Burcu Yavuz is an advanced doctoral student in the Swette Center for Environmental Biotechnology, finishing her degree in Environmental Engineering in the School for Sustainable Engineering and the Built Environment. While writing her dissertation, she has partly focused on applying the mathematical tools she learned through her years in Public Health to some of the problems of environmental engineering. One such tool, logistic regression, will form the cornerstone of her analysis of the toxicological effects of ozone gas to treat recalcitrant crude oil. Today, during lab meeting, she shared a brief insight into her quantitative, linguistic, and philosophical approach to the cornerstone of the logistic regression method, the logit, or log-odds of an outcome.
We have a tradition, in the Rittmann Lab, of sharing the etymology and usage of interesting words with each other, and Burcu was able to connect the etymology of the word “Odd” and later, “Odds,” with the mathematical understanding of the log-odds. The exact understanding of an Odds has important implications for Burcu’s work on this topic, since she limits her data outcomes to binary events (i.e. 1 or 0).
She began her presentation by noting that the etymological heritage of the word “odd” is steeped in the concepts of “evenness” or “fairness”. In other words, at its deepest word roots, the word seems to evaluate how things turn out, whether they or even, and fair, or whether they are “odd”, strange, and ultimately yield an unequal outcome. This was an exciting etymological finding, especially when considering the ultimate use of the logistic regression method to evaluate the potential for different outcomes.
She started by discussing some key advantages of using a binary classification to the outcome of an event. First, the mean of such an outcome is the exact proportion of cases with a value of “1” and can be interpreted as a probability (Pi) of that event occurring, while the proportion of negative cases with a value of “0” ranges of rom 1 to 0. The ratio, then, of Pi/1-Pi, or the odds of a given outcome, ranges from 0 to +∞.
Again, she notes the etymological connection between something that violates “fairness” (i.e. odd), with a comparison of potential outcomes. Within a matter of 200 years, the word “odd” had been extended to the word “odds” used to discuss the relative strength of one outcome or another. Burcu goes onto discuss the conceptual ways in which we think about the way things turn out, or the “odds” of something happening.
Back to the numbers, Burcu notes that this first transformation, from a probability to an odds, removes the “ceiling”, or the upper limit, by which a dependent binary outcome can vary; this transformation is especially important when a binary dependent outcome is predicted by a continuous independent variable, which would usually have greater ranges than that delimited by an outcome varying from 0 to 1 only.
Finally, Burcu shows how the natural log of the odds, otherwise known as the logit transformation, ranges from -∞ to +∞, and removes the “floor”, or lower limit, of the probabilistic outcome. She summarized these transformations in a single slide.
Using the quintessential dice roll as an example, Burcu also showed that the log-odds has advantages over the probability in that changes in the extreme ends of a probabilistic outcome are easier to graphically examine and interpret.
Burcu’s talk prompted Fellow PhD student and mathematical modeler in the Rittmann group, Isa Peraza to share a documentary, in the Zoom chat, on Netflix, about statistics, called Prediction by the Numbers (on Nova). The trailer teases, “Every day, mathematics and data combine to help us imagine what might be…”
In the discussion after the talk, Bruce and Rick referenced the Independent Order of Odd Fellows (IOOF), a non-political and non-sectarian fraternity that promotes the ethic of reciprocity and charity. Their “activities aim to improve and elevate every person to a higher, nobler plane; to extend sympathy and aid to those in need, making their burdens lighter, relieving the darkness of despair; to war against vice in every form, and to be a great moral power and influence for the good of humanity.” How appropriate it was to close our meeting by acknowledging a group considered odd devoted to making the world a more fair and even-handed place, like Burcu and the Members of our Center!
Compiled by Carole Flores, Business Manager
ASU Biodesign Institute | Biodesign Swette Center for Environmental Biotechnology
e: carole.flores@asu.edu | t: 480.727.0395
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Edited by Burcu Manolya Yavuz, Dean’s Fellow, Fulton Fellow, Science Foundation of Arizona Fellow Graduate Research Associate | Swette Center for Environmental Biotechnology
The Biodesign Institute at Arizona State University http://rittmann.environmentalbiotechnology.org/