scholarly journals The Effect of Estimation Methods on SEM Fit Indices

2019 ◽  
Vol 80 (3) ◽  
pp. 421-445 ◽  
Author(s):  
Dexin Shi ◽  
Alberto Maydeu-Olivares
Keyword(s):  
Least Squares ◽  
Root Mean Square ◽  
Structural Equation ◽  
Weighted Least Squares ◽  
Estimation Method ◽  
Estimation Methods ◽  
Equation Modeling ◽  
Model Parameters ◽  
Mean Square ◽  
Fit Indices

We examined the effect of estimation methods, maximum likelihood (ML), unweighted least squares (ULS), and diagonally weighted least squares (DWLS), on three population SEM (structural equation modeling) fit indices: the root mean square error of approximation (RMSEA), the comparative fit index (CFI), and the standardized root mean square residual (SRMR). We considered different types and levels of misspecification in factor analysis models: misspecified dimensionality, omitting cross-loadings, and ignoring residual correlations. Estimation methods had substantial impacts on the RMSEA and CFI so that different cutoff values need to be employed for different estimators. In contrast, SRMR is robust to the method used to estimate the model parameters. The same criterion can be applied at the population level when using the SRMR to evaluate model fit, regardless of the choice of estimation method.

The Effect of Latent and Error Non-Normality on Measures of Fit in Structural Equation Modeling

2021 ◽  
pp. 001316442110462
Author(s):  
Lisa J. Jobst ◽  
Max Auerswald ◽  
Morten Moshagen
Keyword(s):  
Structural Equation Modeling ◽  
Root Mean Square ◽  
Latent Variables ◽  
Structural Equation ◽  
Generalized Least Squares ◽  
Estimation Methods ◽  
Equation Modeling ◽  
Analytic Structure ◽  
Mean Square ◽  
Test Statistic

Prior studies investigating the effects of non-normality in structural equation modeling typically induced non-normality in the indicator variables. This procedure neglects the factor analytic structure of the data, which is defined as the sum of latent variables and errors, so it is unclear whether previous results hold if the source of non-normality is considered. We conducted a Monte Carlo simulation manipulating the underlying multivariate distribution to assess the effect of the source of non-normality (latent, error, and marginal conditions with either multivariate normal or non-normal marginal distributions) on different measures of fit (empirical rejection rates for the likelihood-ratio model test statistic, the root mean square error of approximation, the standardized root mean square residual, and the comparative fit index). We considered different estimation methods (maximum likelihood, generalized least squares, and (un)modified asymptotically distribution-free), sample sizes, and the extent of non-normality in correctly specified and misspecified models to investigate their performance. The results show that all measures of fit were affected by the source of non-normality but with varying patterns for the analyzed estimation methods.

scholarly journals PEMANTAUAN PERSAMAAN MODEL STRUKTURAL DALAM DATA ORDINAL

2009 ◽  
Vol 8 (1) ◽  
pp. 21
Author(s):  
B. SUHARJO ◽  
LA MBAU ◽  
N. K. K. ARDANA
Keyword(s):  
Least Squares ◽  
Structural Equation ◽  
Weighted Least Squares ◽  
Generalized Least Squares ◽  
The Other ◽  
Estimation Methods ◽  
Equation Modeling ◽  
Multivariate Techniques ◽  
Exogenous Variables ◽  
Design Data

Structural equation modeling (SEM) is one of multivariate techniques  that can estimates a series of interrelated dependence relationships from a number of endogenous and exogenous variables, as well as latent (unobserved) variables simultaneously. To estimates their parameters, SEM based on structure covariance matrix, there are severals methods can be used as estimation methods, namely maximum likelihood (ML), weighted least squares (WLS), generalized least squares (GLS) and unweighted least squares (ULS). The purpose of this paper are to learn these methods in estimating SEM parameters and to compare their consistency, accuracy and sensitivity based on sample size and multinormality assumption of observed variables.  Using a fully crossed design, data were generated for 2 conditions of normality  and 5 different sample sizes. The result showed that when data are normally distributed, ML and GLS more consistent and accurate then the  other methods

scholarly journals PERBANDINGAN ANTARA UNWEIGHTED LEAST SQUARES (ULS) DAN PARTIAL LEAST SQUARES (PLS) DALAM PEMODELAN PERSAMAAN STRUKTURAL (STUDI KASUS MODEL ANALISIS PRESTASI BELAJAR MAHASISWA TAHUN PERTAMA PROGRAM STUDI S1 MATEMATIKA FMIPA-INSTUTUT PERTANIAN BOGOR)

2017 ◽  
Vol 2 (1) ◽  
pp. 21
Author(s):  
Muhammad Amin Paris
Keyword(s):  
Least Squares ◽  
Student Learning ◽  
Partial Least Squares ◽  
Structural Equation ◽  
Weighted Least Squares ◽  
Generalized Least Squares ◽  
Primary Data ◽  
Equation Modeling ◽  
Multivariate Techniques ◽  
Mathematics Students

Structural Equation Modeling (SEM) is one of multivariate techniques  that can estimates a series of interrelated dependence relationships from a number of endogenous and exogenous variables, as well as latent (unobserved) variables simultaneously. Estimation of Parameter methods that is often applied in SEM are Maximum Likelihood (ML), Weighted Least Squares (WLS), Unweighted Least Squares (ULS), Generalized Least Squares (GLS) and Partial Least Squares (PLS). This research aims to compare ULS method and PLS method in estimating parameter model of achievement of student learning in first year undergraduate Mathematics students, FMIPA, Bogor  Agricultural University ( IPB). This research use secondary and primary data which amounts to 112. The result of this research indicates that ULS method is more accurate than PLS methods. The analysis done with ULS method shows that motivation, capability and environmental had an effect to achievement of student learning.

A Comparison of Accuracy Based on Data Imputation between Unconstrained Structural Equation Modeling and Weighted Least Squares Regression

2011 ◽  
Vol 130-134 ◽  
pp. 730-733
Author(s):  
Narong Phothi ◽  
Somchai Prakancharoen
Keyword(s):  
Structural Equation Modeling ◽  
Least Squares ◽  
Structural Equation ◽  
Weighted Least Squares ◽  
Equation Modeling ◽  
Data Imputation ◽  
Least Squares Regression ◽  
Waveform Generator ◽  
Data Set ◽  
Testing Group

This research proposed a comparison of accuracy based on data imputation between unconstrained structural equation modeling (Uncon-SEM) and weighted least squares (WLS) regression. This model is developed by University of California, Irvine (UCI) and measured using the mean magnitude of relative error (MMRE). Experimental data set is created using the waveform generator that contained 21 indicators (1,200 samples) and divided into two groups (1,000 for training and 200 for testing groups). In fact, training group was analyzed by three main factors (F1, F2, and F3) for creating the models. The result of the experiment show MMRE of Uncon-SEM method based on the testing group is 34.29% (accuracy is 65.71%). In contrast, WLS method produces MMRE for testing group is 55.54% (accuracy is 44.46%). So, Uncon-SEM is high accuracy and MMRE than WLS method that is 21.25%.

scholarly journals On the Burr XII-moment exponential distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. e0246935
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Mustafa Ç. Korkmaz ◽  
Wenhui Sheng ◽  
Azeem Ali
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Simulation Studies ◽  
Conditional Moments ◽  
Mathematical Properties ◽  
Lifetime Model ◽  
Anderson Darling ◽  
Von Mises

In this study, a new flexible lifetime model called Burr XII moment exponential (BXII-ME) distribution is introduced. We derive some of its mathematical properties including the ordinary moments, conditional moments, reliability measures and characterizations. We employ different estimation methods such as the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling methods for estimating the model parameters. We perform simulation studies on the basis of the graphical results to see the performance of the above estimators of the BXII-ME distribution. We verify the potentiality of the BXII-ME model via monthly actual taxes revenue and fatigue life applications.

scholarly journals Measures of fit impacts: Application to the causal model of consumer involvement

2018 ◽  
Vol 61 (1) ◽  
pp. 77-92
Author(s):  
Eric Rakotoasimbola ◽  
Sam Blili
Keyword(s):  
Sample Size ◽  
Root Mean Square ◽  
Goodness Of Fit ◽  
Causal Model ◽  
Estimation Method ◽  
Generalized Least Squares ◽  
Consumer Involvement ◽  
Mean Square ◽  
Fit Indices ◽  
Fit Index

Using the Monte Carlo simulation method, this study analyzes the impacts on fit indices by the degree of nonnormality of variables, the sample size, and the choice of estimation method. To address these issues, we use the causal model of consumer involvement as elaborated by Mittal and Lee. Results of this study show that adjusted goodness of fit index (AGFI) and goodness of fit index (GFI) are subject to variation in sample size, and their use requires a sample size of at least 300 observations to be reliable. Comparative fit index (CFI) and root mean square error of approximation (RSMEA) are more reliable with the generalized least squares (GLS) compared with maximum likelihood estimation (MLE) method under different settings of sample size and degree of nonnormality. Finally, for the standardized root mean square residual (SRMR), it is recommended that it is used with the MLE method. This study provides prescriptions for the choice of fit indices and the requirements of sample size and estimation method to test the causal model of consumer involvement. The method used here can be extended to any model before fitting it to real data. It helps researchers to prevent conflictual results regarding the choice of fit indices.

The Adult-Oriented Sport Coaching Survey: An Instrument Designed to Assess Coaching Behaviors Tailored to Adult Athletes

2020 ◽  
Vol 42 (5) ◽  
pp. 368-385
Author(s):  
Scott Rathwell ◽  
Bradley W. Young ◽  
Bettina Callary ◽  
Derrik Motz ◽  
Matt D. Hoffmann ◽  
...  
Keyword(s):  
Factor Analysis ◽  
Structural Equation Modeling ◽  
Root Mean Square ◽  
Structural Equation ◽  
Equation Modeling ◽  
Mean Square ◽  
Root Mean Square Residual ◽  
Confirmatory Factor ◽  
Masters Athletes ◽  
Fit Index

Adult sportspersons (Masters athletes, aged 35 years and older) have unique coaching preferences. No existing resources provide coaches with feedback on their craft with Masters athletes. Three studies evaluated an Adult-Oriented Coaching Survey. Study 1 vetted the face validity of 50 survey items with 12 Masters coaches. Results supported the validity of 48 items. In Study 2, 383 Masters coaches completed the survey of 50 items. Confirmatory factor analysis and exploratory structural equation modeling indicated issues with model fit. Post hoc modifications improved fit, resulting in a 22-item, five-factor model. In Study 3, 467 Masters athletes responded to these 22 items reflecting perceptions of their coaches. Confirmatory factor analysis (comparative fit index = .951, standardized root mean square residual = .036, and root mean square error of approximation = .049) and exploratory structural equation modeling (comparative fit index = .977, standardized root mean square residual = .019, and root mean square error of approximation = .041) confirmed the model. The resultant Adult-Oriented Sport Coaching Survey provides a reliable and factorially valid instrument for measuring adult-oriented coaching practices.

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