The overlooked potential of Generalized Linear Models in astronomy, I: Binomial regression

Abstract

Revealing hidden patterns in astronomical data is often the path to fundamental scientific breakthroughs; meanwhile the complexity of scientific inquiry increases as more subtle relationships are sought. Contemporary data analysis problems often elude the capabilities of classical statistical techniques, suggesting the use of cutting edge statistical methods. In this light, astronomers have overlooked a whole family of statistical techniques for exploratory data analysis and robust regression, the so-called Generalized Linear Models (GLMs). In this paper -the first in a series aimed at illustrating the power of these methods in astronomical applications -we elucidate the potential of a particular class of GLMs for handling binary/binomial data, the so-called logit and probit regression techniques, from both a maximum likelihood and a Bayesian perspective. As a case in point, we present the use of these GLMs to explore the conditions of star formation activity and metal enrichment in primordial minihaloes from cosmological hydro-simulations including detailed chemistry, gas physics, and stellar feedback. We predict that for a dark mini-halo with metallicity ≈ 1.3 × 10 −4 Z , an increase of 1.2 × 10 −2 in the gas molecular fraction, increases the probability of star formation occurrence by a factor of 75%. Finally, we highlight the use of receiver operating characteristic curves as a diagnostic for binary classifiers, and ultimately we use these to demonstrate the competitive predictive performance of GLMs against the popular technique of artificial neural networks.

Do the stellar populations of the brightest two group galaxies depend on the magnitude gap?

“…We adopted the logistic regression approach (see e.g. Hilbe 2009;de Souza et al 2015) to compute the propensity scores and the nearest-neighbour method to perform the matching (see details in appendix B). As we discuss in appendix B, LGGs are typically less massive than SGGs.…”

A case study of hurdle and generalized additive models in astronomy: the escape of ionizing radiation

“…Linear models are the second to none if these assumptions are not violated. However, in astronomy, these assumptions are frequently not satisfied, and more flexible models have been developed to defeat these limitations (De Souza et al 2015a;Elliott et al 2015;De Souza et al 2015c. Fitting procedures and conducting statistical inferences have been reviewed not only for linear models but also for generalized linear models, binomial regression, beta regression and generalized additive models.…”

UV bright red-sequence galaxies: how do UV upturn systems evolve in redshift and stellar mass?

“…To model the presence or absence of UV upturn, we employed a Bayesian logistic regression (see Hilbe et al 2017, for a review). Logistic regression has been previously used in astronomy, for example, to probe the likelihood of starforming activity in primordial galaxies (De Souza et al 2015), or to model the environmental effects in the presence/absence of AGN (De Souza et al 2016). It generally aims to model binomial (binary) data.…”