Optimizing Ridge Generalized Least Squares for Structural Equation Modeling

Yang, Miao

doi:10.1080/10705511.2018.1479853

Cited by 13 publications

(21 citation statements)

References 19 publications

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“…The reason for considering both efficiency and accuracy is that estimates are not necessarily unbiased with a small or moderate sample size, and the variance of SE estimates is not a good index for biased estimates. Yang and Yuan (2019), Yuan and Chan (2016) , and Yuan, Jiang, and Cheng (2017) found that a s depend on all aspects of the data and model, including the number of variables, the number of factors, and the population distribution. In practice, a s is unknown and needs to be estimated.…”

Section: Ridge Generalized Least Squares Estimationmentioning

confidence: 99%

“…There were 11 methods considered in the simulation (see Table 1). The distributionally-weighted To investigate both the efficiency and accuracy of parameter estimates, the root mean square error (RMSE) is a widely used index (e.g., Yuan & Chan, 2016;Yuan, Yang, & Jiang, 2017;Yang & Yuan, 2019). Letθ ij be the estimate of the ith parameter in the jth replication.…”

Section: Simulation Designmentioning

confidence: 99%

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Distributionally weighted least squares in structural equation modeling.

Du¹,

Bentler²

2022

Psychological Methods

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In real data analysis with structural equation modeling, data are unlikely to be exactly normally distributed.If we ignore the non-normality reality, the parameter estimates, standard error estimates, and model fit statistics from normal theory based methods such as maximum likelihood (ML) and normal theory based generalized least squares estimation (GLS) are unreliable. On the other hand, the asymptotically distribution free (ADF) estimator does not rely on any distribution assumption but cannot demonstrate its efficiency advantage with small and modest sample sizes. The methods which adopt misspecified loss functions including ridge GLS (RGLS) can provide better estimates and inferences than the normal theory based methods and the ADF estimator in some cases. We propose a distributionally-weighted least squares (DLS) estimator, and expect that it can perform better than the existing generalized least squares, because it combines normal theory based and ADF based generalized least squares estimation. Computer simulation results suggest that model-implied covariance based DLS (DLS M ) provided relatively accurate and efficient estimates in terms of RMSE. In addition, the empirical standard errors, the relative biases of standard error estimates, and the Type I error rates of the Jiang-Yuan rank adjusted model fit test statistic (T JY ) in DLS M were competitive with the classical methods including ML, GLS, and RGLS. The performance of DLS M depends on its tuning parameter a. We illustrate how to implement DLS M and select the optimal a by a bootstrap procedure in a real data example. ModelingStructural equation modeling (SEM) is widely used in social and behavioral research, but its statistical methodology remains marginally capable of dealing with empirical data encountered in many psychological and behavioral studies. First, statistics in SEM rely on large sample size approximation. Distributionally-Weighted Least Squares in Structural Equation Modeling 3 Distributionally-Weighted Least Squares in Structural EquationThat is, their use relies on asymptotic properties as sample size N becomes extremely large (N → ∞).However in real data analysis, sample sizes are usually moderate or even small. Although SEM methods usually provide consistent parameter estimates and consistent standard error (SE) estimates, the estimates are not necessarily unbiased with finite sample size. Second, although data are typically nonnormally distributed (e.g., Cain et al., 2017), the mainstream estimators for SEM are still based on normal theory, such as maximum likelihood (ML) and normal theory based generalized least squares estimation (GLS).

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Section: Ridge Generalized Least Squares Estimationmentioning

confidence: 99%

Section: Simulation Designmentioning

confidence: 99%

Distributionally weighted least squares in structural equation modeling.

Du¹,

Bentler²

2022

Psychological Methods

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“…Hence, estimators of slope parameters tended to have high variability and thus also a large MSE. This led Yuan and Chan ( 2008 ) to develop the ridge technique to mitigate such problems as it modifies the estimator of the covariance matrix by adding a small value to the main diagonal (see also Yuan and Chan, 2016 ; Yang and Yuan, 2019 ). The main idea behind this technique can also be adapted for Bayesian estimation.…”

Section: The Indirect Strategymentioning

confidence: 99%

Prior Specification for More Stable Bayesian Estimation of Multilevel Latent Variable Models in Small Samples: A Comparative Investigation of Two Different Approaches

2021

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Bayesian approaches for estimating multilevel latent variable models can be beneficial in small samples. Prior distributions can be used to overcome small sample problems, for example, when priors that increase the accuracy of estimation are chosen. This article discusses two different but not mutually exclusive approaches for specifying priors. Both approaches aim at stabilizing estimators in such a way that the Mean Squared Error (MSE) of the estimator of the between-group slope will be small. In the first approach, the MSE is decreased by specifying a slightly informative prior for the group-level variance of the predictor variable, whereas in the second approach, the decrease is achieved directly by using a slightly informative prior for the slope. Mathematical and graphical inspections suggest that both approaches can be effective for reducing the MSE in small samples, thus rendering them attractive in these situations. The article also discusses how these approaches can be implemented in Mplus.

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“…In Japan, Saito et al [79] estimated the effects of daily CO 2 exchange on environmental variables by using a path analysis, which showed soil temperature having a significant impact on ecosystem CO 2 exchange throughout the year. Yang and Yuan [80] proposed ridge generalized least squares (RGLS) as part of a structural equation modeling procedure for the development of formulas. Here, RGLS were found beneficial for enhancing parameter estimate efficiency.…”

Section: Literature Reviewmentioning

confidence: 99%

The Efficiency of the Sustainable Development Policy for Energy Consumption under Environmental Law in Thailand: Adapting the SEM-VARIMAX Model

Sutthichaimethee¹,

Naluang²

2019

Energies

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This research aims to predict the efficiency of the Sustainable Development Policy for Energy Consumption under Environmental Law in Thailand for the next 17 years (2020–2036) and analyze the relationships among causal factors by applying a structural equation modeling/vector autoregressive model with exogenous variables (SEM-VARIMAX Model). This model is effective for analyzing relationships among causal factors and optimizing future forecasting. It can be applied to contexts in different sectors, which distinguishes it from other previous models. Furthermore, this model ensures the absence of heteroskedasticity, multicollinearity, and autocorrelation. In fact, it meets all the standards of goodness of fit. Therefore, it is suitable for use as a tool for decision-making and planning long-term national strategies. With the implementation of the Sustainable Development Policy for Energy Consumption under Environmental Law ( S . D . E L ) , the forecast results derived from the SEM-VARIMAX Model indicate a continuously high change in energy consumption from 2020 to 2036the change exceeds the rate determined by the government. In addition, energy consumption is predicted to have an increased growth rate of up to 185.66% (2036/2020), which is about 397.08 ktoe (2036). The change is primarily influenced by a causal relationship that contains latent variables, namely, the economic factor ( E C O N ) , social factor ( S O C I ) , and environmental factor ( E N V I ) . The performance of the SEM-VARIMAX Model was tested, and the model produced a mean absolute percentage error (MAPE) of 1.06% and a root-mean-square error (RMSE) of 1.19%. A comparison of these results with those of other models, including the multiple linear regression model (MLR), back-propagation neural network (BP model), grey model, artificial neural natural model (ANN model), and the autoregressive integrated moving average model (ARIMA model), indicates that the SEM-VARIMAX model fits and is appropriate for long-term national policy formulation in various contexts in Thailand. This study’s results further indicate the low efficiency of Sustainable Development Policy for Energy Consumption under Environmental Law in Thailand. The predicted result for energy consumption in 2036 is greater than the government-established goal for consumption of no greater than 251.05 ktoe.

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Optimizing Ridge Generalized Least Squares for Structural Equation Modeling

Cited by 13 publications

References 19 publications

Distributionally weighted least squares in structural equation modeling.

Distributionally weighted least squares in structural equation modeling.

Prior Specification for More Stable Bayesian Estimation of Multilevel Latent Variable Models in Small Samples: A Comparative Investigation of Two Different Approaches

The Efficiency of the Sustainable Development Policy for Energy Consumption under Environmental Law in Thailand: Adapting the SEM-VARIMAX Model

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