Information-Based Parametrization of Log-Linear Models for Categorical Data Analysis

Valerie Girardin (1) , Justine Lequesne (1) , Anne Ricordeau (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

Zighera (App Stoch Mod Data Anal 1:93–108 1985) introduced a new parameterization of log-linear models for analyzing categorical data, directly linked to a thorough analysis of discrimination information through Kullback-Leibler divergence. The method mainly aims at quantifying in terms of information the variations of a binary variable of interest, by comparing two contingency tables – or sub-tables – through effects of explanatory categorical variables. The present paper settles the mathematical background necessary to rigorously apply Zighera’s parameterization to any categorical data. In particular, identifiability and good properties of asymptotically χ 2-distributed test statistics are proven to hold. Determination of parameters and all tests of effects due to explanatory variables are simultaneous. Application to classical data sets illustrates contribution with respect to existing methods.

Keywords: Categorical data; Contingency table; Kullback-Leibler divergence; Log-linear model; Odds ratio

Domains: Mathematics [math]; Statistics [math.ST]

Valerie Girardin, Justine Lequesne, Anne Ricordeau. Information-Based Parametrization of Log-Linear Models for Categorical Data Analysis. Methodology and Computing in Applied Probability, 2018, 20 (4), pp.1105-1121. ⟨10.1007/s11009-017-9597-9⟩. ⟨hal-02299589⟩