Perturbation Selection and Local Influence Analysis for Nonlinear Structural Equation Model

A Monte Carlo simulation was performed for estimating and testing hypotheses of three-way interaction effect in latent variable regression models. A considerable amount of research has been done on estimation of simple interaction and quadratic effect in nonlinear structural equation. The present study extended to three-way continuous latent interaction in structural equation model. The latent moderated structural equation (LMS) approach was used to estimate the parameters of the three-way interaction in structural equation model and investigate the properties of the method under different conditions though simulations. The approach showed least bias, standard error,and root mean square error as indicator reliability and sample size increased. The power to detect interaction effect and type I error control were also manipulated showing that power increased as interaction effect size, sample size and latent covariance increased.

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NONLINEAR STRUCTURAL ESTIMATION OF LOCALIZED NETWORK USING HOMOTOPHIC TOPOLOGICAL (2(N)+1) DIMENSIONAL FOR DISTANCE THEORY (HTD-DT)

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.10.5.10 ◽

2021 ◽

Vol 10 (5) ◽

pp. 2419-2431

Author(s):

R. Ramya ◽

P. Chandrasekaran

Keyword(s):

Structural Equation ◽

Structural Estimation ◽

Distance Estimation ◽

Simulated Data ◽

Linear Structure ◽

Equation Model ◽

Gradient Algorithm ◽

Dimension Theory ◽

Nonlinear Structural ◽

Nonlinear Structural Equation

A Nonlinear Structural Equation Model (NLSEM) is formed on the basis of various dimension in normal mutual estimation depending on Distance Estimation Theory (DET) and its complex networks structure. The homotophy linear topography analyze the dimension of formal network in hidden paths to consider the linear structure. However, dimension theory is a linear dependence between the variables for observation is problem in nature of distance estimation along the node and these approaches have limitations to form shortest communication. This paper proposes the Nonlinear structural estimation of localized network using homotphic topological (2 (n)+1) dimensional for distance theory Structure equation model based on the Probability distribution theory of evaluation model (PDTE) that compensates for the potential innumerable dependencies between network points. For this unstructural reason, network densities are provided to take advantage of the lower specific margins of density that are present in most real-world networks. The Gambier IV order $(y \frac{d^2 y}{dt^2} (\alpha, \beta)$, complex constant) is used to optimize the Painleve I order $(X’=X’^{(dy/dt)}y^2 + t)$ equation to derive the neighborhood singularities to estimate the distance. This computational provides an efficient integration to the diagonal gradient algorithm has been developed to estimate the SEM coefficients of polymorphic formation and therefore infer the edge structures on distance estimation. Preliminary testing of simulated data demonstrates the effectiveness of the new approach produce high estimation with lower redundancy steps of mathematical solvation.

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Maximum Likelihood Analysis of a Two-Level Nonlinear Structural Equation Model With Fixed Covariates

Journal of Educational and Behavioral Statistics ◽

10.3102/10769986030001026 ◽

2005 ◽

Vol 30 (1) ◽

pp. 1-26 ◽

Cited By ~ 14

Author(s):

Sik-Yum Lee ◽

Xin-Yuan Song

Keyword(s):

Maximum Likelihood ◽

Structural Equation Model ◽

Latent Variables ◽

Structural Equation ◽

Model Comparison ◽

Real Data ◽

Equation Model ◽

Data Set ◽

Nonlinear Structural Equation ◽

Monte Carlo Em

In this article, a maximum likelihood (ML) approach for analyzing a rather general two-level structural equation model is developed for hierarchically structured data that are very common in educational and/or behavioral research. The proposed two-level model can accommodate nonlinear causal relations among latent variables as well as effects of fixed covariate in its various components. Methods for computing the ML estimates, and the Bayesian information criterion (BIC) for model comparison are established on the basis of powerful tools in statistical computing such as the Monte Carlo EM algorithm, Gibbs sampler, Metropolis–Hastings algorithm, conditional maximization, bridge sampling, and path sampling. The newly developed procedures are illustrated by results obtained from a simulation study and analysis of a real data set in education.

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