# A Hybrid Symbolic/Numeric Solution To Polynomial SEM

@inproceedings{Oldenburg2021AHS, title={A Hybrid Symbolic/Numeric Solution To Polynomial SEM}, author={Reinhard Oldenburg}, year={2021} }

There are many approaches to nonlinear SEM (structural equation modeling) but it seems that a rather straightforward approach using Isserlis’ theorem has not yet been investigated although it allows the direct extension of the standard linear approach to nonlinear linear SEM. The reason may be that this method requires some symbolic calculations done at runtime. This paper describes the class of appropriate models and outlines the algorithm that calculates the covariance matrix and higher… Expand

#### References

SHOWING 1-10 OF 12 REFERENCES

Fitting Nonlinear Structural Equation Models in R with Package nlsem

- Mathematics
- 2017

Structural equation mixture modeling (SEMM) has become a standard procedure in latent variable modeling over the last two decades (Jedidi, Jagpal, and DeSarbo'97b; Muthen and Shedden'99; Muthen 2001,… Expand

Estimation of nonlinear latent structural equation models using the extended unconstrained approach

- Psychology
- 2009

Numerous theories within the social and behavioral sci-ences hypothesize interaction, quadratic effects, or both between multiple independent and dependent variables (Ajzen, 1987; Cronbach & Snow,… Expand

A comparison of methods for estimating quadratic effects in nonlinear structural equation models.

- Mathematics, Medicine
- Psychological methods
- 2012

Of the 5 estimation methods, it was found that overall the methods based on maximum likelihood estimation and the Bayesian approach performed best in terms of bias, root-mean-square error, standard error ratios, power, and Type I error control, although key differences were observed. Expand

Advanced Nonlinear Latent Variable Modeling: Distribution Analytic LMS and QML Estimators of Interaction and Quadratic Effects

- Mathematics
- 2011

Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x 1 2,… Expand

Interaction and Nonlinear Effects in Structural Equation Modeling

- Computer Science
- 1998

This paper presents a comparison review of Interaction and Nonlinear Modeling in the context of EQS and LISREL, and outlines the approaches taken to estimate nonlinear effects using a Structured Means Intercept approach. Expand

Maximum likelihood estimation of latent interaction effects with the LMS method

- Mathematics
- 2000

In the context of structural equation modeling, a general interaction model with multiple latent interaction effects is introduced. A stochastic analysis represents the nonnormal distribution of the… Expand

Handbook of structural equation modeling

- Computer Science
- 2012

This work focuses on the implementation of Structural Equation Modeling in R with the sem and OpenMx Packages and on the development of scale construction and development models for this and other applications. Expand

Structural Equations With Latent Variables

- Computer Science
- 2016

The structural equations with latent variables is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can get it instantly. Expand

Bayesian estimation of single and multilevel models with latent variable interactions

- Computer Science
- Structural Equation Modeling: A Multidisciplinary Journal
- 2020

The Bayesian estimation for single and multilevel SEM models with latent variable interactions is described and it is shown through simulation studies that the Bayesian method outperforms other methods such as the maximum-likelihood method. Expand

Asymptotically distribution-free methods for the analysis of covariance structures.

- Mathematics, Medicine
- The British journal of mathematical and statistical psychology
- 1984

Methods for obtaining tests of fit of structural models for covariance matrices and estimator standard errors which are asymptotically distribution free are derived. Modifications to standard normal… Expand