Factor Retention Using Machine Learning With Ordinal Data

Determining the number of factors in exploratory factor analysis is probably the most crucial decision when conducting the analysis as it clearly influences the meaningfulness of the results (i.e., factorial validity). A new method called the Factor Forest that combines data simulation and machine learning has been developed recently. This method based on simulated data reached very high accuracy for multivariate normal data, but it has not yet been tested with ordinal data. Hence, in this simulation study, we evaluated the Factor Forest with ordinal data based on different numbers of categories (2–6 categories) and compared it to common factor retention criteria. It showed higher overall accuracy for all types of ordinal data than all common factor retention criteria that were used for comparison (Parallel Analysis, Comparison Data, the Empirical Kaiser Criterion and the Kaiser Guttman Rule). The results indicate that the Factor Forest is applicable to ordinal data with at least five categories (typical scale in questionnaire research) in the majority of conditions and to binary or ordinal data based on items with less categories when the sample size is large.     

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.     

Further attempts to clarify the importance of category variability for categorisation

The issue of how category variability affects classification of novel instances is an important one for assessing theories of categorisation, yet previous research cannot provide a compelling conclusion. In five experiments we reexamine some of the factors thought to affect participant performance. In Experiments 1 and 2, participants almost always classified the test item as belonging to the high variability category. By contrast, in Experiment 3 we employed an alternative experimental paradigm, where the difference in variability of the two categories was less salient. In that case, participants tended to classify a test item as belonging to the low variability category. Two additional experiments (4 and 5) explored in detail the differences between Experiments 1, 2 on the one hand, and 3 on the other. Some insight into the underlying psychological processes can be provided by computational models of categorisation, and we focus on the continuous version of Anderson's (1991) Rational Model, which has not been explored before in this context. The model predicts that test instances exactly halfway between the prototypes of two categories should be classified into the more variable category, consistent with the bulk of empirical findings. We also provided a comparison with a slightly reduced version of the Generalised Context Model (GCM) to show that its predictions are consistent with those from the Rational Model, for our stimulus sets.     

The Development of Cognitive Reflection in China

Cognitive reflection is the tendency to override an intuitive response so as to engage in the reflection necessary to derive a correct response. Here, we examine the emergence of cognitive reflection in a culture that values nonanalytic thinking styles, Chinese culture. We administered a child-friendly version of the cognitive reflection test, the CRT-D, to 130 adults and 111 school-age children in China and compared performance on the CRT-D to several measures of rational thinking (belief bias syllogisms, base rate sensitivity, denominator neglect, and other-side thinking) and normative thinking dispositions (actively open-minded thinking and need for cognition). The CRT-D was a significant predictor of rational thinking and normative thinking dispositions in both children and adults, as previously found in American samples. Adults’ performance on the CRT-D correlated with their performance on the original CRT, and children's performance on the CRT-D predicted rational thinking and normative thinking dispositions even after adjusting for age. These results demonstrate that cognitive reflection, rational thinking, and normative thinking dispositions converge even in a culture that emphasizes holistic, nonanalytic reasoning.     

内源性注意与外源性注意对数字加工的不同影响

分别采用内源性注意和外源性注意实验范式,材料为小数（1－4）和大数（6－9）的中文与阿拉伯数字,任务为判断数字是否大于5,考察在注意与非注意条件下不同大小数字加工的距离效应和符号效应。结果发现：⑴在内源性线索和外源性线索的注意条件下,大小数都出现了距离效应;但在非注意条件下,内源性线索时的大小数都出现了距离效应,而外源性线索时只有小数出现了距离效应,大数的距离效应明显减弱或消失。⑵在内源性线索和外源性线索的注意条件下,大小数都没有出现符号效应;但在非注意条件下,大数没有出现符号效应,而小数出现了符号效应（阿拉伯数字的绩效比中文数字差）,并且内源性线索时的符号效应强度小于外源性线索。     

负数的空间表征机制

本研究采用快速数字大小分类范式,每次试验呈现一个数字,要求被试快速判断即时呈现的数字大于或小于-5（或5）,探讨负数在心理数字线上的表征方向问题。实验一将负数（-1～-9）和正数（1～9）分两组分别呈现;实验二将正负数混合呈现,仅对负数进行反应。结果表明,负数按照其绝对值大小表征在心理数字线上,绝对值小的负数表征在心理数字线的左侧,绝对值大的负数表征在心理数字线的右侧。该结果支持系统进化论假说     

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.     

Satisficing in financial decision making — a theoretical and experimental approach to bounded rationality

We apply the theoretical construct of bounded rationality to an investment game, allowing participants to invest their monetary endowment in riskless bonds and risky assets. In our experiment, we elicit aspiration levels from participants: one captures a subsistence threshold, the other a success threshold. Participants can be classified according to these aspirations and the corresponding investment behavior. We differentiate between potential and actual satisficing. By presupposing specific cardinal utility functions, we also relate the bounded rationality approach to the traditional rational choice model.