Nominal Association Vector and Matrix

Nominal data are quite common in scientific and engineering research related to biomedical research, consumer behavior analysis, network analysis and search engine marketing optimization. When the population is cross-classified and there is no natural ordering for observed outcomes, association analysis as described in Han and Kamber (2006) can be described nominal association measures. Even if the categorical variables collected in these studies are ordinal, they are often treated as nominal if the ordering is not of interest or a natural and meaningful metric is difficult to establish. When the response variable is multinomial, the classical probabilistic measure such as odds ratio or relative risk are difficult to use due to the multiple 1 levels in the response variable. Instead, the principle of optimal (conditional mode based) or proportional (conditional Monte-Carlo based) prediction can be used to construct nonparametric nominal association measures. For example, Goodman-Kruskal (1954) and others proposed some local-to-global association measures towards optimal predictions. The proportional associations between variables are probabilistically and statistically intrinsic. It reflects the probabilistically averaging effects of input on output distributions. There are quite a few proportional association measures proposed in the literature (cf.