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Journal Article•DOI•

Structural Equation Modelling: Guidelines for Determining Model Fit

Daire Hooper1, Joseph Coughlan1, Michael R. Mullen2•
Dublin Institute of Technology1, Florida Atlantic University2
01 Sep 2008-The Electronic Journal of Business Research Methods (Academic Conferences and Publishing International (ACPI))-Vol. 6, Iss: 1
TL;DR: In this article, a selection of fit indices that are widely regarded as the most informative indices available to researchers is presented, along with guidelines on their use and strategies for their use.
Abstract: The following paper presents current thinking and research on fit indices for structural equation modelling. The paper presents a selection of fit indices that are widely regarded as the most informative indices available to researchers. As well as outlining each of these indices, guidelines are presented on their use. The paper also provides reporting strategies of these indices and concludes with a discussion on the future of fit indices.

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Citations
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Development and Validation of A

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Lao Juan, Kyu-Jin Yoon, Young-Bae Park, Young-Jae Park, Min-Yong Kim 
01 Jan 2015
TL;DR: The results suggest that the LJQ is a reliable and valid instrument for evaluating LJ.
Abstract: Objectives: Lao Juan (LJ, 劳倦) is a syndrome described in Chinese medicine (CM) that manifests with : Lao Juan (LJ, 劳倦) is a syndrome described in Chinese medicine (CM) that manifests with fatigue, fever, spontaneous sweating, indigestion, work-induced pain, weakness of the limbs, and shortness of breath. fatigue, fever, spontaneous sweating, indigestion, work-induced pain, weakness of the limbs, and shortness of breath. The present study was conducted to examine the reliability and validity of a Lao Juan Questionnaire (LJQ). The present study was conducted to examine the reliability and validity of a Lao Juan Questionnaire (LJQ). Methods: A total of 151 outpatients and 73 normal subjects were asked to complete the LJQ. Seventy-three normal subjects A total of 151 outpatients and 73 normal subjects were asked to complete the LJQ. Seventy-three normal subjects were additionally asked to complete the Chalder Fatigue Scale (CFS). Twelve clinicians determined whether the were additionally asked to complete the Chalder Fatigue Scale (CFS). Twelve clinicians determined whether the 151 outpatients exhibited LJ or not. The internal consistency and construct validity for the LJQ were estimated using 151 outpatients exhibited LJ or not. The internal consistency and construct validity for the LJQ were estimated using data from the outpatient subjects. The CFS data were used to examine the concurrent validity of the LJQ. Total LJQ data from the outpatient subjects. The CFS data were used to examine the concurrent validity of the LJQ. Total LJQ scores and the clinicians' diagnoses of the outpatients were used to perform receiver operating characteristics (ROC) scores and the clinicians' diagnoses of the outpatients were used to perform receiver operating characteristics (ROC) curve analyses and to defi ne an optimum cut-off score for the LJQ. curve analyses and to defi ne an optimum cut-off score for the LJQ. Results: The 19-item LJQ had satisfactory internal : The 19-item LJQ had satisfactory internal consistency (α=0.828) and concurrent validity, with signifi cant correlations between the LJQ and the CFS subscales. consistency (α=0.828) and concurrent validity, with signifi cant correlations between the LJQ and the CFS subscales. In the test of construct validity using principal component analysis, a total of six factors were extracted, and the overall In the test of construct validity using principal component analysis, a total of six factors were extracted, and the overall variance explained by all factors was 59.5%. In ROC curve analyses, the sensitivity, specifi city, and area under the variance explained by all factors was 59.5%. In ROC curve analyses, the sensitivity, specifi city, and area under the curve were 76.0%, 59.2%, and 0.709, respectively. The optimum cut-off score was defi ned as six points. curve were 76.0%, 59.2%, and 0.709, respectively. The optimum cut-off score was defi ned as six points. Conclusions: Our results suggest that the LJQ is a reliable and valid instrument for evaluating LJ. Our results suggest that the LJQ is a reliable and valid instrument for evaluating LJ. KEYWORDS Chinese medicine, chronic fatigue syndrome, Chinese medicine-pattern Chinese medicine, chronic fatigue syndrome, Chinese medicine-pattern

3,787 citations

Journal Article•DOI•
Choosing and using diversity indices: Insights for ecological applications from the German Biodiversity Exploratories

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E. Kathryn Morris1, E. Kathryn Morris2, Tancredi Caruso3, François Buscot4, François Buscot5, Markus Fischer6, Christine Hancock7, Tanja S. Maier8, Torsten Meiners1, Caroline Müller8, Elisabeth Obermaier7, Daniel Prati6, Stephanie A. Socher6, Ilja Sonnemann1, Nicole Wäschke1, Tesfaye Wubet4, Susanne Wurst1, Matthias C. Rillig1 •
Free University of Berlin1, Xavier University2, Queen's University Belfast3, Helmholtz Centre for Environmental Research - UFZ4, Leipzig University5, University of Bern6, University of Würzburg7, Bielefeld University8
01 Sep 2014-Ecology and Evolution
TL;DR: This work used path analysis to determine whether compound indices detected more relationships between diversities of different organisms and traits than more basic indices, and demonstrated that while common diversity indices may appear interchangeable in simple analyses, when considering complex interactions, the choice of index can profoundly alter the interpretation of results.
Abstract: Biodiversity, a multidimensional property of natural systems, is difficult to quantify partly because of the multitude of indices proposed for this purpose. Indices aim to describe general properties of communities that allow us to compare different regions, taxa, and trophic levels. Therefore, they are of fundamental importance for environmental monitoring and conservation, although there is no consensus about which indices are more appropriate and informative. We tested several common diversity indices in a range of simple to complex statistical analyses in order to determine whether some were better suited for certain analyses than others. We used data collected around the focal plant Plantago lanceolata on 60 temperate grassland plots embedded in an agricultural landscape to explore relationships between the common diversity indices of species richness (S), Shannon's diversity (H'), Simpson's diversity (D-1), Simpson's dominance (D-2), Simpson's evenness (E), and Berger-Parker dominance (BP). We calculated each of these indices for herbaceous plants, arbuscular mycorrhizal fungi, aboveground arthropods, belowground insect larvae, and P.lanceolata molecular and chemical diversity. Including these trait-based measures of diversity allowed us to test whether or not they behaved similarly to the better studied species diversity. We used path analysis to determine whether compound indices detected more relationships between diversities of different organisms and traits than more basic indices. In the path models, more paths were significant when using H', even though all models except that with E were equally reliable. This demonstrates that while common diversity indices may appear interchangeable in simple analyses, when considering complex interactions, the choice of index can profoundly alter the interpretation of results. Data mining in order to identify the index producing the most significant results should be avoided, but simultaneously considering analyses using multiple indices can provide greater insight into the interactions in a system.

712 citations

Cites background or methods from "Structural Equation Modelling: Guid..."

  • ...As chi-square can be influenced by sample size, we also report the root mean square error of approximation (RMSEA), where smaller values indicate more parsimonious models, and values <0.07 suggest an adequate model fit (Hooper et al. 2008)....

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  • ...The Tucker Lewis Non-Normed Fit Index (TLNNFI) is less sensitive to sample size and accounts for model parsimony, with values close to one indicating good model fit (Hooper et al. 2008)....

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  • ...We ran the same structural model with each of the diversity indices, and we report model fit as chi-square and its associated P-value, with P-values greater than 0.05 indicating an acceptable fit (Hooper et al. 2008)....

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Journal Article•DOI•
The Multidimensional Assessment of Interoceptive Awareness (MAIA).

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Wolf E. Mehling1, Cynthia J. Price2, Jennifer Daubenmier1, M Acree1, Elizabeth Bartmess1, Anita L. Stewart1 •
University of California, San Francisco1, University of Washington2
01 Nov 2012-PLOS ONE
TL;DR: The systematic mixed-methods process involved reviewing the current literature, specifying a multidimensional conceptual framework, evaluating prior instruments, developing items, and analyzing focus group responses to scale items by instructors and patients of body awareness-enhancing therapies.
Abstract: This paper describes the development of a multidimensional self-report measure of interoceptive body awareness. The systematic mixed-methods process involved reviewing the current literature, specifying a multidimensional conceptual framework, evaluating prior instruments, developing items, and analyzing focus group responses to scale items by instructors and patients of body awareness-enhancing therapies. Following refinement by cognitive testing, items were field-tested in students and instructors of mind-body approaches. Final item selection was achieved by submitting the field test data to an iterative process using multiple validation methods, including exploratory cluster and confirmatory factor analyses, comparison between known groups, and correlations with established measures of related constructs. The resulting 32-item multidimensional instrument assesses eight concepts. The psychometric properties of these final scales suggest that the Multidimensional Assessment of Interoceptive Awareness (MAIA) may serve as a starting point for research and further collaborative refinement.

705 citations

Cites methods from "Structural Equation Modelling: Guid..."

  • ...Following conventional guidelines [91], we required at least two [92] of the following fit indices to fall in the desired range: CFI $....

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Journal Article•DOI•
Why Students Choose STEM Majors Motivation, High School Learning, and Postsecondary Context of Support

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Xueli Wang1•
University of Wisconsin-Madison1
01 Oct 2013-American Educational Research Journal
TL;DR: In this article, a conceptual framework for understanding the entrance into science, technology, engineering, and mathematics (STEM) majors by recent high school graduates attending 4-year institutions was proposed.
Abstract: This study draws upon social cognitive career theory and higher education literature to test a conceptual framework for understanding the entrance into science, technology, engineering, and mathematics (STEM) majors by recent high school graduates attending 4-year institutions. Results suggest that choosing a STEM major is directly influenced by intent to major in STEM, high school math achievement, and initial postsecondary experiences, such as academic interaction and financial aid receipt. Exerting the largest impact on STEM entrance, intent to major in STEM is directly affected by 12th-grade math achievement, exposure to math and science courses, and math self-efficacy beliefs—all three subject to the influence of early achievement in and attitudes toward math. Multiple-group structural equation modeling analyses indicated heterogeneous effects of math achievement and exposure to math and science across racial groups, with their positive impact on STEM intent accruing most to White students and least ...

643 citations

Journal Article•DOI•
Evaluating E-learning systems success : an empirical study

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Dimah Al-Fraihat1, Mike Joy1, Ra’ed Masa’deh1, Jane Sinclair1•
University of Warwick1
01 Jan 2020-Computers in Human Behavior
TL;DR: A comprehensive model has been developed which provides a holistic picture and identifies different levels of success related to a broad range of success determinants and was found to be the determinants of e-learning use.

484 citations

References
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Journal Article•DOI•
Cutoff criteria for fit indexes in covariance structure analysis : Conventional criteria versus new alternatives

[...]

Li-tze Hu, Peter M. Bentler1•
University of California, Los Angeles1
01 Jan 1999-Structural Equation Modeling
TL;DR: In this article, the adequacy of the conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice were examined, and the results suggest that, for the ML method, a cutoff value close to.95 for TLI, BL89, CFI, RNI, and G...
Abstract: This article examines the adequacy of the “rules of thumb” conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice. Using a 2‐index presentation strategy, which includes using the maximum likelihood (ML)‐based standardized root mean squared residual (SRMR) and supplementing it with either Tucker‐Lewis Index (TLI), Bollen's (1989) Fit Index (BL89), Relative Noncentrality Index (RNI), Comparative Fit Index (CFI), Gamma Hat, McDonald's Centrality Index (Mc), or root mean squared error of approximation (RMSEA), various combinations of cutoff values from selected ranges of cutoff criteria for the ML‐based SRMR and a given supplemental fit index were used to calculate rejection rates for various types of true‐population and misspecified models; that is, models with misspecified factor covariance(s) and models with misspecified factor loading(s). The results suggest that, for the ML method, a cutoff value close to .95 for TLI, BL89, CFI, RNI, and G...

76,383 citations

"Structural Equation Modelling: Guid..." refers background or methods in this paper

  • ...From this, a value of CFI ≥ 0.95 is presently recognised as indicative of good fit (Hu and Bentler, 1999)....

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  • ...The Chi-Square value is the traditional measure for evaluating overall model fit and, ‘assesses the magnitude of discrepancy between the sample and fitted covariances matrices’ (Hu and Bentler, 1999: 2)....

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  • ...Threshold levels were recently assessed by Hu and Bentler (1999) who suggested a two-index presentation format....

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  • ...However, more recently, a cut-off value close to .06 (Hu and Bentler, 1999) or a stringent upper limit of 0.07 (Steiger, 2007) seems to be the general consensus amongst authorities in this area....

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  • ...A cut-off criterion of CFI ≥ 0.90 was initially advanced however, recent studies have shown that a value greater than 0.90 is needed in order to ensure that misspecified models are not accepted (Hu and Bentler, 1999)....

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Journal Article•DOI•
A new look at the statistical model identification

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Hirotugu Akaike
01 Dec 1974-IEEE Transactions on Automatic Control
TL;DR: In this article, a new estimate minimum information theoretical criterion estimate (MAICE) is introduced for the purpose of statistical identification, which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure.
Abstract: The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.

47,133 citations

"Structural Equation Modelling: Guid..." refers background in this paper

  • ...Probably the best known of these indices is the Akaike Information Criterion (AIC) or the Consistent Version of AIC (CAIC) which adjusts for sample size (Akaike, 1974)....

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Book•
Principles and Practice of Structural Equation Modeling

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Rex B. Kline1•
Concordia University Wisconsin1
27 May 1998
TL;DR: The book aims to provide the skills necessary to begin to use SEM in research and to interpret and critique the use of method by others.
Abstract: Designed for students and researchers without an extensive quantitative background, this book offers an informative guide to the application, interpretation and pitfalls of structural equation modelling (SEM) in the social sciences. The book covers introductory techniques including path analysis and confirmatory factor analysis, and provides an overview of more advanced methods such as the evaluation of non-linear effects, the analysis of means in convariance structure models, and latent growth models for longitudinal data. Providing examples from various disciplines to illustrate all aspects of SEM, the book offers clear instructions on the preparation and screening of data, common mistakes to avoid and widely used software programs (Amos, EQS and LISREL). The book aims to provide the skills necessary to begin to use SEM in research and to interpret and critique the use of method by others.

42,102 citations

Journal Article•DOI•
Comparative fit indexes in structural models

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Peter M. Bentler1•
University of California, Los Angeles1
01 Mar 1990-Psychological Bulletin
TL;DR: A new coefficient is proposed to summarize the relative reduction in the noncentrality parameters of two nested models and two estimators of the coefficient yield new normed (CFI) and nonnormed (FI) fit indexes.
Abstract: Normed and nonnormed fit indexes are frequently used as adjuncts to chi-square statistics for evaluating the fit of a structural model A drawback of existing indexes is that they estimate no known population parameters A new coefficient is proposed to summarize the relative reduction in the noncentrality parameters of two nested models Two estimators of the coefficient yield new normed (CFI) and nonnormed (FI) fit indexes CFI avoids the underestimation of fit often noted in small samples for Bentler and Bonett's (1980) normed fit index (NFI) FI is a linear function of Bentler and Bonett's non-normed fit index (NNFI) that avoids the extreme underestimation and overestimation often found in NNFI Asymptotically, CFI, FI, NFI, and a new index developed by Bollen are equivalent measures of comparative fit, whereas NNFI measures relative fit by comparing noncentrality per degree of freedom All of the indexes are generalized to permit use of Wald and Lagrange multiplier statistics An example illustrates the behavior of these indexes under conditions of correct specification and misspecification The new fit indexes perform very well at all sample sizes

21,588 citations

"Structural Equation Modelling: Guid..." refers background or methods or result in this paper

  • ...This index was first introduced by Bentler (1990) and subsequently included as part of the fit indices in his EQS program (Kline, 2005)....

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  • ...The Comparative Fit Index (CFI: Bentler, 1990) is a revised form of the NFI which takes into account sample size (Byrne, 1998) that performs well even when sample size is small (Tabachnick and Fidell, 2007)....

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  • ...However in situations were small samples are used, the value of the NNFI can indicate poor fit despite other statistics pointing towards good fit (Bentler, 1990; Kline, 2005; Tabachnick and Fidell, 2007)....

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  • ...A major drawback to this index is that it is sensitive to sample size, underestimating fit for samples less than 200 (Mulaik et al, 1989; Bentler, 1990), and is thus not recommended to be solely relied on (Kline, 2005)....

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Using multivariate statistics, 5th ed.

[...]

Barbara G. Tabachnick1, Linda S. Fidell1•
California State University, Northridge1
01 Jan 2007

18,170 citations

"Structural Equation Modelling: Guid..." refers background or methods or result in this paper

  • ...Related to the GFI is the AGFI which adjusts the GFI based upon degrees of freedom, with more saturated models reducing fit (Tabachnick and Fidell, 2007)....

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  • ...However in situations were small samples are used, the value of the NNFI can indicate poor fit despite other statistics pointing towards good fit (Bentler, 1990; Kline, 2005; Tabachnick and Fidell, 2007)....

    [...]

  • ...The Comparative Fit Index (CFI: Bentler, 1990) is a revised form of the NFI which takes into account sample size (Byrne, 1998) that performs well even when sample size is small (Tabachnick and Fidell, 2007)....

    [...]

  • ...The Goodness-of-Fit statistic (GFI) was created by Jöreskog and Sorbom as an alternative to the Chi-Square test and calculates the proportion of variance that is accounted for by the estimated population covariance (Tabachnick and Fidell, 2007)....

    [...]

  • ...Although there is no consensus regarding an acceptable ratio for this statistic, recommendations range from as high as 5.0 (Wheaton et al, 1977) to as low as 2.0 (Tabachnick and Fidell, 2007)....

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Related Papers (5)
Cutoff criteria for fit indexes in covariance structure analysis : Conventional criteria versus new alternatives

[...]

01 Jan 1999-Structural Equation Modeling
Li-tze Hu, Peter M. Bentler
Principles and Practice of Structural Equation Modeling

[...]

27 May 1998
Rex B. Kline
Evaluating Structural Equation Models with Unobservable Variables and Measurement Error

[...]

01 Feb 1981-Journal of Marketing Research
Claes Fornell, David F. Larcker
Using multivariate statistics

[...]

01 Jan 1983
Barbara G. Tabachnick, Linda S. Fidell
Multivariate Data Analysis

[...]

01 Jan 1973
Joseph F. Hair