Empirically Corrected Rescaled Statistics for SEM with Small N and Large p

Survey data often contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. With typical nonnormally distributed data in practice, a rescaled statistic T_rml proposed by Satorra and Bentler was recommended in the literature of SEM. However, T_rml has been shown to be problematic when the sample size N is small and/or the number of variables p is large. There does not exist a reliable test statistic for SEM with small N or large p, especially with nonnormally distributed data. Following the principle of Bartlett correction, this article develops empirical corrections to T_rml so that the mean of the empirically corrected statistics approximately equals the degrees of freedom of the nominal chi-square distribution. Results show that empirically corrected statistics control type I errors reasonably well even when N is smaller than 2p, where T_rml may reject the correct model 100% even for normally distributed data. The application of the empirically corrected statistics is illustrated via a real data example.     

Number comparison and number ordering as predictors of arithmetic performance in adults: Exploring the link between the two skills,and investigating the question of domain-specificity

Recent evidence has highlighted the important role that number-ordering skills play in arithmetic abilities, both in children and adults. In the current study, we demonstrated that number comparison and ordering skills were both significantly related to arithmetic performance in adults, and the effect size was greater in the case of ordering skills. Additionally, we found that the effect of number comparison skills on arithmetic performance was mediated by number-ordering skills. Moreover, performance on comparison and ordering tasks involving the months of the year was also strongly correlated with arithmetic skills, and participants displayed similar (canonical or reverse) distance effects on the comparison and ordering tasks involving months as when the tasks included numbers. This suggests that the processes responsible for the link between comparison and ordering skills and arithmetic performance are not specific to the domain of numbers. Finally, a factor analysis indicated that performance on comparison and ordering tasks loaded on a factor that included performance on a number line task and self-reported spatial thinking styles. These results substantially extend previous research on the role of order processing abilities in mental arithmetic.     

Why Does Frustration Predict Psychopathology? Multiple Prospective Pathways Over Adolescence: A TRAILS Study

Adolescents' temperamental frustration is a developmental precursor of adult neuroticism and psychopathology. Because the mechanisms that underlie the prospective association between adolescents' high frustration and psychopathology (internalizing/externalizing) have not been studied extensively, we quantified three pathways: stress generation [mediation via selection/evocation of stressful life events (SLEs)], cross‐sectional frustration‐psychopathology overlap (‘carry‐over’/common causes), and a direct (non‐mediated) vulnerability effect of frustration, including moderation of SLE impact. Frustration and psychopathology were assessed at age 16 with the Early Adolescent Temperament Questionnaire and the Youth Self‐Report. No gender differences in frustration were observed. At age 19, psychopathology was reassessed by using the Adult Self‐Report, while occurrence of endogenous (self‐generated) and exogenous (not self‐generated) SLEs during the interval (ages 16–19) were ascertained with the Life Stress Interview, an investigator‐based contextual‐stressfulness rating procedure (N = 957). Half of the prospective effect of frustration on psychopathology was explained by baseline overlap, including effects of ‘carry‐over’ and common causes, about 5% reflected stress generation (a ‘vicious’ cycle with the environment adolescents navigate and shape), and 45% reflected unmediated association: a direct vulnerability effect including stress sensitivity or moderation of SLE impact. After adjustment for their overlap, frustration predicted the development of externalizing but not internalizing symptoms. Copyright © 2016 European Association of Personality Psychology     

An Embodiment Perspective on Number–Space Mapping in 3.5‐Year‐Old Dutch Children

Previous research suggests that block adding, subtracting and counting direction are early forms of number–space mapping. In this study, an embodiment perspective on these skills was taken. Embodiment theory assumes that cognition emerges through sensory–motor interaction with the environment. In line with this assumption, it was investigated if counting and adding/subtracting direction in young children is related to the hand they use during task performance. Forty‐eight 3.5‐year‐old children completed a block adding, subtracting and counting task. They had to add and remove a block from a row of three blocks and count a row of five blocks. Adding, subtracting and counting direction were related to the hand the children used for task performance. Most children who used their right hand added, removed and started counting the blocks at the right side of the row. Most children who used their left hand added, removed and started counting the blocks at the left side of the row. It can be concluded that number–space mapping, as measured by direction of adding, subtracting and counting blocks, in young children is embodied: It is not fixed, but is related to the situation. © 2016 The Authors Infant and Child Development Published by John Wiley & Sons, Ltd.     

Experimental control of nodality via equal presentations of conditional discriminations in different equivalence protocols under speed and no-speed conditions

A within-participant comparison of simple-to-complex, complex-to-simple, and simultaneous protocols was conducted establishing different sets of three 7-member equivalence classes for 4 undergraduate students. The protocols were implemented under either accuracy-only or accuracy-plus-speed conditions while keeping number of presentations of training and testing trials equal. The results partially support previous reports of differential effects on acquisition, with participants completing more blocks in training under the simultaneous than the complex-to-simple and the simple-to-complex protocols. Across the protocols, however, the number of trials completed to criterion did not vary systematically. More important, response speed and accuracy did not decrease as a function of nodal number, with or without the speed contingency, or under any protocol. The latter results challenge the generality of previous reports of the nodality effect and the notion of "relatedness" of equivalence-class members, and support a reinforcement-contingency, instead of a structural, perspective on equivalence-class formation.     

靶子的潜在位置数对辨别任务中返回抑制的影响

摘要在严格控制的条件下,以大学生为被试．采用线索一靶子模式的返回抑制范式．考察了靶子在注视点周边可能出现的位置数与辨别任务中返回抑制的关系。实验结果表明．在辨别任务中靶子的潜在位置数对返回抑制量有影响,随着位置数的增加,返回抑制量减小。该结论为返回抑制的注意性观点提供了新的证据。     

Language effects in magnitude comparison: small, but not irrelevant

It is assumed that number magnitude comparison is performed by assessing magnitude representation on a single analog mental number line. However, we have observed a unit-decade-compatibility effect in German which is inconsistent with this assumption (Nuerk, Weger, & Willmes, 2001). Incompatible magnitude comparisons in which decade and unit comparisons lead to different responses (e.g., 37_52 for which 3<5, but 7>2) are slower and less accurately responded to than compatible trials in which decade and unit comparisons lead to the same response (e.g., 42_57, for which 4<5 and 2<7). As overall distance was held constant, a single holistic magnitude representation could not account for this compatibility effect. However, because of the inversion property of the corresponding German two-digit number words ("einundzwanzig" ), the language-generality of the effect is questionable. We have therefore examined the compatibility effect with native English speakers. We were able to replicate the compatibility effect using Arabic notation. Thus, the compatibility effect is not language-specific. However, in cross-linguistic analyses language-specific modulations were observed not only for number words but also for Arabic numbers. The constraints imposed on current models by the verbal mediation of Arabic number comparison are discussed.