Effect size, power, and sample size determination for structured means modeling and mimic approaches to between-groups hypothesis testing of means on a single latent construct

While effect size estimates, post hoc power estimates, and a priori sample size determination are becoming a routine part of univariate analyses involving measured variables (e.g., ANOVA), such measures and methods have not been articulated for analyses involving latent means. The current article presents standardized effect size measures for latent mean differences inferred from both structured means modeling and MIMIC approaches to hypothesis testing about differences among means on a single latent construct. These measures are then related to post hoc power analysis, a priori sample size determination, and a relevant measure of construct reliability.I wish to convey my appreciation to the reviewers and Associate Editor, whose suggestions extended and strengthened the article's content immensely, and to Ralph Mueller of The George Washington University for enhancing the clarity of its presentation.     

Qualitative and Quantitative Shifts in Adolescent Problem Behavior Development: A Cohort-Sequential Multivariate Latent Growth Modeling Approach

The aim of this study was to examine the nature of problem behavior development from late childhood through adolescence, to assess the quantitative development of problem behavior (alcohol use, marijuana use, deviance, academic failure) as well as potential qualitative shifts in problem behavior over time. Multivariate latent growth curve modeling (LGM) analyses and a cohort-sequential design were employed. Data were from the National Youth Survey and included 770 youth from four cohorts (11, 12, 13, 14 years old), assessed annually for 5 years. Results showed significant growth in problem behavior from ages 11 to 18. Alcohol use and marijuana use contributed most, and academic failure contributed least to the problem behavior latent construct. Results of the variant model revealed that the contribution of all four behaviors to the overall problem behavior construct increased similarly as children aged.     

多阶段混合增长模型的影响因素：距离与形态

通过模拟研究, 考察潜类别距离和发展形态等因素对多阶段混合增长模型的模型选择和参数估计的影响：(1)潜类别距离越大, 模型选择和分类效果越好。(2)混合模型的选择, 应以一定样本量(至少200)为前提, 首先考虑BIC选出正确的分类模型, 再通过熵值、ARI等选择分类确定性较高的模型。(3)多阶段的发展形态对正确模型的选择和分类的确定性均有一定程度影响。(4)潜类别距离和样本量越大, 参数估计精度越高。(5)在判断分类准确性的指标中, ARI的选择更偏向于真实的模型。     

我国近十年来心理学研究中HLM方法的应用述评

以2002-2011年中国期刊网收录的50例应用多层线性模型(HLM)的心理学期刊论文为研究对象,从样本描述、模型发展与规范、数据准备、估计方法与假设检验4个角度进行文献计量和内容分析,对我国心理学研究中HLM方法的使用现状进行评估。结果表明,HLM方法主要用于管理、发展和教育心理学,绝大多数应用都是两层模型且层2样本量较大。HLM方法在广泛应用的同时仍存在忽略前提假设检验、分析过程中的重要信息和结果报告不完整等问题,随后提供了4条建议。     

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.