Reliability of Summed Item Scores Using Structural Equation Modeling: An Alternative to Coefficient Alpha

A method is presented for estimating reliability using structural equation modeling (SEM) that allows for nonlinearity between factors and item scores. Assuming the focus is on consistency of summed item scores, this method for estimating reliability is preferred to those based on linear SEM models and to the most commonly reported estimate of reliability, coefficient alpha.     

非正态分布测量数据对克隆巴赫信度α系数的影响

对“增大被试群体异质性,能提高测验信度”观点提出质疑。讨论非正态分布测量数据的偏度对克隆巴赫信度α系数的影响,以模拟方法验证Box—COX正态化变换对信度的高估现象,进而给出对克隆巴赫信度α系数估计的改进方法。     

测验信度估计：从α系数到内部一致性信度

沿用经典的测验信度定义, 简介了信度与a 系数的关系以及a系数的局限。为了推荐替代a系数的信度估计方法, 深入讨论了与a 系数关系密切的同质性信度和内部一致性信度。在很一般的条件下, 证明了a 系数和同质性信度都不超过内部一致性信度, 后者不超过测验信度, 说明内部一致性信度比较接近测验信度。总结出一个测验信度分析流程, 说明什么情况下a 系数还有参考价值; 什么情况下a 系数不再适用, 应当使用内部一致性信度(文献上也常称为合成信度)。提供了计算同质性信度和内部一致性信度的计算程序, 一般的应用工作者可以直接套用。     

Coefficients Alpha,Beta, Omega,and the glb: Comments on Sijtsma

There are three fundamental problems in Sijtsma (Psychometrika, 2008): (1) contrary to the name, the glb is not the greatest lower bound of reliability but rather is systematically less than ω _t (McDonald, Test theory: A unified treatment, Erlbaum, Hillsdale, 1999), (2) we agree with Sijtsma that when considering how well a test measures one concept, α is not appropriate, but recommend ω _t rather than the glb, and (3) the end user needs procedures that are readily available in open source software.     

Reliability Beyond Theory and Into Practice

The critical reactions of Bentler (2009, doi:), Green and Yang (2009a, doi:; 2009b, doi:), and Revelle and Zinbarg (2009, doi:) to Sijtsma’s (2009, doi:) paper on Cronbach’s alpha are addressed. The dissemination of psychometric knowledge among substantive researchers is discussed.     

Perpetrators and Social Death: A Cautionary Tale

Understanding evil requires both addressing the grave wrongs done to the victim and addressing the perpetrator who does these wrongs. Claudia Card's concept of social vitality was developed to explain what génocidaires destroy in their victims. This essay brings that concept into conversation with perpetrator testimony, arguing that the génocidaires’ desire for their own social vitality, achieved through their destruction of the social world of their targets, in fact boomerangs to corrode the vitality of their own lives. This is true whether they succeed or fail in their genocidal project. Card's recent analysis of “being a badass” is brought to bear on the cultivation of evil, and the essay suggests four strategies for meeting Card's “moral challenge of avoiding evil responses to evil.”     

A generalization of coefficient alpha

It is well known that coefficient alpha can be used to estimate the reliability of a test even when the test is split into several parts. It is also known that alpha can severely underestimate test reliability when the several parts have an unequal number of items. A gernalization of alpha,β _k, is proposed to correct this defect. Several properties ofβ _k are also presented. The author gratefully acknowledges the assistance of Dr. Leonard Feldt for reviewing an earlier draft of this paper, and Ms. Rita Karwacki Bode and Mr. Dave Mansell for the analysis of the experimental data reported here. The comments of an unknown referee which contributed substantially to the clarity of the presentation are also gratefully acknowledged.     

Risk and Trust in Public Health: A Cautionary Tale

The leading ethical position on placebo-controlled clinical trials is that whenever proven effective treatment exists for a given condition, it is unethical to test a new treatment for that condition against placebo. Invoking the principle of clinical equipoise, opponents of placebo-controlled trials in the face of proven effective treatment argue that they (1) violate the therapeutic obligation of physicians to offer optimal medical care and (2) lack both scientific and clinical merit. We contend that both of these arguments are mistaken. Clinical equipoise provides erroneous ethical guidance in the case of placebo-controlled trials, because it ignores the ethically relevant distinction between clinical trials and treatment in the context of clinical medicine and the methodological limitations of active-controlled trials. Placebo controls are ethically justifiable when they are supported by sound methodological considerations and their use does not expose research participants to excessive risks of harm.     

Cronbach's Alpha: Review of Limitations and Associated Recommendations

This paper discusses the limitations of Cronbach's alpha as a sole index of reliability, showing how Cronbach's alpha is analytically handicapped to capture important measurement errors and scale dimensionality, and how it is not invariant under variations of scale length, interitem correlation, and sample characteristics. In addition, the limitations and strengths of several recommendations on how to ameliorate these problems were critically reviewed. It was shown that the reliance on Cronbach's alpha as a sole index of reliability is no longer sufficiently warranted. This requires that other indices of internal consistency be reported along with alpha coefficient, and that when a scale is composed of large number of items, factor analysis should be performed, and appropriate internal consistency estimation method applied. This approach, if adopted, will largely minimize and guard against uncritical use of Cronbach's alpha coefficient.     

A test of the hypothesis that Cronbach's alpha reliability coefficient is the same for two tests administered to the same sample

In measurement studies the researcher may wish to test the hypothesis that Cronbach's alpha reliability coefficient is the same for two measurement procedures. A statistical test exists for independent samples of subjects. In this paper three procedures are developed for the situation in which the coefficients are determined from the same sample. All three procedures are computationally simple and give tight control of Type I error when the sample size is 50 or greater.The author is indebted to Jerry S. Gilmer for development of the computer programs used in this study.     

Lower bounds for the reliability of the total score on a test composed of non-homogeneous items: I: Algebraic lower bounds

Let Σ _x be the (population) dispersion matrix, assumed well-estimated, of a set of non-homogeneous item scores. Finding the greatest lower bound for the reliability of the total of these scores is shown to be equivalent to minimizing the trace of Σ _x by reducing the diagonal elements while keeping the matrix non-negative definite. Using this approach, Guttman's bounds are reviewed, a method is established to determine whether his λ₄ (maximum split-half coefficient alpha) is the greatest lower bound in any instance, and three new bounds are discussed. A geometric representation, which sheds light on many of the bounds, is described. Present affiliation of the second author: Department of Statistics, University of Nigeria (Nsukka Campus). Work on this paper was carried out while on study leave in Aberystwyth.     

Note on two generalizations of coefficient alpha

An important relationship is given for two generalizations of coefficient alpha, Rajaratnam, Cronbach and Gleser's generalizability formula for stratified-parallel tests and Raju's coefficient beta.The author gratefully acknowledges the generous assistance given by reviewers and the editor.     

Self Research in Educational Psychology: A Cautionary Tale of Positive Psychology in Action

Recent calls for a positive psychology that would deemphasize human pathology and dysfunction in favor of building an understanding of positive features of human life and human flourishing make two assumptions that the author questions in this article. First, he challenges the assumption that disciplinary psychology has been fixated on pathology and dysfunction by considering work in educational psychology that, both historically and currently, espouses the characteristics of positive psychology as articulated by its major advocates. Second, through a brief, critical consideration of research on the self in educational psychology, he contests the assumption that psychology has sufficient resources to develop into the positive psychology envisioned by its promoters. He argues that psychology's emphasis on the individual, whose core self resides in a deep, internal psyche, radically strips psychology of the historical and sociocultural resources that enable self-development, constrain self-understanding, and constitute the self.     

Virtual Levels and Role Models: N-Level Structural Equations Model of Reciprocal Ratings Data

A general latent variable modeling framework called n-Level Structural Equations Modeling (NL-SEM) for dependent data-structures is introduced. NL-SEM is applicable to a wide range of complex multilevel data-structures (e.g., cross-classified, switching membership, etc.). Reciprocal dyadic ratings obtained in round-robin design involve complex set of dependencies that cannot be modeled within Multilevel Modeling (MLM) or Structural Equations Modeling (SEM) frameworks. The Social Relations Model (SRM) for round robin data is used as an example to illustrate key aspects of the NL-SEM framework. NL-SEM introduces novel constructs such as ‘virtual levels’ that allows a natural specification of latent variable SRMs. An empirical application of an explanatory SRM for personality using xxM, a software package implementing NL-SEM is presented. Results show that person perceptions are an integral aspect of personality. Methodological implications of NL-SEM for the analyses of an emerging class of contextual- and relational-SEMs are discussed.     

Measuring Care and Justice Moral Orientation: Italian Adaptation and Revision of the MMO-2 Scale

This study presents the Italian adaptation of the Measure of Moral Orientation, second revision (MMO-2). Based on Carol Gilligan’s theory of the Ethics of Care, the MMO-2 was designed to measure two complementary moral stances, namely, Care and Justice. For this study, questionnaire responses from 683 university students were assessed against an Italian-adapted MMO-2 scale. Data were analyzed through exploratory structural equation modeling first as separate scenarios and then as a single model. The final model comprises 4 intercorrelated pairs of latent variables and shows highly satisfactory goodness of fit indices with moderate construct validity and reliability. Strengths, limitations, and directions for the future developments of the MMO-2 are discussed.     

A Comparison of Multilevel Mediation Modeling Methods: Recommendations for Applied Researchers

Multilevel structural equation modeling (MSEM) has been proposed as a valuable tool for estimating mediation in multilevel data and has known advantages over traditional multilevel modeling, including conflated and unconflated techniques (CMM & UMM). Recent methodological research has focused on comparing the three methods for 2-1-1 designs, but in regards to 1-1-1 mediation designs, there are significant gaps in the published literature that prevent applied researchers from making educated decisions regarding which model to employ in their own specific research design. A Monte Carlo study was performed to compare MSEM, UMM, and CMM on relative bias, confidence interval coverage, Type I Error, and power in a 1-1-1 model with random slopes under varying data conditions. Recommendations for applied researchers are discussed and an empirical example provides context for the three methods.     

管理胜任力特征分析:结构方程模型检验

管理胜任力特征分析是人事选拔与评价的重要内容之一。本研究在运用基于胜任力的职位分析并总结国内外有关文献的基础上,编制了管理综合素质评价量表,并运用此量表调查了220名中高层管理者,采用因素分析和结构方程模型检验企业高级管理者胜任力特征的结构。结果表明,管理胜任力特征结构由管理素质和管理技能等两个维度构成,但在维度要素及其关键度上,职位层次间存在显著差异。本研究为管理职位的测评选拔提供了新的理论依据。     

Effect of Reward Contingency on Intrinsic Motivation

The effects of type of task and type of reward contingency on intrinsic motivation for subsequent task performance were investigated. The sample consisted of 50 young Indian adults. The results showed a significantly greater amount of free choice time spent on a heuristic task rather than an algorithmic task. The verbal measures of intrinsic motivation yielded a significant effect of reward contingency with greater intrinsic motivation under performance-contingent reward, followed by task-contingent and no-reward conditions, respectively. The results support self-determination and competence processes as important mediators of intrinsic motivation.     

社区老年人的生活质量与心理健康:SEM研究

在Lawton理论框架以及先前研究基础上,进一步对上海社区老年人生活质量与心理健康进行研究。采用结构方程建模的方法对老年人健康生活质量(QHL)、客观生活环境质量(QOE)与心理健康(PWB)的理论构念及其相互关系的理论模型予以实证研究。结果表明,该模型与社区老人测评数据(N=262)的拟合度良好,证明QHL对PWB具有显著正面影响,QOE与QHL显著相关且直接或间接地正面影响PWB。研究表明良好身体健康状况、行为调适能力以及家庭一社区养老环境对促进老人心理健康具有重要意义。