Sample size and bentler and Bonett's nonnormed fit index

Bentler and Bonett's nonnormed fit index is a widely used measure of goodness of fit for the analysis of covariance structures. This note shows that contrary to what has been claimed the nonnormed fit index is dependent on sample size. Specifically for a constant value of a fitting function, the nonnormed index is inversely related to sample size. A simple alternative fit measure is proposed that removes this dependency. In addition, it is shown that this new measure as well as the old nonnormed fit index can be applied to any fitting function that measures the deviation of the observed covariance matrix from the covariance matrix implied by the parameter estimates for a model.     

A semiparametric approach for item response function estimation to detect item misfit

When scaling data using item response theory, valid statements based on the measurement model are only permissible if the model fits the data. Most item fit statistics used to assess the fit between observed item responses and the item responses predicted by the measurement model show significant weaknesses, such as the dependence of fit statistics on sample size and number of items. In order to assess the size of misfit and to thus use the fit statistic as an effect size, dependencies on properties of the data set are undesirable. The present study describes a new approach and empirically tests it for consistency. We developed an estimator of the distance between the predicted item response functions (IRFs) and the true IRFs by semiparametric adaptation of IRFs. For the semiparametric adaptation, the approach of extended basis functions due to Ramsay and Silverman (2005) is used. The IRF is defined as the sum of a linear term and a more flexible term constructed via basis function expansions. The group lasso method is applied as a regularization of the flexible term, and determines whether all parameters of the basis functions are fixed at zero or freely estimated. Thus, the method serves as a selection criterion for items that should be adjusted semiparametrically. The distance between the predicted and semiparametrically adjusted IRF of misfitting items can then be determined by describing the fitting items by the parametric form of the IRF and the misfitting items by the semiparametric approach. In a simulation study, we demonstrated that the proposed method delivers satisfactory results in large samples (i.e., N ≥ 1,000).     

Applying the Bradley-Terry-Luce method to P-E fit

This study attempted to increase the size of the correlation between person-environment (P-E) fit and job satisfaction by rescaling the instrumentation of the Theory of Work Adjustment using the Bradley-Terry-Luce method and a probability-based fit index. This approach worked as well as, but failed to outperform, the currently used correlation-based fit index. However, a probability-based fit index offers the advantage of being intuitively easier to understand than a correlation-based index. The very high correlation between the correlation-based fit index and the probability-based fit index suggests that both assess the same construct. It is argued that, considering the restriction of range common to all assessments of job satisfaction, the correlation between fit index and job satisfaction may not represent an upper limit, but rather a lower bound of the relationship between P-E fit and job satisfaction.     

Un examen empirique de l’intention de quitter des millénariaux à travers diverses dimensions de l’adéquation individu/environnement

The purpose of this paper is to examine the simultaneous effect of three person-environment fit dimensions, namely person-organization fit, person-group fit and person-supervisor fit on the millennials’ intent to leave. Data were collected among a sample of 178 employees born after 1980 working in Quebec organizations from various industries. Results indicate that the three person-environment fit dimensions are linked to intent to leave, but that only person-organization fit has an effect on intent to leave.     

Psychometric properties of the State-Trait Inventory for Cognitive and Somatic Anxiety (STICSA): comparison to the State-Trait Anxiety Inventory (STAI)

The State-Trait Inventory for Cognitive and Somatic Anxiety (STICSA; M. J. Ree, C. MacLeod, D. French, & V. Locke, 2000) was designed to assess cognitive and somatic symptoms of anxiety as they pertain to one's mood in the moment (state) and in general (trait). This study extended the previous psychometric findings to a clinical sample and validated the STICSA against a well-published measure of anxiety, the State-Trait Anxiety Inventory (STAI; C. D. Spielberger, 1983). Patients (N=567) at an anxiety disorders clinic were administered a battery of questionnaires. The results of confirmatory factor analyses (Bentler-Bonnett nonnormed fit index, comparative fit index, and Bollen fit index>.90; root-mean-square error of approximation<.05); convergent and discriminant validity analyses; and group comparisons supported the reliability and validity of the STICSA as a measure of state and trait cognitive and somatic anxiety. In addition, compared with the STAI (anxiety: rs/=.64), the STICSA was more strongly correlated with another measure of anxiety (rs>/=.67) and was less strongly correlated with a measure of depression (rs相似文献   

The Problem with Having Two Watches: Assessment of Fit When RMSEA and CFI Disagree

The root mean square error of approximation (RMSEA) and the comparative fit index (CFI) are two widely applied indices to assess fit of structural equation models. Because these two indices are viewed positively by researchers, one might presume that their values would yield comparable qualitative assessments of model fit for any data set. When RMSEA and CFI offer different evaluations of model fit, we argue that researchers are likely to be confused and potentially make incorrect research conclusions. We derive the necessary as well as the sufficient conditions for inconsistent interpretations of these indices. We also study inconsistency in results for RMSEA and CFI at the sample level. Rather than indicating that the model is misspecified in a particular manner or that there are any flaws in the data, the two indices can disagree because (a) they evaluate, by design, the magnitude of the model's fit function value from different perspectives; (b) the cutoff values for these indices are arbitrary; and (c) the meaning of “good” fit and its relationship with fit indices are not well understood. In the context of inconsistent judgments of fit using RMSEA and CFI, we discuss the implications of using cutoff values to evaluate model fit in practice and to design SEM studies.     

Authenticity at Work: A Matter of Fit?

Authenticity at work refers to the extent to which a worker feels in touch with their true self while at work. At first sight this concept seems to overlap with the concept of person-environment (P-E) fit, that is, the degree to which an individual experiences good fit with their work environment. Drawing on a sample of 867 Dutch gifted workers, structural equation modeling was used to investigate (i) whether authenticity at work and P-E fit can be distinguished, and (ii) how authenticity at work and P-E fit were associated with employee well-being. As expected, confirmatory factor analysis revealed that authenticity at work and P-E fit were distinct from each other. Moreover, the mediated effect of authenticity at work was stronger for two negative forms of well-being (burnout and boredom) than for two positive forms of well-being (work engagement and job satisfaction). The theoretical and practical implications of these findings are discussed, especially focusing on the distinction between authenticity and P-E fit.     

结构方程模型常用拟合指数检验的实质

拟合指数检验是评价结构方程模型(SEM)的重要环节。从协方差结构分析的角度将SEM与传统的回归模型比较,容易理解为什么SEM需要拟合指数。揭示了目前几种流行的拟合指数检验的实质:基于卡方的绝对拟合指数(如RMSEA)检验的实质是重新设定卡方检验的显著性水平(不同于通常的.05),相对拟合指数(如NNFI和CFI)检验的实质是基于虚模型设定均方(卡方与自由度之比)降低到的比例;在NNFI大于临界值后,报告和检验CFI是不必要的。根据研究结果提出了一些方便实用的拟合检验建议。     

The many null distributions of person fit indices

This paper deals with the situation of an investigator who has collected the scores ofn persons to a set ofk dichotomous items, and wants to investigate whether the answers of all respondents are compatible with the one parameter logistic test model of Rasch. Contrary to the standard analysis of the Rasch model, where all persons are kept in the analysis and badly fittingitems may be removed, this paper studies the alternative model in which a small minority ofpersons has an answer strategy not described by the Rasch model. Such persons are called anomalous or aberrant. From the response vectors consisting ofk symbols each equal to 0 or 1, it is desired to classify each respondent as either anomalous or as conforming to the model. As this model is probabilistic, such a classification will possibly involve false positives and false negatives. Both for the Rasch model and for other item response models, the literature contains several proposals for a person fit index, which expresses for each individual the plausibility that his/her behavior follows the model. The present paper argues that such indices can only provide a satisfactory solution to the classification problem if their statistical distribution is known under the null hypothesis that all persons answer according to the model. This distribution, however, turns out to be rather different for different values of the person's latent trait value. This value will be called ability parameter, although our results are equally valid for Rasch scales measuring other attributes.As the true ability parameter is unknown, one can only use its estimate in order to obtain an estimated person fit value and an estimated null hypothesis distribution. The paper describes three specifications for the latter: assuming that the true ability equals its estimate, integrating across the ability distribution assumed for the population, and conditioning on the total score, which is in the Rasch model the sufficient statistic for the ability parameter.Classification rules for aberrance will be worked out for each of the three specifications. Depending on test length, item parameters and desired accuracy, they are based on the exact distribution, its Monte Carlo estimate and a new and promising approximation based on the moments of the person fit statistic. Results for the likelihood person fit statistic are given in detail, the methods could also be applied to other fit statistics. A comparison of the three specifications results in the recommendation to condition on the total score, as this avoids some problems of interpretation that affect the other two specifications.The authors express their gratitude to the reviewers and to many colleagues for comments on an earlier version.     

检验的临界值：真伪差距多大才能辨别？ ——评《不同条件下拟合指数的表现及临界值的选择》

Hu和Bentler（1998,1999）通过模拟研究推荐结构方程模型拟合指数临界值后,受到不少批评和质疑。此后有关拟合指数的研究重点不再是推出新的临界值标准。郭庆科等人的文章《不同条件下拟合指数的表现及临界值的选择》,仿照Hu和Bentler的做法,通过模拟研究推荐新的拟合指数临界值标准。本文旨在揭示这种做法的错误所在。用简单的Z检验,说明检验的临界值是不能通过模拟研究确定的。通过将一个特定真模型的众多错误模型分类,说明结构方程分析中真模型与错误模型差距的多样性,无法通过模拟一对真伪模型来代表。讨论了统计检验的本质和确定临界值的逻辑,还谈到应当从哪些角度检验和评价结构方程模型     

Person-supervisor fit,needs-supplies fit,and team fit as mediators of the relationship between dual-focused transformational leadership and well-being in scientific teams

Team-based work structures have become prevalent in science. Scientific teams, however, are characterized by competing individual-level and team-level needs (i.e., by mixed-motive situations). This makes leading scientific teams particularly challenging: Balancing competing individual-level goals and common team-level goals requires a specific type of leadership that simultaneously considers both satisfying individual-level needs as well as team-level needs. The current study addresses this issue by combining the dual-focused model of transformational leadership with person-environment fit theory. Specifically, we investigated needs-supplies fit, person-supervisor fit, and team fit as mediators of the relationship between transformational leadership and scientific team members’ job satisfaction and work-related strain. In doing so, we provide a new perspective on leadership in scientific teams by explicitly differentiating individual-level and team-level effects of transformational leadership. We tested our hypotheses using a three-wave design with a sample of 134 members of 42 scientific teams. The relationships between individual-focused transformational leadership, job satisfaction, and work-related strain were mediated by needs-supplies fit and person-supervisor fit. Team-focused transformational leadership was positively related to job satisfaction and negatively related to work-related strain. Our findings contribute to further clarifying the mechanisms underlying the relationship between transformational leadership and members’ well-being in scientific teams.     

Evaluation of Model Fit in Cognitive Diagnosis Models

Cognitive diagnosis models (CDMs) estimate student ability profiles using latent attributes. Model fit to the data needs to be ascertained in order to determine whether inferences from CDMs are valid. This study investigated the usefulness of some popular model fit statistics to detect CDM fit including relative fit indices (AIC, BIC, and CAIC), and absolute fit indices (RMSEA2, ABS(fcor) and MAX(χ²_jj′)). These fit indices were assessed under different CDM settings with respect to Q-matrix misspecification and CDM misspecification. Results showed that relative fit indices selected the correct DINA model most of the times and selected the correct G-DINA model well across most conditions. Absolute fit indices rejected the true DINA model if the Q-matrix was misspecified in any way. Absolute fit indices rejected the true G-DINA model whenever the Q-matrix was under-specified. RMSEA2 could be artificially low when the Q-matrix was over-specified.     

个人-工作契合度测量研究的新进展

论文概述了个人-工作契合度测量研究的发展，介绍了测量的角度、测量的内容、方法和指标，分析比较了各种方法的优缺点，最后总结了现有的测量研究的局限并对未来研究的发展趋势作了展望。     

Chameleonic obsessive job passion: demystifying the relationships between obsessive job passion and in-role and extra-role performance

In seeking to address the theoretical ambiguity regarding how and when obsessive job passion (OJP) leads to work performance, we integrate both self-verification and person–environment (P-E) fit perspectives to propose and test a moderated mediation model linking OJP to performance. We argue that OJP is indirectly related to co-worker-rated in-role and extra-role performance through self-verification, and these indirect links are conditioned by perceived demands–abilities (D-A) fit and needs–supplies (N-S) fit. Results from 190 healthcare professionals and their co-workers collected at three different time periods revealed the contrasting roles played by these two moderators. Individuals with higher OJP self-verify more when they perceive low D-A fit, but self-verify less when they perceive high N-S fit, whereas the opposite holds true for high D-A fit and low N-S fit. Contrary to predictions, negative relationships were found between self-verification and both types of performance. Specifically, OJP is associated with greater in- and extra-role performance (because of reduced self-verification) under high perceived D-A but low N-S fit, whereas the opposite results are observed under low perceived D-A and high N-S fit. The findings underscore the contingent nature of OJP and contribute to job passion, self-concept, and person–environment fit research.     

个人—组织匹配的研究现状与展望

个人—组织匹配主要探讨个人和组织之间的相容性以及实现这种相容性的前提和结果。个人与组织可能以附助或补偿的方式形成匹配。尽管在操作指标的选择上,研究者们没有达成共识,但他们的研究结论都同样体现了个人—组织匹配在员工的组织进入、工作态度、离职意向、工作压力、亲社会行为、工作绩效和组织文化培训等方面的管理价值。展望该领域的进一步研究,自我报告的研究方法以及高水平匹配的益处是令人质疑的,匹配的评估指标也亟待明确。     

认知诊断模型资料拟合检验方法和统计量

认知诊断模型界定了测验题目和所考察属性之间的关系, 通过被试的作答反应获取被试对属性或知识技能的掌握情况。认知诊断模型资料拟合检验可以从项目拟合、模型绝对拟合、模型相对拟合和个人拟合方等方面进行。通过对认知诊断拟合检验方法和统计量的详细介绍和评价, 可为认知诊断实践提供借鉴和参考。未来研究可在更丰富的研究条件下对各统计量的性能进行评价和对比, 完善已有的拟合检验方法, 提出新的拟合统计量。     

A Person-Centered Approach to P-E Fit Questions Using a Multiple-Trait Model

The current study first longitudinally examines the validity of person-environment (P-E) RIASEC congruence, adopting a job analytic method to assess the environment and using P-E difference scores to compute congruence, to predict a range of intrinsic career outcomes—including job satisfaction, skill development, work involvement, and perceived stress—in a sample of 401 college seniors involved in the labor market. Second, the incremental validity of an alternative conceptualization of the P component (i.e., the Five-Factor Model of personality [FFM]) is examined over and beyond RIASEC congruence scores. Congruence across RIASEC types significantly predicted job satisfaction and skill development, but FFM traits significantly and substantially contributed to the prediction of all intrinsic career outcomes. Finally, a person-centered perspective to P-E questions is introduced, demonstrating that cluster analysis of individuals' FFM scores resulted in two clusters (i.e., internalizers/externalizers and resilients) showing very different positions on the labor market and reporting differing initial career outcomes. It is concluded that RIASEC P-E fit congruence studies should be complemented with FFM assessment to increase predictive validity. Applications of an FFM-based, person-centered approach in I/O and P-E fit research and practice are discussed.     

领导-团队投入匹配对团队绩效的影响：团队满意度氛围的作用

基于领导-团队匹配的视角,研究以133名领导和645名成员的团队配对数据,采用二次多项式回归与响应面分析对领导工作投入与团队投入氛围的一致性匹配和不一致性匹配,以及团队满意度氛围如何影响团队绩效进行了探讨。结果发现：领导工作投入与团队投入氛围一致与不一致相比,团队绩效较好;并且一致性匹配具有加强效应,即当领导工作投入与团队投入氛围一致时,团队绩效随着双方投入的增加而提高;同时,团队满意度氛围在领导-团队投入的一致性匹配与团队绩效的线性关系中起到部分中介作用。     

Bias-corrected estimation of the Rudas–Clogg–Lindsay mixture index of fit

Rudas, Clogg, and Lindsay (1994, J. R Stat Soc. Ser. B, 56, 623) introduced the so-called mixture index of fit, also known as pi-star (π*), for quantifying the goodness of fit of a model. It is the lowest proportion of ‘contamination’ which, if removed from the population or from the sample, makes the fit of the model perfect. The mixture index of fit has been widely used in psychometric studies. We show that the asymptotic confidence limits proposed by Rudas et al. (1994, J. R Stat Soc. Ser. B, 56, 623) as well as the jackknife confidence interval by Dayton ( 2003 , Br. J. Math. Stat. Psychol., 56, 1) perform poorly, and propose a new bias-corrected point estimate, a bootstrap test and confidence limits for pi-star. The proposed confidence limits have coverage probability much closer to the nominal level than the other methods do. We illustrate the usefulness of the proposed method in practice by presenting some practical applications to log-linear models for contingency tables.     

A quantitative review of the relationship between person-organization fit and behavioral outcomes

This paper extends the meta-analysis of Verquer, Beehr, and Wagner by providing a meta-analytic review of the relationship between person-organization fit (PO fit) and behavioral criteria (job performance, organizational citizenship behaviors, and turnover). Results indicate that PO fit is weakly to moderately related to each of these outcome variables. Results further show that the way in which fit is measured is an important moderator of fit-outcome relationships; however, definition of fit did not moderate the relationship between fit and behavioral criterion. Implications of these findings and avenues for future research are discussed.