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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Maximum Likelihood Analysis of Nonlinear Structural Equation Models With Dichotomous Variables.

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    Multivariate Behavioral Research
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    This study introduces a new maximum likelihood method for analyzing structural equation models with dichotomous data, essential for behavioral and social sciences. The approach effectively models nonlinear causal effects among latent variables, enhancing research capabilities.

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    Area of Science:

    • Behavioral Science
    • Psychological Research
    • Social Science

    Background:

    • Dichotomous variables are prevalent in behavioral, psychological, and social research.
    • Analyzing nonlinear causal effects in structural equation models with these variables presents challenges.

    Purpose of the Study:

    • To develop a maximum likelihood approach for structural equation models with dichotomous variables.
    • To effectively assess nonlinear causal effects among latent variables.

    Main Methods:

    • Augmenting observed dichotomous data with hypothetical missing data representing latent continuous measurements.
    • Implementing an Expectation-Maximization (EM) algorithm.
    • Approximating conditional expectations using Metropolis-Hastings within Gibbs sampling and conditional maximization for the M-step.

    Main Results:

    • The developed methodology provides a robust framework for analyzing complex relationships.
    • Convergence is monitored using bridge sampling, and standard errors are obtained.
    • Simulation studies and a real-world example demonstrate the method's utility.

    Conclusions:

    • The proposed maximum likelihood approach offers a viable solution for structural equation modeling with dichotomous data.
    • This method enhances the analysis of nonlinear causal effects in latent variable models.
    • The approach is applicable to various fields within the behavioral and social sciences.