A Robust Approach to Categorical Data Analysis

摘要

Categorical data analysis is typically performed by fitting models to the observed counts in a contingency table using maximum likelihood. An inherent problem with maximum likelihood fits is their sensitivity to outlier cells, ones whose counts are not consistent with the presupposed model. Robust alternatives to maximum likelihood estimation, including least median of chi-squared residuals, least median of weighted squared residuals, and analogous methods using least trimmed functions, are proposed in this article. Equivariance and breakdown properties are discussed. Monte Carlo simulation results and three real examples are used to illustrate the properties of the estimators in practice. In particular, whereas the maximum likelihood estimates break down in the presence of outlying cells, the robust estimators do not as long as the contamination does not exceed the breakdown point. The proposed estimators perform similarly in the simulations; they are competitive with median polish when fitting independence, and generalize easily to other, more complex, models.