The Promising Future of Mathematical Sociology

May 11, 2012

I strongly believe sociology, especially mathematical sociology, has an extremely promising future. The current trends in information technology clearly indicate a growth in quantitative modeling. Among other things, we are currently witnessing a tsunami of data from a globally-connected world (in fact, big data is the techno-geek buzzword), exponentially faster computing power (Markov Chain Monte Carlo simulations of complex models are now increasingly commonplace), and a rapid uptick in the volume and range of high-quality statistical programs (a great deal of which are open-source).

However, why would I think quantitatively-oriented sociologists are especially well-placed to gain from these structural developments?

The primary reason is that the underlying epistemology of modern quantitative sociology — grounded in complex predictive models, relational and nested data structures, and a folk-Bayesian approach to research design — represents the cutting edge and future direction of modeling in a shockingly vast array of fields. For example, multidimensional scaling, social network analysis, log-linear modeling, and finite mixture models (i.e., latent class analysis) are now at the forefront of disciplines ranging from machine learning to computational genetics (for example, see here, here, here, and here). However, most promising is the growing popularity of Bayesian multilevel models, which sociologists have in effect been using for several decades now. For instance, Bayesian multilevel models are now used by physicists to measure the mysterious properties of dark energy, geneticists to unlock the basic patterns of genomic population differentiation, and neuroscientists to describe the deepest structures of the brain. It is no exaggeration to claim that a human-level form of artificial intelligence, if it is ever developed, will probably be based on multilevel models of the type currently familiar to most quantitatively-oriented sociologists.

A secondary reason why the future looks so promising for mathematical sociology is that a vacuum has been created in the social sciences due to the rise of an alternative approach to quantitative modeling, frequently promoted by mainstream economists. According to this approach, the main goal of quantitative research is to estimate population-averaged causal effects, either by setting up a randomized (controlled) experiment or applying a small suite of techniques to observational data, such as instrumental variables regression, so-called “fixed” effects (rather than “random” effects) regression, difference-in-differences design, and so forth.

This approach is appealing because it promises the extraction of causal estimates with minimal theoretical insight, but it comes at enormous costs. For example, the assumptions of causality are rarely, if ever, satisfied for any particular model fit to observational data (as painfully but clearly outlined by the counterfactual model of causality, and evinced by the growing ranks of not-really-exogenous-but-we’ll-use-it-anyway instrumental variables). Furthermore, although it’s well-known randomized experiments are inferior to controlled experiments, the latter require strong theory that is often absent (and even then experiments in the social sciences often lack generalizability to other populations). Finally, an enormous amount of substantively-rich information is usually discarded when observational data are used primarily¬† for extracting causal estimates, so if we don’t believe our causal estimates then we’re left with a rather meager description of the data at hand (the worst offender is the so-called “fixed” effects technique, which can be viewed as a special case of a Bayesian multilevel model in which the groups are assumed, rather unreasonably, to have infinite variance between them).

Of course, both economics and sociology are large fields, encompassing a wide range of viewpoints, so I caution that my comments embody ideal types. Yet the dominant trends of a globally-networked world, combined with the rise of a distinctive approach to quantitative modeling popularized by economists, has created the conditions for a promising future for sociology more generally, and mathematical sociology in particular.