Keywords: two-way tables, additive model, least-absolute-value estimation
Least-absolute-value Estimation in Two-way Tables and its Application to Explaining Variation in Flight Times
Natasha Yakovchuk
Ph.D. student
Department of Decision Sciences and Engineering Systems
Rensselaer Polytechnic Institute
Thomas R. Willemain, Ph.D.
Professor
Department of Decision Sciences and Engineering Systems
Rensselaer Polytechnic Institute
Data structures known as two-way tables or two-way layouts have each of two factors varying separately, and a single response value observed for each combination of these factors. Such tables arise in many fields like socioeconomic studies, engineering experiments or transportation problems. The easiest and the most natural way to interpret the joint contribution of the factors is by decomposing the response in each cell as
response = common effect + row effect + column effect + residual
The most used technique for estimating effects is classical least squares, as in ANOVA.
We consider a two-way table of temporal deviations from flight plans for commercial US flights. We interpret the factors as system, origin and destination effects, and the residuals as en route effects. Classical least-squares estimation fails to give good estimates in this case because it is not resistant to outliers and 'holes' in the table. We illustrate the use of more robust least-absolute-values (LAV) estimation with the aviation data and present graphical displays derived from the LAV estimates.