Bayesian Estimation for Item Factor Analysis Models with Sparse Categorical Indicators

Psychometric models for item-level data are broadly useful in psychology. A recurring issue for estimating item factor analysis (IFA) models is low-item endorsement (item sparseness), due to limited sample sizes or extreme items such as rare symptoms or behaviors. In this paper, I demonstrate that under conditions characterized by sparseness, currently available estimation methods, including maximum likelihood (ML), are likely to fail to converge or lead to extreme estimates and low empirical power. Bayesian estimation incorporating prior information is a promising alternative to ML estimation for IFA models with item sparseness. In this article, I use a simulation study to demonstrate that Bayesian estimation incorporating general prior information improves parameter estimate stability, overall variability in estimates, and power for IFA models with sparse, categorical indicators. Importantly, the priors proposed here can be generally applied to many research contexts in psychology, and they do not impact results compared to ML when indicators are not sparse. I then apply this method to examine the relationship between suicide ideation and insomnia in a sample of first-year college students. This provides an important alternative for researchers who may need to model items with sparse endorsement.     

What the eyes already ‘know’: using eye movement measurement to tap into children's implicit numerical magnitude representations

To date, a number of studies have demonstrated the existence of mismatches between children's implicit and explicit knowledge at certain points in development that become manifest by their gestures and gaze orientation in different problem solving contexts. Stimulated by this research, we used eye movement measurement to investigate the development of basic knowledge about numerical magnitude in primary school children. Sixty‐six children from grades one to three (i.e. 6–9 years) were presented with two parallel versions of a number line estimation task of which one was restricted to behavioural measures, whereas the other included the recording of eye movement data. The results of the eye movement experiment indicate a quantitative increase as well as a qualitative change in children's implicit knowledge about numerical magnitudes in this age group that precedes the overt, that is, behavioural, demonstration of explicit numerical knowledge. The finding that children's eye movements reveal substantially more about the presence of implicit precursors of later explicit knowledge in the numerical domain than classical approaches suggests further exploration of eye movement measurement as a potential early assessment tool of individual achievement levels in numerical processing. Copyright © 2009 John Wiley & Sons, Ltd.     

Evaluating a model of global psychophysical judgments—I: Behavioral properties of summations and productions

The research presented is a partial empirical evaluation of the second author's proposed psychophysical theory [Luce (2002). Psychological Review, 109, 520-532; Luce (2004). Psychological Review, 111, 446-454]. The theory deals with the global percept of subjective intensity, in which there is a psychophysical function Ψ that maps pairs of physical intensities onto the positive real numbers and represents, in an explicit mathematical way, subjective summation and a form of ratio production. A number of behavioral properties have been shown to follow from these specific representations, and in the presence of certain plausible background assumptions these properties are also sufficient for the representations. In four auditory experiments, key behavioral properties of summation over the two ears and a form of generalized ratio production are evaluated empirically. Considerable support is reported for particular forms of Ψ for summations and ratio productions separately. A second article, Steingrimsson and Luce (Journal of Mathematical Psychology, in press), explores the behavioral properties that link summations and productions.     

听觉经验缺失对时距估计影响的实验研究

采用复制法,通过聋人与听力正常人时距估计的对比实验研究,结果发现听觉经验缺失对时距估计有一定的影响：（1）两类被试在2000ms和10000ms的时距估计中,再现时距的平均数表现出了显著性差异。听力正常被试倾向于低估时距,聋人被试倾向于高估时距。（2）聋人被试不同时距再现相对误差率之间不存在显著性差异;听力正常被试时距再现相对错误率在2000ms与10000ms、30000ms存在显著差异,10000ms和30000ms之间差异不显著。     

Stevens’ Direct Scaling Methods and the Uniqueness Problem

Stevens postulated that we can use the responses of a participant in a ratio scaling experiment directly to construct a psychophysical function representing the participant's sensations. Although Stevens' methods of constructing measurement scales are widely used in the behavioral sciences, the problem of which scale type is appropriate to describe ratio scaling data is still unresolved. To deal with this problem, we develop a theoretical framework to specify the scale type attained by Stevens' direct scaling methods. It is shown, under fairly mild background assumptions, that the behavioral axioms presented in this paper are necessary and sufficient for the psychophysical functions to be ordinal-, interval-, log-interval-, or ratio-scales. Furthermore, suggestions on how to test these behavioral axioms are provided. Requests for reprints should be sent to thomas.     

主体关联性对贝叶斯推理概率估计的影响

用贝叶斯推理问题为实验材料,探讨了主体关联性对贝叶斯推理概率估计的影响。结果表明,当估计的事件与主体有关时,被试对消极事件概率估计较低,对积极事件概率估计值;当估计的事件与主体无关时,被试对消极事件和积极事件的概率估计无显著差异。反应时分析表明,被试对消极事件的概率估计比对积极事件的概率估计时间显著地长,当消极事件与主体有关时概率估计时间就更长;而对积极事件的概率估计,与主体有关和与主体无关时反应时差异不显著。这表明,被试对消极事件的概率估计(特别是消极事件与己有关时)更为慎重。     

短时距估计中刺激物的动态变化效应

用两个实验考查了时距估计中刺激物的动态变化效应。结果发现,刺激物的运动、速度和旋转角度显著地影响着被试的时间判断,刺激物速度的时距延长效应对于较长时距(18s-24s)来说更加明显;运动刺激与较短、较准确的时距判断相关联;旋转角度的减少使得被试低估时距,而旋转角度的增加使得时距估计呈高估倾向。被试在时间估计过程中表现出长时距低估和短时距高估现象,本研究得到的时间估计转换点是11.4s,此点与先前的有关研究基本一致。     

概化理论不同评分方案缺失数据方差分量估计

包含评分者侧面的测验通常不符合任意一种概化理论设计,因此从概化理论的角度来看这类测验下的数据应属于缺失数据,而决定缺失结构的就是测验的评分方案。用R软件模拟出三种评分方案下的数据,并比较传统法、评价法和拆分法在各评分方案下的估计效果,结果表明：（1）传统法估计准确性较差;（2）评分者一致性较高时,适宜用评价法进行估计;（3）拆分法的估计结果最准确,仅在固定评分者评分方案下需注意评分者与考生数量之比,该比值小于等于0.0047 时估计结果较为准确。     

Probabilistic Disjoint Principal Component Analysis

One of the most relevant problems in principal component analysis and factor analysis is the interpretation of the components/factors. In this paper, disjoint principal component analysis model is extended in a maximum-likelihood framework to allow for inference on the model parameters. A coordinate ascent algorithm is proposed to estimate the model parameters. The performance of the methodology is evaluated on simulated and real data sets.     

Evaluating Factorial Invariance: An Interval Estimation Approach Using Bayesian Structural Equation Modeling

In this study, we introduce an interval estimation approach based on Bayesian structural equation modeling to evaluate factorial invariance. For each tested parameter, the size of noninvariance with an uncertainty interval (i.e. highest density interval [HDI]) is assessed via Bayesian parameter estimation. By comparing the most credible values (i.e. 95% HDI) with a region of practical equivalence (ROPE), the Bayesian approach allows researchers to (1) support the null hypothesis of practical invariance, and (2) examine the practical importance of the noninvariant parameter. Compared to the traditional likelihood ratio test, simulation results suggested that the proposed Bayesian approach could offer additional insight into evaluating factorial invariance, thus, leading to more informative conclusions. We provide an empirical example to demonstrate the procedures necessary to implement the proposed method in applied research. The importance of and influences on the choice of an appropriate ROPE are discussed.