40 results on '"Yuan Ke"'
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2. Testing structural equation model fit in psychological studies: A replication study using equivalence testing
- Author
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Marcoulides, Katerina M. and Yuan, Ke-Hai
- Published
- 2024
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- View/download PDF
3. Scale-Invariance, Equivariance and Dependency of Structural Equation Models.
- Author
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Yuan, Ke-Hai, Ling, Ling, and Zhang, Zhiyong
- Subjects
- *
STRUCTURAL equation modeling , *MEASUREMENT errors , *DATA analysis , *BEHAVIORAL sciences , *STANDARDIZATION - Abstract
Data in social and behavioral sciences typically contain measurement errors and do not have predefined metrics. Structural equation modeling (SEM) is widely used for the analysis of such data, where the scales of the manifest and latent variables are often subjective. This article studies how the model, parameter estimates, their standard errors (SEs), and the corresponding z-statistics are affected by the scales of the manifest and latent variables. Analytical and empirical results show that (1) the normal-distribution-based likelihood ratio statistic is scale-invariant with respect to scale changes of manifest and latent variables as well as to anchor change of latent variables; (2) the normal-distribution-based maximum likelihood (NML) parameter estimates are scale-equivariant with respect to scale-change of manifest and latent variables as well as to anchor change of latent variables; (3) standard errors (SEs) following the NML method are parallel-scale-equivariant with respect to scale changes of the manifest and latent variables; and (4) the z-statistics are scale-invariant with respect to scale changes of the manifest and latent variables. However, only (1) and (2) hold if latent variables are rescaled by changing anchors. Nevertheless, parameters that are not directly related to latent variables with changing anchors are still scale-equivariant and their z-statistics are still scale-invariant. The results are expected to advance understanding of SEM analysis, and also facilitate result interpretation and comparison across studies as in meta analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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- View/download PDF
4. Replies to comments on "Which method delivers greater signal‐to‐noise ratio: Structural equation modelling or regression analysis with weighted composites?" by Yuan and Fang (2023).
- Author
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Yuan, Ke‐Hai and Fang, Yongfei
- Subjects
- *
STRUCTURAL equation modeling , *REGRESSION analysis , *SIGNAL-to-noise ratio , *ERRORS-in-variables models , *LATENT variables , *PATH analysis (Statistics) , *SAMPLING errors - Abstract
When the indicators of the HT ht do not have predefined metrics, we can rewrite equation (8) as 9 HT ht where the HT ht are arbitrary positive numbers. [Extracted from the article]
- Published
- 2023
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- View/download PDF
5. Which method delivers greater signal‐to‐noise ratio: Structural equation modelling or regression analysis with weighted composites?
- Author
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Yuan, Ke‐Hai and Fang, Yongfei
- Subjects
- *
STRUCTURAL equation modeling , *REGRESSION analysis , *ERRORS-in-variables models , *SIGNAL-to-noise ratio , *LEAST squares , *MAXIMUM likelihood statistics - Abstract
Observational data typically contain measurement errors. Covariance‐based structural equation modelling (CB‐SEM) is capable of modelling measurement errors and yields consistent parameter estimates. In contrast, methods of regression analysis using weighted composites as well as a partial least squares approach to SEM facilitate the prediction and diagnosis of individuals/participants. But regression analysis with weighted composites has been known to yield attenuated regression coefficients when predictors contain errors. Contrary to the common belief that CB‐SEM is the preferred method for the analysis of observational data, this article shows that regression analysis via weighted composites yields parameter estimates with much smaller standard errors, and thus corresponds to greater values of the signal‐to‐noise ratio (SNR). In particular, the SNR for the regression coefficient via the least squares (LS) method with equally weighted composites is mathematically greater than that by CB‐SEM if the items for each factor are parallel, even when the SEM model is correctly specified and estimated by an efficient method. Analytical, numerical and empirical results also show that LS regression using weighted composites performs as well as or better than the normal maximum likelihood method for CB‐SEM under many conditions even when the population distribution is multivariate normal. Results also show that the LS regression coefficients become more efficient when considering the sampling errors in the weights of composites than those that are conditional on weights. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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6. Bartlett Factor Scores: General Formulas and Applications to Structural Equation Models
- Author
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Yung, Yiu-Fai, Yuan, Ke-Hai, Millsap, Roger E., editor, van der Ark, L. Andries, editor, Bolt, Daniel M., editor, and Woods, Carol M., editor
- Published
- 2013
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7. Comments on the article "Marketing or methodology? Exposing the fallacies of PLS with simple demonstrations" and PLS-SEM in general.
- Author
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Yuan, Ke-Hai
- Subjects
FALSE positive error ,STRUCTURAL equation modeling ,REGRESSION analysis ,MODEL validation - Abstract
Purpose: The purpose of this paper is to discuss the pros and cons of partial least squares approach to structural equation modeling (PLS-SEM). The topics include bias, consistency, maximization of R
2 , reliability and model validation. Design/methodology/approach: The approach in this study is descriptive, and the method consists of logical arguments and analysis that are supported by results in references. Findings: Several optimal properties of the PLS-SEM methodology are clarified. A proposal for transforming PLS-SEM mode A to mode B is highlighted, and the transformed mode possesses the desired properties of both modes A and B. Issues with the application of regression analysis using composite scores are also discussed. The strength of PLS-SEM is also compared against that of covariance-based SEM. Research limitations/implications: Additional studies on PLS-SEM are needed when the population structure contains cross-loadings and/or correlated errors. Practical implications: PLS-SEM may have inflated type I errors and R2 values even with normally distributed data. Originality/value: The content of this paper is new, and there does not exist such an in-depth discussion of the pros and cons of PLS-SEM methodology in the literature. [ABSTRACT FROM AUTHOR]- Published
- 2023
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8. Which method is more powerful in testing the relationship of theoretical constructs? A meta comparison of structural equation modeling and path analysis with weighted composites.
- Author
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Deng, Lifang and Yuan, Ke-Hai
- Subjects
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STRUCTURAL equation modeling , *PATH analysis (Statistics) , *STATISTICAL hypothesis testing , *MEASUREMENT errors , *PARAMETERS (Statistics) - Abstract
Structural equation modeling (SEM) has been deemed as a proper method when variables contain measurement errors. In contrast, path analysis with composite scores is preferred for prediction and diagnosis of individuals. While path analysis with composite scores has been criticized for yielding biased parameter estimates, recent literature pointed out that the population values of parameters in a latent-variable model depend on artificially assigned scales. Consequently, bias in parameter estimates is not a well-grounded concept for models involving latent constructs. This article compares path analysis with composite scores against SEM with respect to effect size and statistical power in testing the significance of the path coefficients, via the z- or t-statistics. The data come from many sources with various models that are substantively determined. Results show that SEM is not as powerful as path analysis even with equally weighted composites. However, path analysis with Bartlett-factor scores and the partial least-squares approach to SEM perform the best with respect to effect size and power. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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9. An Open-source WYSIWYG Web Application for Drawing Path Diagrams of Structural Equation Models.
- Author
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Mai, Yujiao, Xu, Ziqian, Zhang, Zhiyong, and Yuan, Ke-Hai
- Subjects
WEB-based user interfaces ,WEB browsers - Abstract
Structural equation modeling (SEM) is widely used in behavioral, social, and education research. Drawing publication-ready path diagrams for SEM is not a pleasant task with the existing software. The article introduces an open-source web-based graphical application, semdiag, for drawing WYSIWYG SEM path diagrams interactively. The application is an on-going project developed by the authors using JavaScript, and it can be used in major web browsers, both online and offline. Several examples are provided to demonstrate how to use the application. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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10. Sensitivity Analysis of the Weights of the Composites Under Partial Least-Squares Approach to Structural Equation Modeling.
- Author
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Yuan, Ke-Hai, Wen, Yong, and Tang, Jiashan
- Subjects
- *
STRUCTURAL equation modeling , *SENSITIVITY analysis , *STRUCTURAL models , *PARTIAL least squares regression , *PATH analysis (Statistics) - Abstract
Structural equation modeling (SEM) and path analysis using composite-scores are distinct classes of methods for modeling the relationship of theoretical constructs. The two classes of methods are integrated in the partial-least-squares approach to structural equation modeling (PLS-SEM), which systematically generates weighted composites and uses them to conduct path analysis of the structural model via the least-squares method. However, the goodness of PLS-SEM depends on the statistical properties of the composites, which are further determined by the formulations of the weights. This article studies how the formulations of PLS-SEM composites are affected by model specification, with focus on the sensitivity of the weights to common specification errors. Results indicate that the weights under PLS-SEM mode A are not affected by within-block error-covariances but those under mode B are. While between-block error-covariances and cross-loadings only affect the weights of the involved items under both PLS-SEM modes A and B, the weights under mode B are much more sensitive than those under mode A. In contrast, the weights under a recently proposed transformed mode (denoted as B A ) are a compromise between those of modes A and B. The findings not only advance the understanding of the PLS-SEM methodology but also facilitate model diagnostics. Empirical applications of the results are illustrated via the analysis of a real dataset. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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11. A Reply to "Structural Parameters under Partial Least Squares and Covariance-based Structural Equation Modeling: A Comment on Yuan and Deng (2021)" by Schuberth, Rosseel, Rönkkö, Trichera, Kline, and Henseler (2023).
- Author
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Yuan, Ke-Hai and Deng, Lifang
- Subjects
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STRUCTURAL equation modeling , *PARTIAL least squares regression - Abstract
This is a follow-up reply to "Structural parameters under partial least squares and covariance-based structural equation modeling: A comment on Yuan and Deng (2021)" by Schuberth et al. (2023). In this reply, explanations are provided on why the messages in the comment article are mostly from a lack of a coherent understanding of the results in Yuan and Deng (2021, YD21). Implications of the results in YD21 are explicated to facilitate proper comparison between covariance-based structural equation modeling (SEM) and partial least-squares SEM. The meaning of bias and mean-squared errors for parameter estimates is also elaborated for models involving latent variables that have no predefined scales. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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12. Equivalence of Partial-Least-Squares SEM and the Methods of Factor-Score Regression.
- Author
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Yuan, Ke-Hai and Deng, Lifang
- Subjects
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PARTIAL least squares regression , *STRUCTURAL equation modeling , *LATENT variables , *REGRESSION analysis - Abstract
Partial-least-squares approach to structural equation modeling (PLS-SEM) uses proxies of latent variables to conduct regression analysis, which directly addresses the needs of prediction and classification. Regression analysis using factor-scores has the same capacity but different factor scores have been noted with different properties. This article shows that different combinations of Bartlett- and regression-factor-scores are statistically equivalent in regression analysis for the purpose of prediction and parameter testing, and PLS-SEM mode B is equivalent to regression analysis using factor-scores when the model is correctly specified. Because proxies under PLS-SEM mode B enjoy the property of maximum reliability as that of factor-scores and PLS-SEM mode A enjoy numerical stability, a structure-based transformation from mode A to mode B is proposed. This transformation is expected to perform well for PLS-SEM in practice as long as the model has a relatively good fit to the data. Following the equivalence between factor-score regression and mode B of PLS-SEM, this article further proposes to use the maximum reliability coefficient as a formal measure for the goodness of PLS-SEM mode B and another consistent reliability coefficient for the goodness of mode A. The equivalence between PLS-SEM and the method of factor-score regression is examined via the analysis of a real dataset. A robust transformation technique is also introduced and illustrated for conducting empirical data analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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13. Which Method is More Reliable in Performing Model Modification: Lasso Regularization or Lagrange Multiplier Test?
- Author
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Yuan, Ke-Hai and Liu, Fang
- Subjects
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LAGRANGE multiplier , *STRUCTURAL equation modeling , *STATISTICAL learning , *ABSOLUTE value , *FALSE positive error - Abstract
Data-driven model modification plays an important role for a statistical methodology to advance the understanding of subjective matters. However, when the sample size is not sufficiently large model modification using the Lagrange multiplier (LM) test has been found not performing well due to capitalization on chance. With the recent development of lasso regression in statistical learning, lasso regularization for structural equation modeling (SEM) may seem to be a method that could avoid capitalizing on chance in finding an adequate model. But there is little evidence validating the goodness of lasso SEM. The purpose of this article is to examine the performance of lasso SEM by comparing it against the LM test, aiming to answer the following five questions: (1) Can we trust the results of lasso SEM for model modification? (2) Does the performance of lasso SEM depend more on the effect size or the absolute value of the parameter? (3) Does lasso SEM perform better than the widely used LM test for model modification? (4) Are lasso SEM and LM test affected by nonnormally distributed data in practice? and (5) Do lasso SEM and LM test perform better with robustly transformed data? By addressing these questions with real data, results indicate that lasso SEM is unable to deliver the expected promises, and it does not perform better than the LM test. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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14. Using Equivalence Testing to Evaluate Goodness of Fit in Multilevel Structural Equation Models.
- Author
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Marcoulides, Katerina M. and Yuan, Ke-Hai
- Subjects
- *
GOODNESS-of-fit tests , *STRUCTURAL equation modeling , *INTRACLASS correlation , *PROBLEM solving , *MATHEMATICAL models - Abstract
Multilevel structural equation models (MSEM) are typically evaluated on the basis of goodness of fit indices. A problem with these indices is that they pertain to the entire model, reflecting simultaneously the degree of fit for all levels in the model. Consequently, in cases that lack model fit, it is unclear which level model is misspecified. Although some researchers have suggested that model fit be assessed separately at all levels, this is not always ideal as it depends on the choice of fit indices, cutoff points, and magnitude of the intraclass correlation. Equivalence testing has recently been recommended as a superior way to evaluate the goodness of fit of models. The approach has also been heralded as a way to advance the inferential nature of structural equation modeling as a confirmatory tool. The purpose of this paper is to illustrate the use of equivalence testing for assessing multilevel model fit in educational research. Although the described procedures can be easily generalized to models with more than two levels, for simplicity we explicitly consider only two-level models. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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15. Mean and Variance Corrected Test Statistics for Structural Equation Modeling with Many Variables.
- Author
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Tian, Yubin and Yuan, Ke-Hai
- Subjects
- *
STRUCTURAL equation modeling , *STATISTICS , *VARIANCES , *SOCIOBIOLOGY , *ROBUST statistics , *LIKELIHOOD ratio tests - Abstract
Data in social and behavioral sciences are routinely collected using questionnaires, and each domain of interest is tapped by multiple indicators. Structural equation modeling (SEM) is one of the most widely used methods to analyze such data. However, conventional methods for SEM face difficulty when the number of variables ( p) is large even when the sample size ( N) is also rather large. This article addresses the issue of model inference with the likelihood ratio statistic T m l . Using the method of empirical modeling, mean-and-variance corrected statistics for SEM with many variables are developed. Results show that the new statistics not only perform much better than T m l but also are substantial improvements over other corrections to T m l . When combined with a robust transformation, the new statistics also perform well with non-normally distributed data. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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16. What Causes the Mean Bias of the Likelihood Ratio Statistic with Many Variables?
- Author
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Yuan, Ke-Hai, Fan, Chao, and Zhao, Yanyun
- Subjects
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FALSE positive error , *CHI-square distribution , *MONTE Carlo method , *STRUCTURAL equation modeling - Abstract
Survey data often contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. However, conventional SEM methods are not crafted to handle data with a large number of variables (p). A large p can cause Tml, the most widely used likelihood ratio statistic, to depart drastically from the assumed chi-square distribution even with normally distributed data and a relatively large sample size N. A key element affecting this behavior of Tml is its mean bias. The focus of this article is to determine the cause of the bias. To this end, empirical means of Tml via Monte Carlo simulation are used to obtain the empirical bias. The most effective predictors of the mean bias are subsequently identified and their predictive utility examined. The results are further used to predict type I errors of Tml. The article also illustrates how to use the obtained results to determine the required sample size for Tml to behave reasonably well. A real data example is presented to show the effect of the mean bias on model inference as well as how to correct the bias in practice. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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17. New Effect Size Measures for Structural Equation Modeling.
- Author
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Gomer, Brenna, Yuan, Ke-Hai, and Jiang, Ge
- Subjects
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EFFECT sizes (Statistics) , *STRUCTURAL equation modeling - Abstract
Effect size is crucial for quantifying differences and a key concept behind Type I errors and power, but measures of effect size are seldom studied in structural equation modeling (SEM). While fit indices such as the root mean square error of approximation may address the severity of model misspecification, they are not a direct generalization of commonly used effect size measures such as Cohen's d. Moreover, with violations of normality and when a test statistic does not follow a noncentral chi-square distribution, measures of misfit that are defined through the assumed distribution of the test statistic are no longer valid. In this study, two new classes of effect size measures for SEM are developed by generalizing Cohen's d. The first class consists of definitions that are theoretically equivalent to , the population counterpart of the normal-distribution-based discrepancy function. The second class of effect size measures bears a stricter resemblance to Cohen's d in its original form. Several versions of these generalizations are investigated to identify the one that is least affected by sample size and population distribution but most sensitive to model misspecification. Their performances under violated distributional assumptions, severity of model misspecification, and various sample sizes are examined using both normal maximum likelihood estimation and robust M-estimation. Monte Carlo results indicate that one measure in the first class of effect size measures is little affected by sample size and distribution while preserving sensitivity to model misspecification and thus is recommended for researchers to report in publications. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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18. Optimizing Ridge Generalized Least Squares for Structural Equation Modeling.
- Author
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Yang, Miao and Yuan, Ke-Hai
- Subjects
- *
PARAMETER estimation , *LEAST squares , *STRUCTURAL equation modeling - Abstract
Ridge generalized least squares (RGLS) is a recently proposed estimation procedure for structural equation modeling. In the formulation of RGLS, there is a key element, ridge tuning parameter, whose value determines the efficiency of parameter estimates. This article aims to optimize RGLS by developing formulas for the ridge tuning parameter to yield the most efficient parameter estimates in practice. For the formulas to have a wide scope of applicability, they are calibrated using empirical efficiency and via many conditions on population distribution, sample size, number of variables, and model structure. Results show that RGLS with the tuning parameter determined by the formulas can substantially improve the efficiency of parameter estimates over commonly used procedures with real data being typically nonnormally distributed. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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19. The Performance of Ten Modified Rescaled Statistics as the Number of Variables Increases.
- Author
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Yang, Miao, Jiang, Ge, and Yuan, Ke-Hai
- Subjects
STRUCTURAL equation modeling ,SAMPLE size (Statistics) - Abstract
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 ofhave 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 toN . Asp becomes relatively large, none of the corrected versions can properly control Type I errors even whenN is rather large. [ABSTRACT FROM AUTHOR]- Published
- 2018
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20. Empirically Corrected Rescaled Statistics for SEM with Small N and Large p.
- Author
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Yuan, Ke-Hai, Yang, Miao, and Jiang, Ge
- Subjects
- *
STRUCTURAL equation modeling , *DATA analysis , *STATISTICAL accuracy - Abstract
Survey data often contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. With typical nonnormally distributed data in practice, a rescaled statisticTrmlproposed by Satorra and Bentler was recommended in the literature of SEM. However,Trmlhas been shown to be problematic when the sample sizeNis small and/or the number of variablespis large. There does not exist a reliable test statistic for SEM with smallNor largep, especially with nonnormally distributed data. Following the principle of Bartlett correction, this article develops empirical corrections toTrmlso that the mean of the empirically corrected statistics approximately equals the degrees of freedom of the nominal chi-square distribution. Results show that empirically corrected statistics control type I errors reasonably well even whenNis smaller than 2p, whereTrmlmay reject the correct model 100% even for normally distributed data. The application of the empirically corrected statistics is illustrated via a real data example. [ABSTRACT FROM PUBLISHER]
- Published
- 2017
- Full Text
- View/download PDF
21. Four New Corrected Statistics for SEM With Small Samples and Nonnormally Distributed Data.
- Author
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Jiang, Ge and Yuan, Ke-Hai
- Subjects
- *
STRUCTURAL equation modeling , *MONTE Carlo method , *MULTIVARIATE analysis - Abstract
When the assumption of multivariate normality is violated and the sample sizes are relatively small, existing test statistics such as the likelihood ratio statistic and Satorra–Bentler’s rescaled and adjusted statistics often fail to provide reliable assessment of overall model fit. This article proposes four new corrected statistics, aiming for better model evaluation with nonnormally distributed data at small sample sizes. A Monte Carlo study is conducted to compare the performances of the four corrected statistics against those of existing statistics regarding Type I error rate. Results show that the performances of the four new statistics are relatively stable compared with those of existing statistics. In particular, Type I error rates of a new statistic are close to the nominal level across all sample sizes under a condition of asymptotic robustness. Other new statistics also exhibit improved Type I error control, especially with nonnormally distributed data at small sample sizes. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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22. Improving the convergence rate and speed of Fisher-scoring algorithm: ridge and anti-ridge methods in structural equation modeling.
- Author
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Yuan, Ke-Hai and Bentler, Peter
- Subjects
- *
FISHER discriminant analysis , *STRUCTURAL equation modeling , *MONTE Carlo method , *ESTIMATION theory , *SPEED , *STOCHASTIC convergence - Abstract
In structural equation modeling (SEM), parameter estimates are typically computed by the Fisher-scoring algorithm, which often has difficulty in obtaining converged solutions. Even for simulated data with a correctly specified model, non-converged replications have been repeatedly reported in the literature. In particular, in Monte Carlo studies it has been found that larger factor loadings or smaller error variances in a confirmatory factor model correspond to a higher rate of convergence. However, studies of a ridge method in SEM indicate that adding a diagonal matrix to the sample covariance matrix also increases the rate of convergence for the Fisher-scoring algorithm. This article addresses these two seemingly contradictory phenomena. Using statistical and numerical analyses, the article clarifies why both approaches increase the rate of convergence in SEM. Monte Carlo results confirm the analytical results. Recommendations are provided on how to increase both the speed and rate of convergence in parameter estimation. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
23. Reliable and More Powerful Methods for Power Analysis in Structural Equation Modeling.
- Author
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Yuan, Ke-Hai, Zhang, Zhiyong, and Zhao, Yanyun
- Subjects
- *
STATISTICAL power analysis , *STRUCTURAL equation modeling , *MONTE Carlo method - Abstract
The normal-distribution-based likelihood ratio statisticis widely used for power analysis in structural Equation modeling (SEM). In such an analysis, power and sample size are computed by assuming thatfollows a central chi-square distribution underand a noncentral chi-square distribution under. However, with either violation of normality or not a large enough sample size, both empirical and analytical results indicate that the chi-square distribution assumptions are not realistic and consequently methods of power analysis based on such assumptions are not valid. This article describes a Monte Carlo (MC) method for power analysis. A measure of effect size for characterizing the power property of different rescaled statistics is also provided. Robust methods are proposed to increase the power ofand other statistics. Simulation results show that the MC method reliably controls Type I errors and robust estimation methods effectively increase the power, and their combination is thus recommended for conducting power analysis in SEM. [ABSTRACT FROM PUBLISHER]
- Published
- 2017
- Full Text
- View/download PDF
24. New Ways to Evaluate Goodness of Fit: A Note on Using Equivalence Testing to Assess Structural Equation Models.
- Author
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Marcoulides, Katerina M. and Yuan, Ke-Hai
- Subjects
- *
STRUCTURAL equation modeling , *CONFIRMATORY factor analysis , *INDEXES - Abstract
Structural equation models are typically evaluated on the basis of goodness-of-fit indexes. Despite their popularity, agreeing what value these indexes should attain to confidently decide between the acceptance and rejection of a model has been greatly debated. A recently proposed approach by means of equivalence testing has been recommended as a superior way to evaluate the goodness of fit of models. The approach has also been proposed as providing a necessary vehicle that can be used to advance the inferential nature of structural equation modeling as a confirmatory tool. The purpose of this article is to introduce readers to key ideas in equivalence testing and illustrate its use for conducting model–data fit assessments. Two confirmatory factor analysis models in which a priori specified latent variable models with known structure and tested against data are used as examples. It is advocated that whenever the goodness of fit of a model is to be assessed researchers should always examine the resulting values obtained via the equivalence testing approach. [ABSTRACT FROM PUBLISHER]
- Published
- 2017
- Full Text
- View/download PDF
25. Meta analytical structural equation modeling: comments on issues with current methods and viable alternatives.
- Author
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Yuan, Ke‐Hai
- Subjects
- *
STRUCTURAL equation modeling , *META-analysis , *ERRORS , *LEAST squares , *COVARIANCE matrices , *STATISTICAL correlation - Abstract
The author discusses aspects relates to structural equation modeling including meta-analysis of factors affecting its viability. Topics discussed include combined effect of computational standard errors (SEs), use of generalized least squares (GLS) methods, application of covariance matrix, and correlation of random variables.
- Published
- 2016
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26. Assessing Structural Equation Models by Equivalence Testing With Adjusted Fit Indexes.
- Author
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Yuan, Ke-Hai, Chan, Wai, Marcoulides, George A., and Bentler, Peter M.
- Subjects
- *
STRUCTURAL equation modeling , *MATHEMATICAL equivalence , *LIKELIHOOD ratio tests , *STANDARD deviations , *APPROXIMATION error - Abstract
Conventional null hypothesis testing (NHT) is a very important tool if the ultimate goal is to find a difference or to reject a model. However, the purpose of structural equation modeling (SEM) is to identify a model and use it to account for the relationship among substantive variables. With the setup of NHT, a nonsignificant test statistic does not necessarily imply that the model is correctly specified or the size of misspecification is properly controlled. To overcome this problem, this article proposes to replace NHT by equivalence testing, the goal of which is to endorse a model under a null hypothesis rather than to reject it. Differences and similarities between equivalence testing and NHT are discussed, and new “T-size” terminology is introduced to convey the goodness of the current model under equivalence testing. Adjusted cutoff values of root mean square error of approximation (RMSEA) and comparative fit index (CFI) corresponding to those conventionally used in the literature are obtained to facilitate the understanding ofT-size RMSEA and CFI. The single most notable property of equivalence testing is that it allows a researcher to confidently claim that the size of misspecification in the current model is below theT-size RMSEA or CFI, which gives SEM a desirable property to be a scientific methodology. R code for conducting equivalence testing is provided in an appendix. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
27. Structural Equation Modeling With Unknown Population Distributions: Ridge Generalized Least Squares.
- Author
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Yuan, Ke-Hai and Chan, Wai
- Subjects
- *
LEAST squares , *STRUCTURAL equation modeling , *MATRICES (Mathematics) , *MAXIMUM likelihood statistics , *PARAMETER estimation - Abstract
This article proposes 2 classes of ridge generalized least squares (GLS) procedures for structural equation modeling (SEM) with unknown population distributions. The weight matrix for the first class of ridge GLS is obtained by combining the sample fourth-order moment matrix with the identity matrix. The weight matrix for the second class is obtained by combining the sample fourth-order moment matrix with its diagonal matrix. Empirical results indicate that, with data from an unknown population distribution, parameter estimates by ridge GLS can be much more accurate than those by either GLS or normal-distribution-based maximum likelihood; and standard errors of the parameter estimates also become more accurate in predicting the empirical ones. Rescaled and adjusted statistics are proposed for overall model evaluation, and they also perform much better than the default statistic following from the GLS method. The use of the ridge GLS procedures is illustrated with a real data set. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
28. Multiple-Group Analysis for Structural Equation Modeling With Dependent Samples.
- Author
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Deng, Lifang and Yuan, Ke-Hai
- Subjects
- *
CHI-squared test , *STRUCTURAL equation modeling , *LONGITUDINAL method , *TEAMS in the workplace , *BUSINESSPEOPLE - Abstract
Multigroup structural equation modeling (SEM) plays a key role in studying measurement invariance and in group comparison. However, existing methods for multigroup SEM assume that different samples are independent. This article develops a method for multigroup SEM with correlated samples. Parallel to that for independent samples, the focus here is on the cross-group stability of the within-group structure and parameters. In particular, the method does not require the specification of any between-group relationship. Rescaled and adjusted statistics as well as sandwich-type covariance matrices make the developed method work for possibly nonnormal variables with finite 4th-order moments. The method is applied to a longitudinal data set on the development of entrepreneurial teams across 4 phases. Detailed analysis is provided regarding the stability of the effect of psychological compatibility on team performance, as it is mediated by fairness perception and team cohesion. [ABSTRACT FROM PUBLISHER]
- Published
- 2015
- Full Text
- View/download PDF
29. Empirical Correction to the Likelihood Ratio Statistic for Structural Equation Modeling with Many Variables.
- Author
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Yuan, Ke-Hai, Tian, Yubin, and Yanagihara, Hirokazu
- Subjects
LIKELIHOOD ratio tests ,MATHEMATICAL optimization ,STRUCTURAL equation modeling ,MULTIVARIATE analysis ,STATISTICS on social sciences - Abstract
Survey data typically contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. The most widely used statistic for evaluating the adequacy of a SEM model is T, a slight modification to the likelihood ratio statistic. Under normality assumption, T approximately follows a chi-square distribution when the number of observations ( N) is large and the number of items or variables ( p) is small. However, in practice, p can be rather large while N is always limited due to not having enough participants. Even with a relatively large N, empirical results show that T rejects the correct model too often when p is not too small. Various corrections to T have been proposed, but they are mostly heuristic. Following the principle of the Bartlett correction, this paper proposes an empirical approach to correct T so that the mean of the resulting statistic approximately equals the degrees of freedom of the nominal chi-square distribution. Results show that empirically corrected statistics follow the nominal chi-square distribution much more closely than previously proposed corrections to T, and they control type I errors reasonably well whenever N≥max(50,2 p). The formulations of the empirically corrected statistics are further used to predict type I errors of T as reported in the literature, and they perform well. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
30. Bias and Efficiency for SEM With Missing Data and Auxiliary Variables: Two-Stage Robust Method Versus Two-Stage ML.
- Author
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Yuan, Ke-Hai, Tong, Xin, and Zhang, Zhiyong
- Subjects
- *
STRUCTURAL equation modeling , *MISSING at random (Statistics) , *STANDARD deviations , *COVARIANCE matrices , *GAUSSIAN distribution - Abstract
This article compares parameter estimates by 2-stage ML (TSML) and a recently developed 2-stage robust (TSR) method for structural equation modeling (SEM) with missing data. In the design, data are missing at random (MAR) after an auxiliary variable (AV) is included, and they are missing not at random (MNAR) otherwise. Results indicate that, when either the substantive variables or the AV is nonnormally distributed, TSR most likely yields more accurate parameter estimates than TSML; TSML is only slightly preferred to TSR when all variables are normally distributed. Including normally distributed AVs with TSML reduces the bias and improves the accuracy in parameter estimates. However, when the distribution of AVs has heavier tails than that of the normal distribution, including them with TSML could result in less accurate parameter estimates. When the sample sizeNis medium to large, including AVs with TSR most likely yields more accurate parameter estimates. WhenNis small, missing data rate is low, and when the AV is nonnromally distributed, TSML or even TSR could yield more accurate parameter estimates under MNAR mechanism than under MAR mechanism. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
31. Evaluation of Test Statistics for Robust Structural Equation Modeling With Nonnormal Missing Data.
- Author
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Tong, Xin, Zhang, Zhiyong, and Yuan, Ke-Hai
- Subjects
STRUCTURAL equation modeling ,MISSING data (Statistics) ,CHI-squared test ,GROWTH curves (Statistics) ,SAMPLE size (Statistics) ,ANALYSIS of covariance ,MATHEMATICAL ability - Abstract
A 2-stage robust procedure as well as an R package, rsem, were recently developed for structural equation modeling with nonnormal missing data by Yuan and Zhang (2012). Several test statistics that have been used for complete data analysis are employed to evaluate model fit in the 2-stage robust method. However, properties of these statistics under robust procedures for incomplete nonnormal data analysis have never been studied. This study aims to systematically evaluate and compare 5 test statistics, including a test statistic derived from normal-distribution-based maximum likelihood, a rescaled chi-square statistic, an adjusted chi-square statistic, a corrected residual-based asymptotical distribution-free chi-square statistic, and a residual-basedFstatistic. These statistics are evaluated under a linear growth curve model by varying 8 factors: population distribution, missing data mechanism, missing data rate, sample size, number of measurement occasions, covariance between the latent intercept and slope, variance of measurement errors, and downweighting rate of the 2-stage robust method. The performance of the test statistics varies and the one derived from the 2-stage normal-distribution-based maximum likelihood performs much worse than the other four. Application of the 2-stage robust method and of the test statistics is illustrated through growth curve analysis of mathematical ability development, using data on the Peabody Individual Achievement Test mathematics assessment from the National Longitudinal Survey of Youth 1997 Cohort. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
32. Data-driven sensitivity analysis to detect missing data mechanism with applications to structural equation modelling.
- Author
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Jamshidian, Mortaza and Yuan, Ke-Hai
- Subjects
- *
STRUCTURAL equation modeling , *PARAMETER estimation , *ASYMPTOTIC distribution , *DATA analysis , *SENSITIVITY analysis , *MEASURE theory - Abstract
Missing data are a common problem in almost all areas of empirical research. Ignoring the missing data mechanism, especially when data are missing not at random (MNAR), can result in biased and/or inefficient inference. Because MNAR mechanism is not verifiable based on the observed data, sensitivity analysis is often used to assess it. Current sensitivity analysis methods primarily assume a model for the response mechanism in conjunction with a measurement model and examine sensitivity to missing data mechanism via the parameters of the response model. Recently, Jamshidian and Mata (Post-modelling sensitivity analysis to detect the effect of missing data mechanism, Multivariate Behav. Res. 43 (2008), pp. 432–452) introduced a new method of sensitivity analysis that does not require the difficult task of modelling the missing data mechanism. In this method, a single measurement model is fitted to all of the data and to a sub-sample of the data. Discrepancy in the parameter estimates obtained from the the two data sets is used as a measure of sensitivity to missing data mechanism. Jamshidian and Mata describe their method mainly in the context of detecting data that are missing completely at random (MCAR). They used a bootstrap type method, that relies on heuristic input from the researcher, to test for the discrepancy of the parameter estimates. Instead of using bootstrap, the current article obtains confidence interval for parameter differences on two samples based on an asymptotic approximation. Because it does not use bootstrap, the developed procedure avoids likely convergence problems with the bootstrap methods. It does not require heuristic input from the researcher and can be readily implemented in statistical software. The article also discusses methods of obtaining sub-samples that may be used to test missing at random in addition to MCAR. An application of the developed procedure to a real data set, from the first wave of an ongoing longitudinal study on aging, is presented. Simulation studies are performed as well, using two methods of missing data generation, which show promise for the proposed sensitivity method. One method of missing data generation is also new and interesting in its own right. [ABSTRACT FROM PUBLISHER]
- Published
- 2013
- Full Text
- View/download PDF
33. Structural Equation Modeling Diagnostics Using R Package semdiag and EQS.
- Author
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Yuan, Ke-Hai and Zhang, Zhiyong
- Subjects
- *
STRUCTURAL equation modeling , *MULTIVARIATE analysis , *MATHEMATICS , *MATHEMATICAL analysis , *MATHEMATICAL models - Abstract
Yuan and Hayashi (2010) introduced 2 scatter plots for model and data diagnostics in structural equation modeling (SEM). However, the generation of the plots requires in-depth understanding of their underlying technical details. This article develops and introduces an R package semdiag for easily drawing the 2 plots. With a model specified in EQS syntax, one only needs to supply as few as 2 parameters to generate the 2 plots using the semdiag package. Two examples are provided to illustrate the use of the package. Multiple figures are used to explain the elements of data and model diagnostics. Advice on selecting proper estimation methods following the diagnostics is also given. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
34. Robust Structural Equation Modeling with Missing Data and Auxiliary Variables.
- Author
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Yuan, Ke-Hai and Zhang, Zhiyong
- Subjects
STRUCTURAL equation modeling ,DATA analysis ,ANALYSIS of covariance ,ERROR analysis in mathematics ,MATHEMATICAL models ,ESTIMATION theory - Abstract
The paper develops a two-stage robust procedure for structural equation modeling (SEM) and an R package rsem to facilitate the use of the procedure by applied researchers. In the first stage, M-estimates of the saturated mean vector and covariance matrix of all variables are obtained. Those corresponding to the substantive variables are then fitted to the structural model in the second stage. A sandwich-type covariance matrix is used to obtain consistent standard errors (SE) of the structural parameter estimates. Rescaled, adjusted as well as corrected and F-statistics are proposed for overall model evaluation. Using R and EQS, the R package rsem combines the two stages and generates all the test statistics and consistent SEs. Following the robust analysis, multiple model fit indices and standardized solutions are provided in the corresponding output of EQS. An example with open/closed book examination data illustrates the proper use of the package. The method is further applied to the analysis of a data set from the National Longitudinal Survey of Youth 1997 cohort, and results show that the developed procedure not only gives a better endorsement of the substantive models but also yields estimates with uniformly smaller standard errors than the normal-distribution-based maximum likelihood. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
35. Ridge structural equation modelling with correlation matrices for ordinal and continuous data.
- Author
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Yuan, Ke‐Hai, Wu, Ruilin, and Bentler, Peter M.
- Subjects
- *
STRUCTURAL equation modeling , *MATRICES (Mathematics) , *STOCHASTIC convergence , *RANDOM variables , *MULTIPLE integrals , *LOGARITHMS , *ANALYSIS of covariance - Abstract
This paper develops a ridge procedure for structural equation modelling (SEM) with ordinal and continuous data by modelling the polychoric/polyserial/product-moment correlation matrix R. Rather than directly fitting R, the procedure fits a structural model to R a= R+ a I by minimizing the normal distribution-based discrepancy function, where a > 0. Statistical properties of the parameter estimates are obtained. Four statistics for overall model evaluation are proposed. Empirical results indicate that the ridge procedure for SEM with ordinal data has better convergence rate, smaller bias, smaller mean square error, and better overall model evaluation than the widely used maximum likelihood procedure. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
36. FINITE NORMAL MIXTURE SEM ANALYSIS BY FITTING MULTIPLE CONVENTIONAL SEM MODELS.
- Author
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Yuan, Ke-Hai and Bentler, Peter M.
- Subjects
- *
MATRICES (Mathematics) , *STATISTICAL sampling , *STRUCTURAL equation modeling , *SOCIOLOGY methodology , *STATISTICAL methods in sociology , *MONTE Carlo method - Abstract
This paper proposes a two-stage maximum likelihood (ML) approach to normal mixture structural equation modeling (SEM) and develops a statistical inference that allows distributional misspecification. Saturated means and covariances are estimated at stage 1 together with a sandwich-type covariance matrix. These are used to evaluate structural models at stage 2. Techniques accumulated in the conventional SEM literature for model diagnosis and evaluation can be used to study the model structure for each component. Examples show that the two-stage ML approach leads to correct or nearly correct models even when the normal mixture assumptions are violated and initial models are misspecified. Compared to single-stage ML, two-stage ML avoids the confounding effect of model specification and the number of components, and it is computationally more efficient. Monte Carlo results indicate that two-stage ML loses only minimal efficiency under the condition where single-stage ML performs best. Monte Carlo results also indicate that the commonly used model selection criterion BIC is more robust to distribution violations for the saturated model than that for a structural model at moderate sample sizes. The proposed two-stage ML approach is also extremely flexible in modeling different components with different models. Potential new developments in the mixture modeling literature can be easily adapted to study issues with normal mixture SEM. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
37. OUTLIERS, LEVERAGE OBSERVATIONS, AND INFLUENTIAL CASES IN FACTOR ANALYSIS: USING ROBUST PROCEDURES TO MINIMIZE THEIR EFFECT.
- Author
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Yuan, Ke-Hai and Zhong, Xiaoling
- Subjects
- *
FACTOR analysis , *REGRESSION analysis , *ROBUST statistics , *STRUCTURAL equation modeling , *OUTLIERS (Statistics) , *STATISTICAL weighting - Abstract
Parallel to the development in regression diagnosis, this paper defines good and bad leverage observations in factor analysis. Outliers are observations that deviate from the factor model, not from the center of the data cloud. The effects of each kind of outlying observations on the normal distribution-based maximum likelihood estimator and the associated likelihood ratio statistic are studied through analysis. The distinction between outliers and leverage observations also clarifies the roles of three robust procedures based on different Mahalanobis distances. All the robust procedures are designed to minimize the effect of certain outlying observations. Only the robust procedure with a residual-based distance properly controls the effect of outliers. Empirical results illustrate the strength or weakness of each procedure and support those obtained in analysis. The relevance of the results to general structural equation models is discussed and formulas are provided. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
38. Robust mean and covariance structure analysis through iteratively reweighted least squares.
- Author
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YUAN, KE-HAI and BENTLER, PETER M.
- Subjects
ROBUST statistics ,ANALYSIS of covariance ,LEAST squares ,STRUCTURAL equation modeling ,ERROR analysis in mathematics - Abstract
Robust schemes in regression are adapted to mean and covariance structure analysis, providing an iteratively reweighted least squares approach to robust structural equation modeling. Each case is properly weighted according to its distance, based on first and second order moments, from the structural model. A simple weighting function is adopted because of its flexibility with changing dimensions. The weight matrix is obtained from an adaptive way of using residuals. Test statistic and standard error estimators are given, based on iteratively reweighted least squares. The method reduces to a standard distribution-free methodology if all cases are equally weighted. Examples demonstrate the value of the robust procedure. [ABSTRACT FROM AUTHOR]
- Published
- 2000
- Full Text
- View/download PDF
39. Structural equation modeling with near singular covariance matrices
- Author
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Yuan, Ke-Hai and Chan, Wai
- Subjects
- *
STRUCTURAL equation modeling , *MULTIVARIATE analysis , *ANALYSIS of covariance , *MATRICES (Mathematics) - Abstract
Abstract: Conventional structural equation modeling involves fitting a structural model to the sample covariance matrix . Due to collinearity or small samples with practical data, nonconvergences often occur in the estimation process. For a small constant , this paper proposes to fit the structural model to the covariance matrix . When treating as the sample covariance matrix in the maximum likelihood (ML) procedure, consistent parameter estimates are still obtained. The asymptotic distributions of the parameter estimates and the corresponding likelihood ratio statistic are studied and compared to those by the conventional ML. Two rescaled statistics for the overall model evaluation with modeling are constructed. Empirical results imply that the estimates from modeling are more efficient than those of fitting the structural model to even when data are normally distributed. Simulations and real data examples indicate that modeling allows us to evaluate the overall model structure even when is literally singular. Implications of modeling in a broader context are discussed. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
40. Abstract: Evaluation of Test Statistics for Robust Structural Equation Modeling With Nonnormal Missing Data.
- Author
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Tong, Xin, Zhang, Zhiyong, and Yuan, Ke-Hai
- Subjects
STRUCTURAL equation modeling ,MISSING data (Statistics) - Abstract
Traditional structural equation modeling (SEM) techniques have trouble dealing with incomplete and/or nonnormal data that are often encountered in practice. Yuan and Zhang (2011a) developed a two-stage procedure for SEM to handle nonnormal missing data and proposed four test statistics for overall model evaluation. Although these statistics have been shown to work well with complete data, their performance for incomplete data has not been investigated in the context of robust statistics. Focusing on a linear growth curve model, a systematic simulation study is conducted to evaluate the accuracy of the parameter estimates and the performance of five test statistics including the naive statistic derived from normal distribution based maximum likelihood (ML), the Satorra-Bentler scaled chi-square statistic (RML), the mean- and variance-adjusted chi-square statistic (AML), Yuan-Bentler residual-based test statistic (CRADF), and Yuan-Bentler residual-based F statistic (RF). Data are generated and analyzed in R using the package rsem (Yuan & Zhang, 2011b). Based on the simulation study, we can observe the following: (a) The traditional normal distribution-based method cannot yield accurate parameter estimates for nonnormal data, whereas the robust method obtains much more accurate model parameter estimates for nonnormal data and performs almost as well as the normal distribution based method for normal distributed data. (b) With the increase of sample size, or the decrease of missing rate or the number of outliers, the parameter estimates are less biased and the empirical distributions of test statistics are closer to their nominal distributions. (c) The ML test statistic does not work well for nonnormal or missing data. (d) For nonnormal complete data, CRADF and RF work relatively better than RML and AML. (e) For missing completely at random (MCAR) missing data, in almost all the cases, RML and AML work better than CRADF and RF. (f) For nonnormal missing at random (MAR) missing data, CRADF and RF work better than AML. (g) The performance of the robust method does not seem to be influenced by the symmetry of outliers. [ABSTRACT FROM PUBLISHER]
- Published
- 2011
- Full Text
- View/download PDF
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