of the empirical fourth order moment matrix. Using quasi-maximum likelihood theory a Hausman misspecification test is developed. This test is sensitive to misspecification caused by errors that are correlated with the independent variables. This misspecification cannot be detected by the test statistics currently used in covariance structure analysis.For helpful comments on a previous draft of the paper we are indebted to Kenneth A. Bollen, Ulrich L. Küsters, Michael E. Sobel and the anonymous reviewers of Psychometrika. For partial research support, the first author wishes to thank the Department of Sociology at the University of Arizona, where he was a visiting professor during the fall semester 1987.     

4~8年级学生分数数量表征的准确性及形式

在分数学习中,分数数量表征是非常重要的方面。本研究利用数字线估计任务对四到八年级学生分数数量表征的情况进行探索。研究结果表明：随着年级升高,被试分数数量表征的准确性也随之提高;被试对单位分数和非单位分数表征的准确性存在显著差异,表现为对单位分数表征的准确性显著高于对非单位分数的表征,这种差异在低年级显著,随着年级的增长,差异逐渐消失;四到八年级学生在0~3数字线上,对分数数量的表征表现为线性形式而非对数形式,且这种线性表征形式是在六年级开始出现并随着年龄增长逐渐发展起来的。中西方儿童在分数数量表征的准确性和形式上有相似的发展路径,但是在表征准确性上中国儿童更高、线性形式出现年级上中国儿童可能更早。     

时间赋义对数字空间表征的影响：来自数字线估计任务的证据

数字线估计任务的大量研究以纯数字为研究对象而忽视了赋义数字。本研究以Siegler等的数字线估计任务为原型,探讨在对数字时间赋义条件下小学二、四和六年级儿童的数字表征形式是否发生变化。结果表明,小学二年级是0-1000范围内数字表征从对数形式转换为线性形式的转折点,对数字赋予时间含义后,三个年级均出现了赋义效应。在线性模型和对数模型中时间赋义的作用相反,时间赋义表现出抑线升对（抑制线性模型提升对数模型解释力）的效果。     

Orienting numbers in mental space: Horizontal organization trumps vertical

While research on the spatial representation of number has provided substantial evidence for a horizontally oriented mental number line, recent studies suggest vertical organization as well. Directly comparing the relative strength of horizontal and vertical organization, however, we found no evidence of spontaneous vertical orientation (upward or downward), and horizontal trumped vertical when pitted against each other (Experiment 1). Only when numbers were conceptualized as magnitudes (as opposed to nonmagnitude ordinal sequences) did reliable vertical organization emerge, with upward orientation preferred (Experiment 2). Altogether, these findings suggest that horizontal representations predominate, and that vertical representations, when elicited, may be relatively inflexible. Implications for spatial organization beyond number, and its ontogenetic basis, are discussed.     

An age-related view of the role of object and spatial cognitive styles in distance estimation

Distance estimations require identifying characteristics of the object and its spatial surroundings. With the present study, we examined the relationship between visual object and spatial (cognitive) styles and distance estimations in children and adults. Participants were administered the Object-Spatial Imagery Questionnaire (OSIQ) and two distance estimation tasks—one required estimating reach distance (reach task [RT]) from the self and the other required estimating distance between targets (perceptual task[PT]). Overall, our findings indicated that age was the best predictor of estimation for RT and PT tasks, and individuals were more accurate in the task requiring an egocentric frame of reference (RT) compared to tasks that require allocentric judgements (PT). In addition, children had higher ratings on cognitive styles in comparison to adults, but both object and spatial styles only related to RT accuracy in adults. Cognitive styles seem to be associated to distance estimation accuracy, but only when there is a clear preference.     

数学学业不良儿童的估算情感特点研究

运用自编估算测试材料,通过与学优生相比较,考察了数学学业不良儿童的估算情感特点及与估算能力的关系,被试为40名小学六年级学生。结果表明:1.学业不良儿童的估算情感总分明显低于学优儿童,学业不良儿童在数学自信心和估算情感认同这两个维度上表现较为消极。2.学业不良儿童的估算情感认同与他们的估算成绩之间关系更为密切。     

‘I feel better when…’: An analysis of the memory-experience gap for peoples’ estimates of the relationship between health behaviours and experiences

Objective: People often overestimate how strongly behaviours and experiences are related. This memory-experience gap might have important implications for health care settings, which often require people to estimate associations, such as “my mood is better when I exercise”. This study examines how subjective correlation estimates between health behaviours and experiences relate to calculated correlations from online reports and whether subjective estimates are associated with engagement in actual health behaviour.

Design: Seven-month online study on physical activity, sleep, affect and stress, with 61 online assessments.

Main Outcome Measures: University students (N = 168) retrospectively estimated correlations between physical activity, sleep, positive affect and stress over the seven-month study period.

Results: Correlations between experiences and behaviours (online data) were small (r = ?.12–.14), estimated correlations moderate (r = ?.35–.24). Correspondence between calculated and estimated correlations was low. Importantly, estimated correlations of physical activity with stress, positive affect and sleep were associated with actual engagement in physical activity.

Conclusion: Estimation accuracy of relations between health behaviours and experiences is low. However, association estimates could be an important predictor of actual health behaviours. This study identifies and quantifies estimation inaccuracies in health behaviours and points towards potential systematic biases in health settings, which might seriously impair intervention efficacy.