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Maximal point-polyserial correlation for non-normal random distributions.

Alessandro Barbiero1

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Summary
This summary is machine-generated.

This study introduces methods to maximize point-polyserial correlation between continuous and ordinal variables. It presents formulas and algorithms for finding optimal discrete variable values, enhancing data analysis.

Keywords:
attainable correlationsbiserial correlationdiscretizationlatent variablenon‐normal distribution

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Area of Science:

  • Statistics
  • Data Analysis

Background:

  • The point-polyserial correlation measures the association between a continuous and an ordinal variable.
  • Determining the maximum possible correlation requires optimizing the discrete variable's structure.

Purpose of the Study:

  • To derive a closed-form formula for the maximal point-polyserial correlation for various distributions.
  • To develop a numerical algorithm for finding this maximum value.
  • To investigate the equivalence between optimizing ordinal variable values and optimal quantization.

Main Methods:

  • Derivation of closed-form formulas for maximal point-polyserial correlation.
  • Development of a numerical algorithm for optimization.
  • Proof of equivalence to optimal quantization when ordinal values are not pre-assigned.

Main Results:

  • Formulas and algorithms provided for maximizing point-polyserial correlation.
  • Demonstration that optimizing ordinal variable values is equivalent to optimal quantization.
  • Potential for significant increase in correlation by including ordinal value optimization.

Conclusions:

  • The study offers practical tools for maximizing the association between continuous and ordinal data.
  • Optimal quantization provides a framework for enhancing point-polyserial correlation.
  • Findings are applicable to real-world data analysis and statistical modeling.