This is a simulation of some of the ideas in a preprint by Claeskens et al, offering a new theoretical explanation of the forecast combination puzzle. Claeskens, Gerda & Magnus, Jan R. & Vasnev, Andrey L. & Wang, Wendun, 2016. “The forecast combination puzzle: A simple theoretical explanation,” International Journal of Forecasting, Elsevier, vol. 32(3), pages 754-762.

(Corrected.) Which heuristics do well on wide, noisy data? Wide means lots of cues relative to rows. Integrating information can be better than using the best cues in this case.

Updated to use ttbBinModel.

Compare heuristics like Take the Best, a unit-weight linear model, and multiple linear regression on wide, noisy data sets, such as those found in genetics.

This is the source data for: http://www-abc.mpib-berlin.mpg.de/sim/Heuristica/environments/shl.world (That version is missing column headers, and cue/predictor values were binaritized at the median.) The data name has been prefixed by "abc" because it was originally used for research in the Adaptive Behavior and Cognition group: https://www.mpib-berlin.mpg.de/en/research/adaptive-behavior-and-cognition The data is based on: Morton, Felicia B. (1995). Charting a School¹s Course. Chicago. February, pp. 86-95. Rodkin, Dennis. (1995). 10 Keys for Creating Top High Schools. Chicago. February, pp. 78-85.

A first rough draft of using resampling and ggplot2 to visualize sample variance. I illustrate with a data set on high school drop-out rates.