Applying mixed‐effects modeling to single‐subject designs: An introduction

Behavior analysis and statistical inference have shared a conflicted relationship for over fifty years. However, a significant portion of this conflict is directed toward statistical tests (e.g., t‐tests, ANOVA) that aggregate group and/or temporal variability into means and standard deviations and as a result remove much of the data important to behavior analysts. Mixed‐effects modeling, a more recently developed statistical test, addresses many of the limitations of more basic tests by incorporating random effects. Random effects quantify individual subject variability without eliminating it from the model, hence producing a model that can predict both group and individual behavior. We present the results of a generalized linear mixed‐effects model applied to single‐subject data taken from Ackerlund Brandt, Dozier, Juanico, Laudont, & Mick, 2015, in which children chose from one of three reinforcers for completing a task. Results of the mixed‐effects modeling are consistent with visual analyses and importantly provide a statistical framework to predict individual behavior without requiring aggregation. We conclude by discussing the implications of these results and provide recommendations for further integration of mixed‐effects models in the analyses of single‐subject designs.     

On Standardizing Within-Person Effects: Potential Problems of Global Standardization

Person-mean centering has been recommended for disaggregating between-person and within-person effects when modeling time-varying predictors. Multilevel modeling textbooks recommended global standardization for standardizing fixed effects. An aim of this study is to evaluate whether and when person-mean centering followed by global standardization can accurately estimate fixed-effects within-person relations (the estimand of interest in this study) in multilevel modeling. We analytically derived that global standardization generally yields inconsistent (asymptotically biased) estimates for the estimand when between-person differences in within-person standard deviations exist and the average within-person relation is nonzero. Alternatively, a person-mean-SD standardization (P-S) approach yields consistent estimates. Our simulation results further revealed (1) how misleading the results from global standardization were under various circumstances and (2) the P-S approach had accurate estimates and satisfactory coverage rates of fixed-effects within-person relations when the number of occasions is 30 or more (in many conditions, performance was satisfactory with 10 or 20 occasions). A daily diary data example, focused on emotional complexity, was used to empirically illustrate the approaches. Researchers should choose standardization approaches based on theoretical considerations and should clearly describe the purpose and procedure of standardization in research articles.     

Factor Indeterminacy as Metrological Uncertainty: Implications for Advancing Psychological Measurement

Researchers have long been aware of the mathematics of factor indeterminacy. Yet, while occasionally discussed, the phenomenon is mostly ignored. In metrology, the measurement discipline of the physical sciences, uncertainty – distinct from both random error (but encompassing it) and systematic error – is a crucial characteristic of any measurement. This research argues that factor indeterminacy is uncertainty. Factor indeterminacy fundamentally threatens the validity of psychometric measurement, because it blurs the linkage between a common factor and the conceptual variable that the factor represents. Acknowledging and quantifying factor indeterminacy is important for progress in reducing this component of uncertainty in measurement, and thus improving psychological measurement over time. Based on our elaborations, we offer a range of recommendations toward achieving this goal.     

Model Implied Instrumental Variables (MIIVs): An Alternative Orientation to Structural Equation Modeling

Few dispute that our models are approximations to reality. Yet when it comes to structural equation models (SEMs), we use estimators that assume true models (e.g. maximum likelihood) and that can create biased estimates when the model is inexact. This article presents an overview of the Model Implied Instrumental Variable (MIIV) approach to SEMs from Bollen (1996). The MIIV estimator using Two Stage Least Squares (2SLS), MIIV-2SLS, has greater robustness to structural misspecifications than system wide estimators. In addition, the MIIV-2SLS estimator is asymptotically distribution free. Furthermore, MIIV-2SLS has equation-based overidentification tests that can help pinpoint misspecifications. Beyond these features, the MIIV approach has other desirable qualities. MIIV methods apply to higher order factor analyses, categorical measures, growth curve models, dynamic factor analysis, and nonlinear latent variables. Finally, MIIV-2SLS permits researchers to estimate and test only the latent variable model or any other subset of equations. In addition, other MIIV estimators beyond 2SLS are available. Despite these promising features, research is needed to better understand its performance under a variety of conditions that represent empirical applications. Empirical and simulation examples in the article illustrate the MIIV orientation to SEMs and highlight an R package MIIVsem that implements MIIV-2SLS.     

小学低年级儿童阅读流畅性的发展轨迹及其对阅读理解的预测作用

对149名小学一年级儿童的阅读流畅性进行历时三年五次的追踪测试,采用潜变量增长模型探索了儿童阅读流畅性的发展轨迹,并在控制相关变量后,考察了阅读流畅性的起始水平和发展速度对阅读理解的预测作用。结果发现：（1）小学低年级儿童字词阅读流畅性呈非线性发展,其中一年级快速发展,二、三年级时进一步发展,但发展速度变缓,起始水平低的儿童其后发展速度快,表现出补偿模式;句子阅读流畅性呈线性发展,儿童个体之间的差异随时间逐渐增大,表现出马太效应;（2）控制一般认知能力、家庭社会经济地位及相关语言认知技能后,字词阅读流畅性的起始水平和发展速度均可预测儿童三年级时阅读理解水平,而句子阅读流畅性的起始水平不能预测,但发展速度有显著预测作用。结果说明字词阅读流畅性和句子阅读流畅性有不同的发展轨迹和发展模式,在小学低年级阶段,相比句子阅读流畅性,儿童字词阅读流畅性的起始水平对阅读理解有预测作用,且两者的发展速度均对阅读理解有预测作用。     

Cross-National Comparison of Attitudes Toward Fathers' and Mothers' Participation in Household Tasks and Childcare

The purpose of this study was to explore attitudes toward the division of fathers' and mothers' participation in childcare/household tasks through a multilevel modeling approach. Data from the Euro-barometer surveys, including over 10,000 respondents from 13 European countries, were used. Respondents' attitudes were related to several individual-and macro-level factors. At the individual level (based on a separate regression equation for each country), it was found that respondents were most likely to hold egalitarian attitudes toward household work and childcare when they were younger, female, and politically liberal. At the macro level, countries' United Nations ratings on women's empowerment, Gross National Product, and cultural individualism were related to egalitarian attitudes. Study implications, strengths and weaknesses, and suggestions for future research are discussed.     

基于空间分割的手写输入系统的用户绩效模型

为定量估计与提高基于空间分割的手写输入系统用户绩效 ,运用Fitts定律及离散变量的数学期望等方法推导了用户绩效的数学模型。实验验证了该模型在具体界面中能较好地拟合用户在 8次 (8× 2 4字 )训练后的实际操作绩效。应用该模型可较好地拟合用户使用手写系统完成抄写任务的时间、推算输入系统某些参数的最佳设置值 ;并发现当输入系统的其它参数为定值时 ,缩短用户单字手写时间会比缩短系统识别时间能更有效地提高用户绩效。     

贝叶斯结构方程模型及其研究现状

在心理学研究中结构方程模型(Structural Equation Modeling, SEM)被广泛用于检验潜变量间的因果效应, 其估计方法有频率学方法(如, 极大似然估计)和贝叶斯方法两类。近年来由于贝叶斯统计的流行及其在结构方程建模中易于处理小样本、缺失数据及复杂模型等方面的优势, 贝叶斯结构方程模型发展迅速, 但其在国内心理学领域的应用不足。主要介绍了贝叶斯结构方程模型的方法基础和优良特性, 及几类常用的贝叶斯结构方程模型及其应用现状, 旨在为应用研究者介绍新的研究工具。     

小学低年级儿童口语词汇知识的发展轨迹及其影响因素

以149名小学生为研究对象, 对其口语词汇知识进行了历时3年的5次追踪测试, 采用潜变量增长模型探索了小学1~3年级学生汉语口语词汇知识的发展轨迹, 并考察了语音意识、同形语素意识、复合语素意识和家庭社会经济地位对口语词汇知识发展轨迹的影响。结果发现：(1) 1~3年级学生口语词汇知识发展轨迹呈曲线形式, 其中前两年呈线性发展, 三年级时呈加速发展, 发展速度是前期发展的两倍, 起始水平和发展速度均存在显著的个体差异; (2)语音意识、同形语素意识、复合语素意识和家庭社会经济地位均可以正向预测学生口语词汇知识的起始水平; (3)只有同形语素意识和家庭社会经济地位可以正向预测学生口语词汇知识的发展速度。     

Quantifying the psychopathic stare: Automated assessment of head motion is related to antisocial traits in forensic interviews

Clinicians have long noted that individuals with high psychopathic traits exhibit unique interpersonal style often observable during forensic interviews. Here we develop an automated approach for quantifying head dynamics during video-recorded naturalistic clinical interviews. We expected head dynamics would be related to psychopathic traits. As predicted, dwell times indicate that those with higher levels of psychopathic traits are characterized by more stationary head positions, focused directly towards the camera/interviewer, than were individuals low in psychopathic traits. These associations were primarily driven by developmental/antisocial features of psychopathy, indicating that those with severe and life-course persistent antisocial behavior exhibit more rigid and focused orienting of their head during interpersonal communication. These results encourage more research into the automated quantification of behavioral manifestations of personality to support clinical observations that psychopaths exhibit unique qualities in non-verbal interpersonal communication.