Entropy-Based Solutions for Ecological Inference Problems: A Composite Estimator

Abstract

Information-based estimation techniques are becoming more popular in the field of Ecological Inference. Within this branch of estimation techniques, two alternative approaches can be pointed out. The first one is the Generalized Maximum Entropy (GME) approach based on a matrix adjustment problem where the only observable information is given by the margins of the target matrix. An alternative approach is based on a distributionally weighted regression (DWR) equation. These two approaches have been studied so far as completely different streams, even when there are clear connections between them. In this paper we present these connections explicitly. More specifically, we show that under certain conditions the generalized cross-entropy (GCE) solution for a matrix adjustment problem and the GME estimator of a DWR equation differ only in terms of the a priori information considered. Then, we move a step forward and propose a composite estimator that combines the two priors considered in both approaches. Finally, we present a numerical experiment and an empirical application based on Spanish data for the 2010 year.

Forecasting: theory and practice

“…After them, some key references include McCarthy and Ryan (1977), Tziafetas (1986), Corominas et al (2015), and Romero et al (2020). Solutions based on other strategies, for instance, entropy maximization, have been also suggested (see, for example, Johnston and Pattie, 2000;Bernardini Papalia and Fernandez Vazquez, 2020).…”

ei.Datasets: Real Data Sets for Assessing Ecological Inference Algorithms

“…Different procedures have been proposed in the literature to learn about the internal cells' values by exploiting, under the homogeneity hypothesis, the covariations that the row and column margins of the different tables display. The interested reader may find methods proposed from frameworks as diverse as frequentist and Bayesian statistics (e.g., Goodman, 1953Goodman, , 1959Greiner & Quinn, 2010;King, 1997;King et al, 1999King et al, , 2004Klima et al, 2019;Puig & Ginebra, 2015;Rosen et al, 2001), mathematical programming (e.g., Corominas et al, 2015;Hawkes, 1969;McCarthy & Ryan, 1977;Pavía & Romero, 2021a;Romero et al, 2020;Tziafetas, 1986), or information theory (e.g., Bernardini-Papalia & Fernández-Vázquez, 2020;Johnston & Pattie, 2000;. Some of the above methods are programmed in different R packages: MCMCpack (Martin et al, 2011), eiwild (Schlesinger, 2014), ei (King & Roberts, 2016), eco (Imai et al, 2017), RxCEcolInf (Greiner et al, 2019), eiPack (Olivia et al, 2020), eiCompare (Collingwood et al, 2020), and lphom (Pavía & Romero, 2021b).…”

The Statistical Foundations of Entropy

“…In the first contribution [1], the authors discuss the important topic of ecological inference used to estimate individual behavior from the knowledge-aggregated data. The authors discuss two popular approaches: the Generalized Maximum Entropy approach and the Distributionally Weighted Regression equation.…”