Maximally selected chi-square statistics and binary splits of nominal variables.

Area of Science:

• Statistics
• Biostatistics
• Computational Statistics

Background:

• Maximally selected chi-square statistics are used for variable selection.
• Existing methods cover continuous or ordinal predictor variables.
• The distribution for nominal predictor variables was previously unaddressed.

Purpose of the Study:

• To derive the exact distribution of the maximally selected chi-square statistic for a binary outcome and a nominal predictor.
• To provide a method for variable selection and hypothesis testing with nominal predictors.
• To illustrate the application of the derived distribution using real-world data.

Main Methods:

• A combinatorial approach was used to derive the exact distribution.
• Simulations were conducted to assess the applications of the derived distribution.
• The method was applied to a birth data set for practical illustration.

Main Results:

• The exact distribution of the maximally selected chi-square statistic for nominal predictors was successfully derived.
• The derived distribution enables accurate variable selection and hypothesis testing.
• Simulations confirmed the utility and applicability of the new method.

Conclusions:

• The derived distribution provides a valuable tool for statistical analysis involving nominal predictor variables.
• This research fills a gap in the methodology for maximally selected chi-square statistics.
• The findings have practical implications for various fields, including biostatistics and social sciences.