Measure of Proportional Reduction in Variation for Multi-Way Contingency Tables with Multiple Response Variables | ||
| The Egyptian Statistical Journal | ||
| Article 6, Volume 43, Issue 2, December 1999, Pages 167-182 PDF (6.06 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.1999.314528 | ||
| Authors | ||
| Sadao Tomizawa* ; Mitsuaki Machida | ||
| Dep. of Information Sciences, Faclty of Science & Technology Science University of Tokyo, Japan | ||
| Abstract | ||
| For a two-way contingency table with an explanatory and a response variables, Tomizawa, Seo and Ebi (1997) proposed a measure which describes the proportional reduction in variation from the marginal distribution to the conditional distributions of the response. Also, Tomizawa and Ebi (1998) extended this measure into a multi-way contingency table with only one response variable (and the multiple explanatory variables). This paper extends these measures into a multi-way contingency table with multiple L (L ≥ 2) response variables (and the multiple explanatory variables), which have nominal categories. Examples are given. | ||
| Keywords | ||
| Association; Gini Concentration; Independence; Patil and Taillie's Diversity Index; Multiple Response; Shannon Entropy; Variation | ||
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