Fit Of Structural Equation Models Research Articles

Common health problems in safety‐net primary care: Modeling the roles of trauma history and mental health

This study described trauma exposure and investigated mediational effects of mental health on the relationships between trauma and pain, sleep, smoking, and general health. Participants were 210 low-income primary care patients. The study used a crosssectional, self-report survey design. Eighty-five percent of the sample reported adult trauma and 54% reported four or more childhood traumas. Moderate or higher depression and anxiety levels were present in 59% and 48% of participants, respectively. Structural equation model fit was good for sleep, pain, and general health, showing that trauma indirectly affected health variables via mental health. Participants endorsed substantial adult and childhood trauma, which likely had cascading effects on mental health and common primary care presenting health issues.

Testing Model Fit by Bootstrap Selection

Over the last few decades, many robust statistics have been proposed in order to assess the fit of structural equation models. To date, however, no clear recommendations have emerged as to which test statistic performs best. It is likely that no single statistic will universally outperform all contenders across all conditions of data, sample size, and model characteristics. In a real-world situation, a researcher must choose which statistic to report. We propose a bootstrap selection mechanism that identifies the test statistic that exhibits the best performance under the given data and model conditions among any set of candidates. This mechanism eliminates the ambiguity of the current practice and offers a wide array of test statistics available for reporting. In a Monte Carlo study, the bootstrap selector demonstrated promising performance in controlling Type I errors compared to current test statistics.

Testing small variance priors using prior-posterior predictive p values.

Muthén and Asparouhov (2012) propose to evaluate model fit in structural equation models based on approximate (using small variance priors) instead of exact equality of (combinations of) parameters to zero. This is an important development that adequately addresses Cohen's (1994) The Earth is Round (p < .05), which stresses that point null-hypotheses are so precise that small and irrelevant differences from the null-hypothesis may lead to their rejection. It is tempting to evaluate small variance priors using readily available approaches like the posterior predictive p value and the DIC. However, as will be shown, both are not suited for the evaluation of models based on small variance priors. In this article, a well behaving alternative, the prior-posterior predictive p value, will be introduced. It will be shown that it is consistent, the distributions under the null and alternative hypotheses will be elaborated, and it will be applied to testing whether the difference between 2 means and the size of a correlation are relevantly different from zero. (PsycINFO Database Record

Carbon limitation, stem growth rate and the biomechanical cause of Corner's rules.

Corner's rules describe a global spectrum from large-leaved plants with thick, sparingly branched twigs with low-density stem tissues and thick piths to plants with thin, highly branched stems with high-density stem tissues and thin piths. The hypothesis was tested that, if similar crown areas fix similar amounts of carbon regardless of leaf size, then large-leaved species, with their distantly spaced leaves, require higher stem growth rates, lower stem tissue densities and stiffnesses, and therefore thicker twigs. Structural equation models were used to test the compatibility of this hypothesis with a dataset on leaf size, shoot tip spacing, stem growth rate and dimensions, and tissue density and mechanics, sampling 55 species drawn from across the angiosperm phylogeny from a morphologically diverse dry tropical community. Very good fit of structural equation models showed that the causal model is highly congruent with the data. Given similar amounts of carbon to allocate to stem growth, larger-leaved species require greater leaf spacing and therefore greater stem extension rates and longer stems, in turn requiring lower-density, more flexible, stem tissues than small-leaved species. A given stem can have high resistance to bending because it is thick (has high second moment of area I) or because its tissues are stiff (high Young's modulus E), the so-called E-I trade-off. Because of the E-I trade-off, large-leaved species have fast stem growth rates, low stem tissue density and tissue stiffness, and thick twigs with wide piths and thick bark. The agreement between hypothesis and data in structural equation analyses strongly suggests that Corner's rules emerge as the result of selection favouring the avoidance of self-shading in the context of broadly similar rates of carbon fixation per unit crown area across species.

On congruence and incongruence of measures of fit in structural equation modeling.

Guidelines to evaluate the fit of structural equation models can only offer meaningful insights to the extent that they apply equally to a wide range of situations. However, a number of previous studies found that statistical power to reject a misspecified model increases and descriptive fit-indices deteriorate when loadings are high, thereby inappropriately panelizing high reliability indicators. Based on both theoretical considerations and empirical simulation studies, we show that previous results only hold for a particular definition and a particular type of model error. At a constant degree of misspecification (as measured through the minimum of the fit-function), statistical power to reject a wrong model and noncentrality based fit-indices (such as the root-mean squared error of approximation; RMSEA) are independent of loading magnitude. If the degree of model error is controlled through the average residuals, higher loadings are associated with increased statistical power and a higher RMSEA when the measurement model is misspecified, but with decreased power and a lower RMSEA when the structural model is misspecified. In effect, inconsistencies among noncentrality and residual based fit-indices can provide information about possible sources of misfit that would be obscured when considering either measure in isolation. (PsycINFO Database Record

Marketing effectiveness of hotel Twitter accounts: the case of Saudi Arabia

论酒店Twitter营销的有效性：沙特阿拉伯案例分析摘要研究目的本研究旨在于探索酒店消费者对于酒店Twitter营销的态度以及酒店Twitter营销对打造酒店品牌、消费者预订酒店行为、和电子口碑营销的影响。由于Twitter在沙特阿拉伯地区的广泛流行，本研究将沙特阿拉伯为案例进行调研。研究设计/方法/途径本研究在前人建立的社交媒体营销有效性模型的基础上，进行改进创新，并且实地调研了消费者对于酒店Twitter营销账户的态度。本研究采用网上问卷采样的方式，样本经过验证性因子分析法和结构方程模型的分析，来进行模型的测试。研究结果本研究表明，当消费者对于酒店Tweets持有积极态度的时候，他们对于酒店Twitter账户也同样保持积极态度，同时这种积极态度也会增进他们对于酒店品牌的认知，消费者更加愿意预订酒店房间，以及为酒店电子口碑营销。研究原创性/价值本研究结果对于酒店行业中社交媒体的营销有效性的探索有着积极贡献。

Assessing the fit of structural equation models with multiply imputed data.

Multiple imputation has enjoyed widespread use in social science applications, yet the application of imputation-based inference to structural equation modeling has received virtually no attention in the literature. Thus, this study has 2 overarching goals: evaluate the application of Meng and Rubin's (1992) pooling procedure for likelihood ratio statistic to the SEM test of model fit, and explore the possibility of using this test statistic to define imputation-based versions of common fit indices such as the TLI, CFI, and RMSEA. Computer simulation results suggested that, when applied to a correctly specified model, the pooled likelihood ratio statistic performed well as a global test of model fit and was closely calibrated to the corresponding full information maximum likelihood (FIML) test statistic. However, when applied to misspecified models with high rates of missingness (30%-40%), the imputation-based test statistic generally exhibited lower power than that of FIML. Using the pooled test statistic to construct imputation-based versions of the TLI, CFI, and RMSEA worked well and produced indices that were well-calibrated with those of full information maximum likelihood estimation. This article gives Mplus and R code to implement the pooled test statistic, and it offers a number of recommendations for future research. (PsycINFO Database Record

Evaluation of Corrections to the Rescaled Statistic for SEM with Big Data

Trustworthy test statistics are of critical importance for evaluating overall model fit in structural equation modeling (SEM). While the likelihood ratio statistic TML derived from the normality as...

Personal Accomplishment, Resilience, and Perceived Mattering as Inhibitors of Physical Educators’ Perceptions of Marginalization and Isolation

Purpose: This study sought to develop a quantitative understanding of factors that reduce perceived isolation and marginalization among physical educators. A conceptual model for the relationships among study variables was developed. Method: Data were collected through an online survey completed by 419 inservice physical educators (210 females, 209 males, 93.60% Caucasian). Variables included perceived mattering, resilience, personal accomplishment, as well as isolation and marginalization. Primary data analyses included structural equation modeling to test the hypothesized relationships in the conceptual model. Results: The structural equation model fit was good, χ2(315) = 669.38, p < .001, RMSEA = .05 (90% CI = [.05, .06], p = .285), SRMR = .05, NNFI = .93, CFI = .94. After removing non-significant regression pathways, the structural model generally confirmed the study hypotheses. Discussion/Conclusion: Enhancing personal accomplishment and resilience helps to foster perceptions of mattering, which redu...

The Performance of Ten Modified Rescaled Statistics as the Number of Variables Increases

Among test statistics for assessing overall model fit in structural equation modeling (SEM), the Satorra–Bentler rescaled statistic is most widely used when the normality assumption is violated. However, many researchers have found that tends to overreject correct models when the number of variables (p) is large and/or the sample size (N) is small. Modifications of have been proposed, but few studies have examined their performance against each other, especially when p is large. This article systematically evaluates 10 corrected versions of . Results show that the Bartlett correction and a recently proposed rank correction perform better than others in controlling Type I error rates, according to their deviations from the nominal rate. Nevertheless, the performance of both corrections depends heavily on p in addition to N. As p becomes relatively large, none of the corrected versions can properly control Type I errors even when N is rather large.

Assessing Fit in Structural Equation Models: A Monte-Carlo Evaluation of RMSEA Versus SRMR Confidence Intervals and Tests of Close Fit

We compare the accuracy of confidence intervals (CIs) and tests of close fit based on the root mean square error of approximation (RMSEA) with those based on the standardized root mean square residual (SRMR). Investigations used normal and nonnormal data with models ranging from p = 10 to 60 observed variables. CIs and tests of close fit based on the SRMR are generally accurate across all conditions (even at p = 60 with nonnormal data). In contrast, CIs and tests of close fit based on the RMSEA are only accurate in small models. In larger models (p ≥ 30), they incorrectly suggest that models do not fit closely, particularly if sample size is less than 500.

A twin study exploring the association between childhood emotional and behaviour problems and specific psychotic experiences in a community sample of adolescents.

BackgroundChildhood emotional and behaviour problems are antecedents for later psychopathology. This study investigated genetic and environmental influences shaping the longitudinal association between childhood emotional and behaviour problems and specific PEs.MethodIn a community‐based twin sample, parents reported on emotional and behaviour problems when twins were ages 7 and 12 years. At age 16 years, specific PEs were measured using self‐reports and parent reports. Structural equation model‐fitting was conducted.ResultsChildhood emotional and behaviour problems were significantly associated with paranoia, cognitive disorganisation and parent‐rated negative symptoms in adolescence (mean r = .15–.38), and to a lesser extent with hallucinations, grandiosity and anhedonia (mean r = .04‐.12). Genetic influences on childhood emotional and behaviour problems explained significant proportions of variance in adolescent paranoia (4%), cognitive disorganisation (8%) and parent‐rated negative symptoms (3%). Unique environmental influences on childhood emotional and behaviour problems explained ≤1% of variance in PEs. Common environmental influences were only relevant for the relationship between childhood emotional and behaviour problems and parent‐rated negative symptoms (explaining 28% of variance) and are partly due to correlated rater effects.ConclusionsChildhood emotional and behaviour problems are significantly, if weakly, associated with adolescent PEs. These associations are driven in part by common genetic influences underlying both emotional and behaviour problems and PEs. However, psychotic experiences in adolescence are largely influenced by genetic and environmental factors that are independent of general childhood emotional and behaviour problems, suggesting they are not merely an extension of childhood emotional and behaviour problems.

Confidence Intervals of Fit Indexes by Inverting a Bootstrap Test

Fit indexes are an important tool in the evaluation of model fit in structural equation modeling (SEM). Currently, the newest confidence interval (CI) for fit indexes proposed by Zhang and Savalei (2016) is based on the quantiles of a bootstrap sampling distribution at a single level of misspecification. This method, despite a great improvement over naive and model-based bootstrap methods, still suffers from unsatisfactory coverage. In this work, we propose a new method of constructing bootstrap CIs for various fit indexes. This method directly inverts a bootstrap test and produces a CI that involves levels of misspecification that would not be rejected in a bootstrap test. Similar in rationale to a parametric CI of root mean square error of approximation (RMSEA) based on a noncentral χ2 distribution and a profile-likelihood CI of model parameters, this approach is shown to have better performance than the approach of Zhang and Savalei (2016), with more accurate coverage and more efficient widths.

Limitations in the systematic analysis of structural equation model fit indices

Limitations in the systematic analysis of structural equation model fit indices

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

ABSTRACTThe 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.

Development of evaluation index system of reputation for higher medical institutions based on factor analysis method

Objective To develop an evaluation index system of reputation for higher medical institutions and to test its reliability and validity. Methods Using literature method and small-group discussion to collect the evaluation indexes, the data was collected by the questionnaire survey and the 1 493 effective questionnaires were collected with effective recovery rates of 61.90%. And the exploratory and confirmatory factor analysis methods were conducted to develop evaluation index system with using the SPSS 17.0 software for statistics analysis. Results The evaluation index system of reputation for higher medical institutions included six dimensionalities: social responsibility, opinion direction, social image, management quality, emotional attract and environmental facility. The Cronbachs'α coefficients of evaluation index system were greater than 0.7, RMSEA is 0.063<0.08, χ2/df is 3.933<5, therefore, the structural equation model fitting was good and evaluation index system had good validity. Conclusion This article has developed an evaluation index system of reputation for higher medical institutions, which has a good reliability and validity. To test the model’s reliability and validity, the suggestion that the future research will be performed between more other medical universities has been given. Key words: Factor analysis method; Higher medical university; Medical students' perspective; Reputation evaluation; Scale development

Robust estimation in structural equation models using Bregman and other divergences with t-centre approach to estimate the covariance matrix

Structural equation models seek to find causal relationships between latent variables by analysing the mean and the covariance matrix of some observable indicators of the latent variables. Under a multivariate normality assumption on the distribution of the latent variables and of the errors, maximum likelihood estimators are asymptotically efficient. The estimators are significantly influenced by violation of the normality assumption and hence there is a need to robustify the inference procedures. Previous work minimized the von Neuman divergence or its variant the total von Neumann divergence to estimate the parameters, with the minimum covariance determinant used as a robust estimator of the covariance matrix. We extend this approach by considering other divergences and by developing a robust estimate of the covariance matrix. The robust estimator of the covariance matrix developed is a t-centre like estimator based on several minimum covariance determinant estimators ranging from 0% contamination to 50% contamination. The simulation results are promising. The results can be used for robustifying the fit of structural equation models. References K. A. Bollen. Structural equations with latent variables . Wiley, New York, 1989. http://au.wiley.com/WileyCDA/WileyTitle/productCd-0471011711.html R. W. Butler, P. L. Davies and M. Jhun. Asymptotics for the minimum covariance determinant estimator. Ann. Stat. , 21(3):1385–1400, 1993. http://www.jstor.org/stable/2242201 N. J. Higham. Functions of matrices: Theory and computation. SIAM, Philadelphia, 2008. doi:10.1137/1.9780898717778 S. Jayasumana, R. Hartley, M. Salzmann, H. Li and M. Harandi. Kernel methods on the Riemannian manifold of symmetric positive definite matrices. Proc. CVPR IEEE 2013 , 73–80, 2013. doi:10.1109/CVPR.2013.17 S. Penev and T. Prvan. Robust estimation in structural equation models using Bregman divergences. CTAC2012, ANZIAM J. , 54:C574–C589, 2013. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6306 B. C. Vemuri, M. Liu, S.-I. Amari, and F. Nielsen. Total Bregman divergence and its applications to DTI analysis. IEEE T. Med. Imaging. , 30(2):475–483, 2011. doi:10.1109/TMI.2010.2086464 S. Verboven and M. Hubert. LIBRA: a MATLAB library for robust analysis, Chemometr. Intell. Lab. , 75(2):127–136, 2005. doi:10.1016/j.chemolab.2004.06.003

How should the fit of structural equation models be judged? Insights from Monte Carlo simulations

At small sample sizes or when the model is complex, the χ2 test of model fit is known to over-reject correctly specified structural equation models. To counter these limitations, corrections to the...

Validation of the Postgraduate Hospital Educational Environment Measure (PHEEM) in a sample of 731 Greek residents.

BackgroundThe Greek version of the Postgraduate Hospital Educational Environment Measure (PHEEM) was evaluated to determine its psychometric properties, i.e., validity, internal consistency, sensitivity and responsiveness to be used for measuring the learning environment in Greek hospitals. MethodsThe PHEEM was administered to Greek hospital residents. Internal consistency was measured using Cronbach’s alpha. Root Mean Square Error of Approximation (RMSEA) was used to evaluate the fit of Structural Equation Models. Content validity was addressed by the original study. Construct validity was tested using confirmatory (to test the set of underlying dimensions suggested by the original study) and exploratory (to explore the dimensions needed to explain the variability of the given answers) factor analysis using Varimax rotation. Convergent validity was calculated by Pearson’s correlation coefficient regarding the participant’s PHEEM score and participant’s overall satisfaction score of the added item “Overall, I am very satisfied with my specialization in this post”. Sensitivity was checked by comparing good versus poor aspects of the educational environment and by satisfied versus unsatisfied participants.ResultsA total of 731 residents from 83 hospitals and 41 prefectures responded to the PHEEM. The original three-factor model didn’t fit better compared to one factor model that is accounting for 32 % of the variance. Cronbach’s α was 0.933 when assuming one-factor model. Using a three-factor model (autonomy, teaching, social support), Cronbach’s α were 0.815 (expected 0.830), 0.908 (0.839), 0.734 (0.793), respectively. The three-factor model gave an RMSEA value of 0.074 (90 % confidence interval 0.071, 0.076), suggesting a fair fit. Pearson’s correlation coefficient between total PHEEM and global satisfaction was 0.765. Mean question scores ranged from 19.0 (very poor) to 73.7 (very good), and mean participant scores from 5.5 (very unsatisfied) to 96.5 (very satisfied).ConclusionsThe Greek version of PHEEM is a valid, reliable, and sensitive instrument measuring the educational environment among junior doctors in Greek hospitals and it can be used for evidence-based SWOT analysis and policy.

Correcting Too Much or Too Little? The Performance of Three Chi-Square Corrections

This simulation study investigates the performance of three test statistics, T1, T2, and T3, used to evaluate structural equation model fit under non normal data conditions. T1 is the well-known mean-adjusted statistic of Satorra and Bentler. T2 is the mean-and-variance adjusted statistic of Sattertwaithe type where the degrees of freedom is manipulated. T3 is a recently proposed version of T2 that does not manipulate degrees of freedom. Discrepancies between these statistics and their nominal chi-square distribution in terms of errors of Type I and Type II are investigated. All statistics are shown to be sensitive to increasing kurtosis in the data, with Type I error rates often far off the nominal level. Under excess kurtosis true models are generally over-rejected by T1 and under-rejected by T2 and T3, which have similar performance in all conditions. Under misspecification there is a loss of power with increasing kurtosis, especially for T2 and T3. The coefficient of variation of the nonzero eigenvalues of a certain matrix is shown to be a reliable indicator for the adequacy of these statistics.