This submit by John Cook dinner on the hierarchy of census divisions in the USA (nation, area, division, state, county, census tract, block group, census block, family, household, particular person) jogged my memory of one thing which I’ve talked about earlier than however by no means actually addressed. elaborated, which is the development of households of hierarchical fashions for taxonomic information constructions.
A couple of concepts come into play right here:
1. Taxonomic constructions typically come up in social sciences. Cook dinner provides the instance of geography. Two different examples are occupation and faith, every of which might be categorized into a number of ranges. Go to the Census Bureau classifications of industries and occupations or the numerous classes of faith, non secular denomination, and so on.
2. Hierarchical modeling. You probably have a nationwide survey of, say, 2,000 individuals categorized by county, you will not need to simply do a easy “”8 faculties“-hierarchical mannequin type, as a result of for those who try this you’ll cluster the small counties roughly as much as the nationwide common. You go need to embrace county-level predictors. A technique to do that is to incorporate indicators for state, division and area: that’s, a hierarchical mannequin on taxonomy. This is able to be a easy instance of the “unfolding flower” construction which expands to incorporate extra mannequin construction as extra information arrives, thus avoiding the issue that ordinary types of Weak priors grow to be very sturdy because the dimensionality of the mannequin will increase whereas information is collected. stay mounted (see part 3 of my Building of Bayesian fashions by pure thought article from 1996).
I feel there’s a connection right here with quantum mechanics, within the sense that when a system is heated, new power ranges seem.
3. Taxonomies are likely to have a fractal construction. Some nodes have numerous branches and many depth, others simply cease. For instance, within the taxonomy of non secular denominations, Christians could also be divided into Catholics, Protestants, and others, after which Protestants could also be divided into mainline and evangelical teams, every of which can be subdivided, whereas some others, resembling Mormons, won’t. will not be divided in any respect. Equally, some index entries in a ebook may have many sub-entries and will span a number of columns, inside which some sub-entries have many sub-sub-entries, and so on., and different entries represent just one line. You get the kind of lengthy tail distribution attribute of self-similar processes. Mandelbrot I wrote about this in 1955! This can be his first publication on fractals, a topic he labored on productively for a number of extra many years.
My colleagues and I’ve been working with some taxonomic fashions for geography-based voting:
– Part 5 of our 2002 article on the arithmetic and statistics of voting energy,
– Our current unpublished article, How democracies grow to be polarized: a multi-level perspective.
These are just like spatial fashions or community fashions, however structured particularly on the idea of a hierarchical taxonomy. Each articles include enjoyable math.
I feel there are some common rules right here, or at the least one thing extra to say on the topic.