A smooth subclass of graphical models for chain graph: towards measuring gender gaps

Recent gender literature shows a growing demand of sound statistical methods for analysing gender gaps, for capturing their complexity and for exploring the pattern of relationships among a collection of observable variables selected in order to disentangle the latent trait of gender equity. In this paper we consider parametric Hierarchical Marginal Models applying to binary and categorical data, as a promising statistical tool for gender studies. We explore the potential of Chain Graphical Models, by focusing on a special smooth subclass of models known as Graphical Models of type II as recently developed (Nicolussi in Marginal parameterizations for conditional independence models and graphical models for categorical data, 2013) i.e. an advanced methodology for untangling and highlighting any dependence/independence pattern between gender and a set of covariates of mixed nature, either categorical, ordinal or quantitative. With respect to traditional methodologies for treating categorical variables, such as Logistic Regression and Chi-Squared test for contingency table, the proposed model lead to a full multivariate analysis, allowing for isolating the effect of each dependent variable from all other response variables. At the same time, the resulting graph offers an immediate visual idea of the association pattern in the entire set of study variables. The empirical performance of the method is tested by using data from a recent survey about sexual harassment issues inside university, granted by the Equal Opportunities Committee of the University of Milano-Bicocca (Italy).