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.     

Centering Predictor Variables in Three-Level Contextual Models

Hierarchical data are becoming increasingly complex, often involving more than two levels. Centering decisions in multilevel models are closely tied to substantive hypotheses and require researchers to be clear and cautious about their choices. This study investigated the implications of group mean centering (i.e., centering within context; CWC) and grand mean centering (CGM) of predictor variables in three-level contextual models. The goals were to (a) determine equivalencies in the means and variances across the centering options and (b) use the algebraic relationships between the centering choices to clarify the interpretation of the estimated parameters. We provide recommendations to assist the researcher in making centering decisions for analysis of three-level contextual models     

A daily diary study of relationships between feelings of gratitude and well-being

Much of the research on relationships between gratitude and well-being has concerned between-person level relationships, and this research suggests that increasing people’s feelings of gratitude can increase their well-being. To complement this research, we examined such relationships at the within-person level. Participants (N = 130) in the present study described their well-being and how grateful they felt each day for two weeks. MLM analyses found that at the within-person level, daily feelings of gratitude and hedonic and eudaimonic well-being were positively related. Lagged analyses found that feelings of gratitude on one day were positively related to hedonic (but not eudaimonic) well-being on the next day, and well-being on one day was not related to gratitude on the next day. These results complement existing research and suggest that causal relationships between gratitude and well-being may vary as a function of whether gratitude is measured in more affective or cognitive terms.     

Mechanisms of Reference Frame Selection in Spatial Term Use: Computational and Empirical Studies

Previous studies have shown that multiple reference frames are available and compete for selection during the use of spatial terms such as “above.” However, the mechanisms that underlie the selection process are poorly understood. In the current paper we present two experiments and a comparison of three computational models of selection to shed further light on the nature of reference frame selection. The three models are drawn from different areas of human cognition, and we assess whether they may be applied to a reference frame selection by examining their ability to account for both existing and new empirical data comprising acceptance rates, response times, and response time distributions. These three models are the competitive shunting model (Schultheis, 2009 ), the leaky competing accumulator (LCA) model (Usher & McClelland, 2001 ), and a lexical selection model (Howard, Nickels, Coltheart, & Cole‐Virtue, 2006 ). Model simulations show that only the LCA model satisfactorily accounts for the empirical observations. The key properties of this model that seem to drive its success are its bounded linear activation function, its number and type of processing stages, and its use of decay. Uncovering these critical properties has important implications for our understanding not only of spatial term use, in particular, but also of conflict and selection in human cognition more generally.     

Grammaticality,Acceptability, and Probability: A Probabilistic View of Linguistic Knowledge

The question of whether humans represent grammatical knowledge as a binary condition on membership in a set of well‐formed sentences, or as a probabilistic property has been the subject of debate among linguists, psychologists, and cognitive scientists for many decades. Acceptability judgments present a serious problem for both classical binary and probabilistic theories of grammaticality. These judgements are gradient in nature, and so cannot be directly accommodated in a binary formal grammar. However, it is also not possible to simply reduce acceptability to probability. The acceptability of a sentence is not the same as the likelihood of its occurrence, which is, in part, determined by factors like sentence length and lexical frequency. In this paper, we present the results of a set of large‐scale experiments using crowd‐sourced acceptability judgments that demonstrate gradience to be a pervasive feature in acceptability judgments. We then show how one can predict acceptability judgments on the basis of probability by augmenting probabilistic language models with an acceptability measure. This is a function that normalizes probability values to eliminate the confounding factors of length and lexical frequency. We describe a sequence of modeling experiments with unsupervised language models drawn from state‐of‐the‐art machine learning methods in natural language processing. Several of these models achieve very encouraging levels of accuracy in the acceptability prediction task, as measured by the correlation between the acceptability measure scores and mean human acceptability values. We consider the relevance of these results to the debate on the nature of grammatical competence, and we argue that they support the view that linguistic knowledge can be intrinsically probabilistic.     

Longitudinal associations between athletes' controlled motivation,ill-being,and perceptions of controlling coach behaviors: A Bayesian latent growth curve approach

Although many scholars have argued that leadership is a dynamic process jointly produced by leaders and followers, leadership in sports is most often researched as a unidirectional process from coaches to athletes. Within self-determination theory (SDT), individual characteristics are suggested to influence how people perceive external events such as coaches' behaviors. In the present study, we examined this jointly produced leadership process by investigating longitudinal associations between athletes' controlled motivation, ill-being, and perceptions of coaches' controlling behaviors at the between- and within-person levels. The participants were 247 young elite skiers enrolled at Swedish sport high schools who responded to self-report questionnaires at three time points over the course of an athletic season. At the between-person level, increases in perceptions of coaches' controlling behaviors over the season positively predicted controlled motivation at the end of the season, and controlled motivation at the beginning of the season positively predicted ill-being at the end of the season. At the within-person level, athletes' controlled motivation positively predicted perceptions of coaches' controlling behaviors. The results at the between-person level support the unidirectional perspective and the tenets of SDT. The results at the within-person level suggest that individual characteristics such as motivation can influence how athletes perceive external events, which has been proposed theoretically but seldom examined empirically. Three plausible explanations for this reversed association are presented in the discussion.     

发展级联:解释个体纵向发展的新视角

发展级联(developmental cascades)近年来已成为发展心理学追踪研究中一种重要的理论视角。其基本观点是:人的发展过程是一个诸多发展特征不断产生级联效应的过程,某个时间点上个体特征的发展状况会对该特征的后续发展产生影响,并影响其他领域的发展,进而影响到个体的整个发展进程。在发展级联的理论观点基础上形成的相关方法学模型,为探究发展系统中多个因素之间的纵向关联提供了方法学依据与指导。本文介绍了发展级联的相关概念、理论基础、主要观点以及相关的方法学问题,并对其在实证研究中的应用进行了展望。     

An evaluation of in vivo desensitization and video modeling to increase compliance with dental procedures in persons with mental retardation

Fear of dental procedures deters many individuals with mental retardation from accepting dental treatment. This study was conducted to assess the effectiveness of two procedures, in vivo desensitization and video modeling, for increasing compliance with dental procedures in participants with severe or profound mental retardation. Desensitization increased compliance for all 5 participants, whereas video modeling increased compliance for only 1 of 3 participants.