scholarly journals Comparative Analysis of Some Structural Equation Model Estimation Methods with Application to Coronary Heart Disease Risk

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
David Adedia ◽  
Atinuke O. Adebanji ◽  
Simon Kojo Appiah
Keyword(s):  
Coronary Heart Disease ◽  
Maximum Likelihood ◽  
Least Squares ◽  
Asymptotic Distribution ◽  
Structural Equation ◽  
Generalized Least Squares ◽  
Least Squares Estimator ◽  
Coronary Risk ◽  
Distribution Free ◽  
Better Than

This study compared a ridge maximum likelihood estimator to Yuan and Chan (2008) ridge maximum likelihood, maximum likelihood, unweighted least squares, generalized least squares, and asymptotic distribution-free estimators in fitting six models that show relationships in some noncommunicable diseases. Uncontrolled hypertension has been shown to be a leading cause of coronary heart disease, kidney dysfunction, and other negative health outcomes. It poses equal danger when asymptomatic and undetected. Research has also shown that it tends to coexist with diabetes mellitus (DM), with the presence of DM doubling the risk of hypertension. The study assessed the effect of obesity, type II diabetes, and hypertension on coronary risk and also the existence of converse relationship with structural equation modelling (SEM). The results showed that the two ridge estimators did better than other estimators. Nonconvergence occurred for most of the models for asymptotic distribution-free estimator and unweighted least squares estimator whilst generalized least squares estimator had one nonconvergence of results. Other estimators provided competing outputs, but unweighted least squares estimator reported unreliable parameter estimates such as large chi-square test statistic and root mean square error of approximation for Model 3. The maximum likelihood family of estimators did better than others like asymptotic distribution-free estimator in terms of overall model fit and parameter estimation. Also, the study found that increase in obesity could result in a significant increase in both hypertension and coronary risk. Diastolic blood pressure and diabetes have significant converse effects on each other. This implies those who are hypertensive can develop diabetes and vice versa.

Comparison of Maximum Likelihood, Generalized Least Squares, Ordinary Least Squares, and Asymptotically Distribution Free Parameter Estimates in Drug Abuse Latent Variable Causal Models

1983 ◽  
Vol 13 (4) ◽  
pp. 387-404 ◽  
Author(s):  
G. J. Huba ◽  
L. L. Harlow
Keyword(s):  
Drug Abuse ◽  
Maximum Likelihood ◽  
Least Squares ◽  
Latent Variable ◽  
Generalized Least Squares ◽  
Causal Models ◽  
Multivariate Normal ◽  
Distribution Free ◽  
Asymptotically Distribution Free ◽  
Normally Distributed

Latent variable causal modeling techniques are sometimes criticized when applied to drug abuse data because the commonly-employed maximum likelihood parameter estimation method requires that the data be normally distributed for the statistical tests to be accurate. In this article, four estimators for the parameters in two large latent variable causal models are compared in real drug abuse datasets. One estimator does not require that the data be multivariate normal and does, in fact, correct for data non-normality. Specifically, maximum likelihood and generalized least squares estimators for normally-distributed variables are compared with Browne's asymptotically distribution free techniques for continuous non-normally distributed data. Additionally, ordinary (unweighted) least squares estimates are used. Descriptions of the techniques are given and actual results in two “real” datasets are provided. It is concluded that the distribution free technique provides results which are generally comparable to those obtained with maximum likelihood estimation for datasets which depart in typical ways from the ideal of the multivariate normal distribution.

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.

The Robustness of the Likelihood Ratio Chi-Square Test for Structural Equation Models: A Meta-Analysis

2001 ◽  
Vol 26 (1) ◽  
pp. 105-132 ◽  
Author(s):  
Douglas A. Powell ◽  
William D. Schafer
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Type I Error ◽  
Meta Analysis ◽  
Generalized Least Squares ◽  
Error Rates ◽  
Type I ◽  
Chi Square ◽  
Distribution Free ◽  
Projection Techniques

The robustness literature for the structural equation model was synthesized following the method of Harwell which employs meta-analysis as developed by Hedges and Vevea. The study focused on the explanation of empirical Type I error rates for six principal classes of estimators: two that assume multivariate normality (maximum likelihood and generalized least squares), elliptical estimators, two distribution-free estimators (asymptotic and others), and latent projection. Generally, the chi-square tests for overall model fit were found to be sensitive to non-normality and the size of the model for all estimators (with the possible exception of the elliptical estimators with respect to model size and the latent projection techniques with respect to non-normality). The asymptotic distribution-free (ADF) and latent projection techniques were also found to be sensitive to sample sizes. Distribution-free methods other than ADF showed, in general, much less sensitivity to all factors considered.

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.

Estimating an Autoregressive Current Effects Model of Sales Response when Observations are Aggregated over Time: Least Squares versus Maximum Likelihood

1988 ◽  
Vol 25 (3) ◽  
pp. 301-307
Author(s):  
Wilfried R. Vanhonacker
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Serial Correlation ◽  
Mean Squared Error ◽  
Generalized Least Squares ◽  
Parameter Estimates ◽  
Squared Error ◽  
Positive Serial Correlation ◽  
Serial Correlation Coefficient ◽  
Over Time

Estimating autoregressive current effects models is not straightforward when observations are aggregated over time. The author evaluates a familiar iterative generalized least squares (IGLS) approach and contrasts it to a maximum likelihood (ML) approach. Analytic and numerical results suggest that (1) IGLS and ML provide good estimates for the response parameters in instances of positive serial correlation, (2) ML provides superior (in mean squared error) estimates for the serial correlation coefficient, and (3) IGLS might have difficulty in deriving parameter estimates in instances of negative serial correlation.

ASYMPTOTIC EFFICIENCY OF THE ORDINARY LEAST SQUARES ESTIMATOR FOR REGRESSIONS WITH UNSTABLE REGRESSORS

2002 ◽  
Vol 18 (5) ◽  
pp. 1121-1138 ◽  
Author(s):  
DONG WAN SHIN ◽  
MAN SUK OH
Keyword(s):  
Least Squares ◽  
Asymptotic Efficiency ◽  
Characteristic Root ◽  
Sufficient Conditions ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Least Squares Estimator ◽  
Characteristic Roots ◽  
Generalized Least Squares Estimator ◽  
Ordinary Least Squares Estimator

For regression models with general unstable regressors having characteristic roots on the unit circle and general stationary errors independent of the regressors, sufficient conditions are investigated under which the ordinary least squares estimator (OLSE) is asymptotically efficient in that it has the same limiting distribution as the generalized least squares estimator (GLSE) under the same normalization. A key condition for the asymptotic efficiency of the OLSE is that one multiplicity of a characteristic root of the regressor process is strictly greater than the multiplicities of the other roots. Under this condition, the covariance matrix Γ of the errors and the regressor matrix X are shown to satisfy a relationship (ΓX = XC + V for some matrix C) for V asymptotically dominated by X, which is analogous to the condition (ΓX = XC for some matrix C) for numerical equivalence of the OLSE and the GLSE.

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