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Not all that wiggle are LOESS: Archaeological detection of multimillennial population dynamics using proportionate juvenility indexes and radial basis function logistic regression

William Brown

Archaeological demography presents population researchers with unique opportunities to monitor human population dynamics over vast expanses of time, allowing us to better evaluate relationships between ongoing changes in population and in natural and human systems. Over the last two decades, a distinctive research framework has emerged in archaeological demography coupling the calculation of timestamped proportionate juvenility indexes (PJIs) and the application of robust locally weighted regression (i.e. 'local estimation' or LOESS) toward the modeling of temporal trends in these indexes. PJIs summarize the age-at-death distributions of cemetery populations based on the relative frequency of juvenile members and are regarded as proxies for both period fertility and population growth rates. When applied to the temporal modeling of PJIs, LOESS often yields satisfyingly nonmonotonic trends, coherent with the intuition of similarly nonmonotonic long-run population dynamics.

However, LOESS is poorly suited to the analysis of count data, including PJIs. It also tends to yield nonmonotonic models when presented with data showing gaps in the independent variable(s). Finally, guidance is thin regarding the optimization of LOESS's tuning parameters, as well as for including LOESS models alongside others in model selection. In this presentation I introduce an alternative approach to the modeling of PJI temporal trends, radial basis function logistic regression, which overcomes these limitations. I illustrate the utility of this approach based on a preliminary analysis of recently published PJI data from Mainland Southeast Asia, spanning a 5500-year period and the emergence of intensive agricultural economies in the region.