Maximal Point-Polyserial Correlation for Non-Normal Random Distributions
Author Information
Author(s): Alessandro Barbiero
Primary Institution: Università degli Studi di Milano
Hypothesis
The study aims to derive the expression for the maximal point-polyserial correlation between a continuous random variable and an ordinal random variable with k categories.
Conclusion
The maximum point-polyserial correlation can be significantly increased by optimizing the scores assigned to the ordinal random variable.
Supporting Evidence
- The study provides a closed-form formula for the maximal point-polyserial correlation as a function of the probabilities and parameters of the distribution.
- An algorithm is devised to obtain the maximum value numerically for any given number of categories.
- The findings are illustrated with real data examples.
Takeaway
This study looks at how to find the best way to measure the relationship between a continuous number and a set of ordered categories, like ratings from 1 to 5.
Methodology
The study derives closed-form formulas for the maximal point-polyserial correlation and uses numerical algorithms to find maximum values for various distributions.
Limitations
The study does not specify the joint distribution of the continuous and ordinal variables, which may affect the results.
Digital Object Identifier (DOI)
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