| 1. |
- Giordano, Michael L., et al.
(author)
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Estimating and Testing Random Intercept Multilevel Structural Equation Models with Model Implied Instrumental Variables
- 2022
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In: Structural Equation Modeling. - : Taylor & Francis Group. - 1070-5511 .- 1532-8007. ; 29:4, s. 584-599
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Journal article (peer-reviewed)abstract
- This study develops a new limited information estimator for random intercept Multilevel Structural Equation Models (MSEM). It is based on the Model Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS) estimator, which has been shown to be an excellent alternative or supplement to maximum likelihood (ML) in SEMs (Bollen, 1996). We also develop a multilevel overidentification test statistic that applies to equations at the within or between levels. Our Monte Carlo simulation analysis suggests that MIIV-2SLS is more robust than ML to misspecification at within or between levels, performs well given fewer than 100 clusters, and shows that our multilevel overidentification test for equations performs well at both levels of the model.
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| 2. |
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| 3. |
- Jin, Shaobo, et al.
(author)
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A Marginal Maximum Likelihood Approach for Extended Quadratic Structural Equation Modeling with Ordinal Data
- 2020
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In: STRUCTURAL EQUATION MODELING: A MULTIDISCIPLINARY JOURNAL. - USA : Taylor & Francis Group. - 1070-5511 .- 1532-8007. ; 27:6, s. 864-873
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Journal article (peer-reviewed)abstract
- The literature on non-linear structural equation modeling is plentiful. Despite this fact, few studies consider interactions between exogenous and endogenous latent variables. Further, it is well known that treating ordinal data as continuous produces bias, a problem that is enhanced when non-linear relationships between latent variables are incorporated. A marginal maximum likelihood-based approach is proposed in order to fit a non-linear structural equation model, including interactions between exogenous and endogenous latent variables in the presence of ordinal data. In this approach, the exact gradient of the approximated observed log-likelihood is calculated in order to attain the approximated maximum likelihood estimator. A simulation study shows that the proposed method provides estimates with low bias and accurate coverage probabilities
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| 4. |
- Jin, Shaobo, et al.
(author)
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A Simulation Study of Polychoric Instrumental Variable Estimation in Structural Equation Models
- 2016
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In: Structural Equation Modeling. - : Informa UK Limited. - 1070-5511 .- 1532-8007. ; 23:5, s. 680-694
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Journal article (peer-reviewed)abstract
- Data collected from questionnaires are often in ordinal scale. Unweighted least squares (ULS), diagonally weighted least squares (DWLS) and normal-theory maximum likelihood (ML) are commonly used methods to fit structural equation models. Consistency of these estimators demands no structural misspecification. In this article, we conduct a simulation study to compare the equation-by-equation polychoric instrumental variable (PIV) estimation with ULS, DWLS, and ML. Accuracy of PIV for the correctly specified model and robustness of PIV for misspecified models are investigated through a confirmatory factor analysis (CFA) model and a structural equation model with ordinal indicators. The effects of sample size and nonnormality of the underlying continuous variables are also examined. The simulation results show that PIV produces robust factor loading estimates in the CFA model and in structural equation models. PIV also produces robust path coefficient estimates in the model where valid instruments are used. However, robustness highly depends on the validity of instruments.
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| 5. |
- Jin, Shaobo, 1987-, et al.
(author)
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H-Likelihood Approach to Factor Analysis for Ordinal Data
- 2018
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In: Structural Equation Modeling. - : Informa UK Limited. - 1070-5511 .- 1532-8007. ; 25:4, s. 530-540
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Journal article (peer-reviewed)abstract
- Marginal likelihood-based methods are commonly used in factor analysis for ordinal data. To obtain the maximum marginal likelihood estimator, the full information maximum likelihood (FIML) estimator uses the (adaptive) Gauss-Hermite quadrature or stochastic approximation. However, the computational burden increases rapidly as the number of factors increases, which renders FIML impractical for large factor models. Another limitation of the marginal likelihood-based approach is that it does not allow inference on the factors. In this study, we propose a hierarchical likelihood approach using the Laplace approximation that remains computationally efficient in large models. We also proposed confidence intervals for factors, which maintains the level of confidence as the sample size increases. The simulation study shows that the proposed approach generally works well.
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| 6. |
- Jin, Shaobo, 1987-
(author)
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On Inconsistency of the Overidentification Test for the Model-implied Instrumental Variable Approach
- 2023
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In: Structural Equation Modeling. - : Routledge. - 1070-5511 .- 1532-8007. ; 30:2, s. 245-257
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Journal article (peer-reviewed)abstract
- In the context of structural equation modeling, the model-implied instrumental variable (MIIV) approach has been shown to be more robust against model misspecification than the systemwide approaches (e.g., maximum likelihood and least squares). Besides the goodness-of-fit tests that test the fit of the entire hypothesized covariance structure, the overidentification tests for MIIV can be used to test model specification on an equation-by-equation basis. However, it is known in the econometrics literature that the overidentification tests are inconsistent against general misspecification, if it is used to test a zero correlation between the instrumental variables and the error terms. In this paper, we show that such inconsistency can also occur for the MIIV approach. Numerical examples where the powers of the tests converge to the size are presented. Theoretical results are proved to support the numerical findings. Implications on when the overidentification tests are consistent are also presented.
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| 7. |
- Jin, Shaobo, 1987-, et al.
(author)
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Robust nonlinear structural equation modeling with interaction between exogenous and endogenous latent variables
- 2021
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In: Structural Equation Modeling. - : Taylor & Francis Group. - 1070-5511 .- 1532-8007. ; 28:4, s. 547-556
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Journal article (peer-reviewed)abstract
- A handful of studies have been devoted to nonlinear structural equation modeling (SEM) in the literature. However, they generally overlooked the interactions among exogenous and endogenous latent variables and the interactions among endogenous latent variables. In this study, we propose a maximum likelihood approach for a nonlinear SEM model that incorporates such overlooked interactions. We also propose a two-stage pseudo maximum likelihood approach under the assumption of a normal mixture, being computationally efficient and robust against distributional misspecification. The simulation study shows that both approaches accurately estimate the unknown parameters if the distribution is correctly specified. However, only the pseudo maximum likelihood approach is robust against distributional misspecification.
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| 8. |
- Jöreskog, Karl
(author)
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Classical Models for Twin Data
- 2021
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In: Structural Equation Modeling. - : Taylor & Francis. - 1070-5511 .- 1532-8007. ; 28:1, s. 121-126
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Journal article (peer-reviewed)abstract
- The classical models ACE and ADE were used in the 1990s to estimate heredity of a phenotype from data on monozygotic and dizygotic twins. These models are extended to a model called ACDE with four parameters instead of only three. It is showed how these models can be easily estimated by maximum likelihood. The models and methods are extended to two populations in which the heredity is the same in both populations. Examples are given to estimate the heredity of BMI using twin data from the UK and Australia.
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| 9. |
- Jöreskog, Karl Gustav
(author)
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Classical Models for Twin Data : The Case of Categorical Data
- 2021
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In: Structural Equation Modeling. - : Taylor & Francis. - 1070-5511 .- 1532-8007. ; 28:6, s. 859-862
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Journal article (peer-reviewed)abstract
- The classical models ACE and ADE were used in the 1990's to estimate heredity of a phenotype from data on monozygotic and dizygotic twins. The author extended these models to a model called ACDE with four parameters instead of only three. In that paper, the data were assumed to be continuous. This paper considers the same models in the case where the data is categorical. It is showed how these models can be estimated by maximum likelihood. An example is given based on twin data on BMI from the UK. This is the same data as in the previous paper but in categorized form.
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| 10. |
- Kreiberg, David, et al.
(author)
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A Faster Procedure for Estimating CFA Models Applying Minimum Distance Estimators with a Fixed Weight Matrix
- 2020
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In: Structural Equation Modeling. - : Informa UK Limited. - 1070-5511 .- 1532-8007. ; 28:5, s. 725-739
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Journal article (peer-reviewed)abstract
- This paper presents a numerically more efficient implementation of the quadratic form minimum distance (MD) estimator with a fixed weight matrix for confirmatory factor analysis (CFA) models. In structural equation modeling (SEM) computer software, such as EQS, lavaan, LISREL and Mplus, various MD estimators are available to the user. Standard procedures for implementing MD estimators involve a one-step approach applying non-linear optimization techniques. Our implementation differs from the standard approach by utilizing a two-step estimation procedure. In the first step, only a subset of the parameters are estimated using non-linear optimization. In the second step, the remaining parameters are obtained using numerically efficient linear least squares (LLS) methods. Through examples, it is demonstrated that the proposed implementation of MD estimators may be considerably faster than what the standard implementation offer. The proposed procedure will be of particular interest in computationally intensive applications such as simulation, bootstrapping, and other procedures involving re-sampling.
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