Confidence regions for simple correspondence analysis using the Cressie-Read family of divergence statistics

When examining the association between symmetrically associated categorical variables, correspondence analysis provides a visual means of identifying the structure of this association. An important and sometimes overlooked feature that can help the analyst determine whether those categories that provide a statistically significant contribution to the association is the confidence region. When constructing these regions, correspondence analysis traditionally (but not always) considers Pearson's chi-squared statistic as the core measure of association between the variables. Such a statistic is a special case of the Cressie-Read family of divergence statistics as is the log-likelihood ratio statistic, Freedman-Tukey statistic, and other such measures. Therefore, this paper will consider the construction of confidence regions in correspondence analysis where this family of divergence statistics is used as the measure of association. Doing so provides a means of simply constructing confidence regions for each category of a contingency table and allows for such regions to be constructed when log-ratio analysis (LRA) or the Hellinger distance decomposition (HDD) method is applied to the contingency table.