Graduate How Does Maximum Likelihood Estimate Factor Loadings in PCA Path Models?

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Maximum Likelihood Estimation (MLE) is used to derive factor loadings in Principal Component Analysis (PCA) path models from correlation matrices. The discussion highlights the challenge of determining the appropriate parameters and population for constructing a path diagram with one or more factors. The "reverse" exercise mentioned involves starting with a correlation matrix to create a path model. Understanding the relationship between factors and variables is crucial for accurate modeling. Clarification on these concepts is essential for effective application in PCA path analysis.
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Trying to understand the role of Maximum Likelihood in PCA.
Hi,
I am looking into a text on PCA obtained through path diagrams ( a diagram rep of the relationship between factors and the dependent and independent variables) and correlation matrices . There is a "reverse" exercise in which we are given a correlation matrix there is mention of the use of Max Likelihood used to obtain a path model that uses a single factor in PCA. I am having trouble figuring out just what parameter and even what population we are using to derive a path diagram with a single ( or any number of ) factors. Thanks.
 
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