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A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n)  to the number of categories (k).
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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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How to Generate Non-normal Data for Simulation of Structural Equation Models.

S Mattson

    Multivariate Behavioral Research
    |January 19, 2016
    PubMed
    Summary

    This study introduces a method for generating non-normal data for structural equation model simulations. The procedure allows control over skewness and kurtosis in observed variables by transforming latent and error variables.

    Area of Science:

    • Statistics
    • Psychometrics
    • Computational Statistics

    Background:

    • Structural equation modeling (SEM) often requires normally distributed data for accurate simulations.
    • Generating non-normal data that adheres to a specified SEM structure presents a methodological challenge.
    • Existing methods may lack flexibility in controlling specific distributional characteristics.

    Purpose of the Study:

    • To propose a flexible procedure for generating non-normal data suitable for structural equation model simulations.
    • To demonstrate how univariate skewness and kurtosis of observed variables can be controlled.
    • To illustrate the application of the procedure using real-world examples and software.

    Main Methods:

    • A transformation method is applied to univariate random variables to generate latent and error variables.

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  • Data for observed variables are computed based on the specified structural equation model.
  • Restrictions are imposed on covariance matrices for latent and error variables.
  • Univariate distributions are utilized, allowing for a wide selection of distributions.

    • Main Results:

    • The proposed procedure successfully generates non-normal data for SEM simulations.
    • Controlling skewness and kurtosis in latent and error variables allows for a wide range of characteristics in observed variables.
    • The method is demonstrated to be effective for two distinct structural equation models.
    • The PRELIS software can be utilized to implement the data generation procedure.

    Conclusions:

    • The developed procedure offers a practical and flexible approach to generating non-normal data for SEM simulations.
    • Researchers can effectively manipulate skewness and kurtosis to better match real-world data characteristics.
    • The method enhances the utility of SEM simulations by accommodating a broader range of data distributions.