Path analysis and maximum likelihood
Bill Shipley · Cambridge University Press eBooks · 2016
James Burke (1996), in his fascinating book The Pinball Effect , demonstrates the curious and unexpected paths of influence leading to most scientific discoveries. People often speak of the ‘marriage of ideas’. If this is true then the most prolific intellectual offspring come not from the arranged marriages preferred by research administrators but from chance meetings, and even illicit unions. The popular view of scientific discoveries as being linear causal chains from idea to solution is profoundly wrong; a better image would be a tangled web with many dead ends and broken strands. If most present knowledge depends on unlikely chains of events and personalities, what paths of discovery have been deflected because the right people did not come together at the right time? Which historical developments in science have been changed because two people, each with one half of the solution, were prevented from communicating due to linguistic or disciplinary boundaries? The second stage in the development of modern structural equation modelling is a case study in such historical contingencies and interdisciplinary incomprehension. During the First World War, and in connection with the American war effort, Sewall Wright was on a committee allocating pork production to various states based on the availability of corn. He was confronted with a problem that had a familiar feel. Given a whole series of variables related to corn availability and pork production, how do all these variables interact to determine the relationship between supply and demand, and the fluctuations between these two? It occurred to him that his new method of path analysis might help. He calculated the correlation coefficients between each pair of variables for five years, giving 510 separate correlations. After much trial and error he developed a model involving only four variables (corn price, summer hog price, winter hog price and hog breeding) and only fourteen paths that still gave a ‘good match’ between observed and predicted correlations. He described his results in a manuscript that was submitted as a bulletin of the US Bureau of Animal Industry. It was promptly rejected, perhaps because officials at the Bureau of Agricultural Economics considered it as an intrusion onto their turf. Happily for Wright, he had also shown it to the son of the secretary of agriculture (Henry A. Wallace), who was interested in animal breeding and quantitative modelling.