Penalized power-divergence test statistics for testing linear-by-linear association

Abstract

Two different families of penalized power-divergence test statistics have been defined to find alternatives to the likelihood ratio and the Pearson chi-squared test statistics for testing linear- by-linear association in two-way contingency tables with empty cell(s). The exact size and power properties of these test statistics and the ordinary power-divergence test statistics have been studied based on an extensive designed simulation study. Different penalized test statistics have been proposed depending on their exact size and power performances.

Keywords:

• contingency table
• empty cells
• ordinal categorical variable
• linear-by-linear association
• log-linear model
• penalization
• power-divergence test statistics

2000 Mathematics Subject Classifications :

• 62H12
• 62H15
• 62H17

Acknowledgements

The author thanks Prof. Alan Agresti, the referee and Andrew Howe for their valuable comments about the manuscript.