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.

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.

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%.

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 Lagrange Multiplier Test for Spatial Autoregressive Model with Latent Variables

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1375
Author(s):  
Anik Anekawati ◽  
Bambang Widjanarko Otok ◽  
Purhadi Purhadi ◽  
Sutikno Sutikno
Keyword(s):  
Least Squares ◽  
Lagrange Multiplier ◽  
Latent Variables ◽  
Autoregressive Model ◽  
Structural Equation ◽  
Weighted Least Squares ◽  
Equation Modeling ◽  
Spatial Autoregressive Model ◽  
Lm Test ◽  
Spatial Autoregressive

The focus of this research is to develop a Lagrange multiplier (LM) test of spatial dependence for the spatial autoregressive model (SAR) with latent variables (LVs). It was arranged by the standard SAR, where the independent variables were replaced by factor scores of the exogenous latent variables from a measurement model (in structural equation modeling) as well as their dependent variables. As a result, an error distribution of the SAR-LVs should have a different distribution from the standard SAR. Therefore, this LM test for the SAR-LVs is based on the new distribution. The estimation of the latent variables used a weighted least squares (WLS) method. The estimation of the SAR-LVs parameter used a two-stage least squares (2SLS) method. The SAR-LVs model was applied to the model with a positive and negative spatial autoregressive coefficient to illustrate how it was interpreted.

Meta-Analytical SEM: Equivalence Between Maximum Likelihood and Generalized Least Squares

2018 ◽  
Vol 43 (6) ◽  
pp. 693-720
Author(s):  
Ke-Hai Yuan ◽  
Yutaka Kano
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Correlation Matrix ◽  
Structural Equation ◽  
Structural Model ◽  
Meta Analysis ◽  
Generalized Least Squares ◽  
Equation Modeling ◽  
Correlation Matrices ◽  
Latent Constructs

Meta-analysis plays a key role in combining studies to obtain more reliable results. In social, behavioral, and health sciences, measurement units are typically not well defined. More meaningful results can be obtained by standardizing the variables and via the analysis of the correlation matrix. Structural equation modeling (SEM) with the combined correlations, called meta-analytical SEM (MASEM), is a powerful tool for examining the relationship among latent constructs as well as those between the latent constructs and the manifest variables. Three classes of methods have been proposed for MASEM: (1) generalized least squares (GLS) in combining correlations and in estimating the structural model, (2) normal-distribution-based maximum likelihood (ML) in combining the correlations and then GLS in estimating the structural model (ML-GLS), and (3) ML in combining correlations and in estimating the structural model (ML). The current article shows that these three methods are equivalent. In particular, (a) the GLS method for combining correlation matrices in meta-analysis is asymptotically equivalent to ML, (b) the three methods (GLS, ML-GLS, ML) for MASEM with correlation matrices are asymptotically equivalent, (c) they also perform equally well empirically, and (d) the GLS method for SEM with the sample correlation matrix in a single study is asymptotically equivalent to ML, which has being discussed extensively in the SEM literature regarding whether the analysis of a correlation matrix yields consistent standard errors and asymptotically valid test statistics. The results and analysis suggest that a sample-size weighted GLS method is preferred for combining correlations and for MASEM.

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