The Promising Future of Mathematical Sociology

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.


9 Responses to The Promising Future of Mathematical Sociology

  1. ‘Furthermore, although it’s well-known randomized experiments are inferior to controlled experiments’
    hmm, I would be curious to see any references to that.

    • ethanfosse says:

      Look at experiments in physics: there is as little randomization (i.e., noise) as possible, just an entirely controlled environment. Of course we don’t have this level of theory and control in the social sciences so instead we design an experiment in which we control for a few observables (e.g., sex, race) and then randomly assign subjects to treatment and control conditions (which is better for achieving balance than just randomly assigning subjects). As far as citations, James Heckman has written on the promises and pitfalls of randomized (controlled) experiments in economics.

  2. Michael Bishop says:

    Thanks for the contribution Ethan! I’m eager to hear more. It sounds like you’re channeling my advisor, John Levi Martin.

    You are certainly right that many researchers focus on estimating causal effects and invest less in describing other aspects of the data. Therefore I think we should ask: “What can we do with estimates of causal effects? What can we do other forms of non-causal knowledge?” Perhaps you can tackle the latter question, it seems harder to me, I’ll tell you what causal knowledge seems helpful for.

    If I want to know whether to treat my heart-disease with drug X, or drug Y, or neither, I’d like someone to estimate the causal effect of those options on mortality, heart-attacks, cancer, psychological well-being, and other things that people think might be affected.

    If I want to decide how much to tax high-income individuals, or how much to transfer to poorer individuals, there are another host of causal-effects I would like good estimates of, e.g. how much will it improve the health and happiness of the poor?

    Those are important decisions, do you agree that good estimates of causal effects should have a big effect on what we decide?

    Feel free to also tell me more about what non-causal knowledge is good for.

    • ethanfosse says:

      Hi Michael! Thanks for the compliment on channeling John Levi Martin! I view observational data as absolutely essential to uncovering causal effects. For example, how did we first find out that smoking caused cancer in the 1950s? Briefly, scientists used a folk-Bayesian triangulation approach based on qualitative data from the histology of lungs, a simple observational study with a sensitivity analysis, first-hand observations from doctors, and a strong theory of how smoking causes cancer. That is, rich, thick description plus strong theory led to a convincing causal narrative.

      Rich, thick description is the hallmark of the most important discoveries of modern science, in fact. I can just point to the major discoveries in physics, most of which are non-causal: the red shift, cosmic background radiation, discovery of the Kuiper belt, and so on. And even when experiments are conducted, such as with the double-slit experiment, there is no randomization whatsoever (i.e., it is a controlled environment with the minimization of noise). So the economistic approach, which downplays thick description and privileges randomization, is rather baffling to me.

      As far as causal estimation, the claim that the economistic approach produces causal estimates is, from a Humean perspective, questionable. More down-to-earth, the problem with experiments is that even if we can obtain a reliable estimate from a particular study, we have no idea whether or not it is generalizable to other populations. Moreover, due to the cost of replication, few of these studies are conducted again.

      • Michael Bishop says:

        I agree that observational data is part of the process of identifying causal effects for a couple reasons. 1) We always have observational data before we have experimental data. 2) We can analyze observational data cleverly to give us some causal insight.

        Perhaps economists over-value fixed-effects and instrumental variables in general, and given the prominence those studies get it is important to call attention to that. But in my opinion sociologists currently seem to under-value (based on how often they use them) instrumental variables and randomized controlled experiments.

        Description is not only desirable for its contribution to subsequent developments in causal knowledge, but lets focus on that for a minute. How big is the payoff in causal knowledge, for a marginal investment in description? How big is the payoff in causal knowledge, for a marginal investment in RCTs?

        Its hard to generalize, because I think the answer will differ across research areas but I think the payoff of RCTs is very high and I’d definitely like to see more of them. There are ways they can be done without spending too much, and I think the value of the type of knowledge they contribute easily pays for itself in many areas of research (e.g. public policy).

        That said, your point about generalizability is incredibly important to consider.

  3. ethanfosse says:

    Thanks for the thought-provoking remarks, Michael. I view counterfactuals as theoretical knowledge, so I think causal knowledge comes (mostly) from thick description and careful theorizing, with experiments as a subset of a very wide range of tools (I’ve conducted an experiment myself, in fact). Perhaps sociologists under-value instrumental variables and experiments, but incidentally so do physicists, geneticists, computer scientists, statisticians, and engineers (among others), who engage largely in analytical theorizing and thick, rich description.Take, for instance, computational geneticists: their goal is “merely” to describe the human genome, and how this varies across populations. Or computer scientists: their goal is “merely” to predict what people will type in a search engine. Or cosmologists: their goal is to “merely” describe which planets might be inhabited.

    What I find odd about this is that economists are often accused of “physics envy” yet they approach knowledge construction in a way at odds with physics and the natural sciences.

    • Michael Bishop says:

      Thank you for such a stimulating first post! I think its really helpful to think about how sociologists project is (or should be) similar and different to economists as well as physical scientists. (as well, of course, of the diversity within these traditions). I hope we have many more exchanges like this! 🙂

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