Distance‐based logistic model for cross‐classified categorical data

Abstract

Logistic regression models are a powerful research tool for the analysis of cross-classified data in which a categorical response variable is involved. In a logistic model, the effect of a covariate refers to odds, and the simple relationship between the coefficients and the odds ratio often makes these the parameters of interest due to their easy interpretation. In this article we present a distance-based logistic model that allows a simple graphical interpretation of the association coefficients using the odds ratio in a contingency table. Two configurations are estimated, one for the rows and one for the columns, as the categories of a polytomous predictor and a nominal response variable respectively, such that the local odds ratio and the distances between the predictor and response categories are inversely related. The associations in terms of the odds ratios, or the ratios of the odds to their geometric means, are interpreted through distances for the most common coding schemes of the predictor variable, and the relationship between the distances related to different codings is investigated in its full dimension. The performance of the estimation procedure is analysed with a Monte Carlo experiment. The interpretation of the model and its performance, as well as its comparison with a two-step procedure involving first a logistic regression and then unfolding, is illustrated using real data sets.

A unified approach based on multidimensional scaling for calibration estimation in survey sampling with qualitative auxiliary information

“…For example, an interesting case is when several categorical explanatory variables are combined to conform a large number of profiles. [40][41][42] In this situation, the combination of categories forming the profiles causes a large number of auxiliary variables to emerge after recoding using dummy variables, and a problem of over-calibration may arise in this qualitative information framework. Other methods for selecting the optimal set of variables are also being investigated, in particular, related to combined MDS and cluster methods that allow reducing dimensionality.…”