The Promising Future of Mathematical Sociology

I'm now an occasional blogger at Permutations, the official blog of the Mathematical Sociology Section of the American Sociological Association. You can read my blog post here, in which I outline why I think global trends in information technology and the meta-theroetical foundations of sociology provide conditions for a promising future for sociology in general and mathematical sociology in particular.

90+ Two-Minute Videos on R

I highly recommend Anthony Damico's excellent two-minute videos on programming in R. You can find the full list of 90+ videos here. This is the first of the series, which tells you how to download and install R:

More generally, Anthony's video collection is another reminder of the immense sociological benefits that come from sharing educational materials and expert knowledge in the style of the Khan Academy.

Complex Sociotechnical Systems

In a fascinating, informative talk, the interim director of the Engineering Systems Division at MIT makes the case for a new field of study on complex sociotechnical systems. I ask a question near the end of the video, pointing out that the core concepts of the proposed new field are in fact those endemic to sociology: mixed methods, open systems, social change, and so forth. You can watch the full video here.

The Future of the Academy in 2032

Just before he died, for a few years I helped the great sociologist Dan Bell with using his computer, and as a result I got to know him very well. One thing I learned from him (besides the distinction between "criticism" and "critique") is the usefulness of prediction as an endeavor in itself (as opposed to explanation). In this spirit, I offer five predictions about the future of the academy in 2032:

1. First, despite opposition from many established institutions, there will be an enormous increase in open-source education. Classes on any topic will be available online for free, with lecture notes, videos, presentations, and chat services (with other students) available to anyone with a computer. Exemplars of this trend include MIT OpenCourseWare, Khan Academy, and videolectures.net. 
2. Second, academic publishing will be increasingly online, with peer review a continuous process. Rather than books and articles published at one time in paper form after a process of peer review, academic projects will be ongoing, process-oriented, available online, and subjected to a continual process of peer review. In essence, everything that academics produce will be works-in-progress, and updated when errors are noted. Early indications of this trend include the NBER archive and  arxiv.org.
3. Third,due to technological changes and increased monitoring of people's activity, academics will have to be adept with managing and analyzing big data. Common statistical methods will often be difficult to use on such large data sets, straining the computational capacities of computers. While not common in the academy yet, big data is one of the top buzzwords of 2012, and I expect this to spread to academic work relatively soon. An exemplar of this kind of academic work is the Google ngrams project. (One danger, however, is that private corporations might be hostile to information-sharing, and the values of profit-making may severely inhibit the availability of big data to academics.)
4. Fourth, big ideas will actually be in greater demand in the future. Precisely because there will increasingly be an excess of information, grand theories and master narratives will be increasingly desired to help guide attention, avoid fragmentation of different research traditions, and unify otherwise disparate theories. For example, Josh Tenenbaum's efforts at unifying artificial intelligence (which suffers from disciplinary fragmentation) with probabilistic graphical models is a promising endeavor.
5. Finally, the skills in demand will be increasingly modular rather than topical. For example, as part of the Cold War in the 1960s, the United States government funded various "area studies" programs to educate Americans on the traditions, customs, and practices of various geographic regions around the world. In the future, there will be less emphasis on this kind of topical knowledge, and greater emphasis on modular skills  such as critical analysis of any kind of texts or arguments, understanding the basic structures of any set of languages, and gathering and analyzing various kinds of qualitative and quantitative data. 

To the extent any of these predictions are correct, sociology is particularly well-suited to take advantage of these trends. Sociologists are generally supportive of the democratic, inclusive principles of open-source education and online publishing, and sociology has an unparalleled tradition of big ideas. Moreover, modularity is ingrained in the discipline; in fact, sociology is almost by definition a modular discipline, inasmuch sociology is an approach to a particular subject matter rather a particular subject matter per se.

Top 5 Unsolved Sociological Questions

Physicists and other natural scientists often spend time specifying and focusing attention on unsolved questions, such as how particles obtain mass, the origins of dark matter, and how time is related to entropy. In general, I think it's a good practice for any field of endeavor to revisit the questions that are stubbornly and perplexing unsolved, including sociology. Thus, in this spirit of refining our ignorance (and clarifying our sociological "known unknowns"), here is my list of the top unsolved sociological questions of the early 21st century:

• What is causing the unprecedented, nearly-monotonic drop in crime rates across the developed world over the last several decades? As the NYT mentions, this question has been perplexing criminologists and sociologists, and everything from changing demographics to the legalization of abortion has been cited (although the latter cause is most probably incorrect, pace Steven Levitt).
• Why are various forms of inequality increasing across the developed world, from Sweden to the United States, since the early 1970s? Although many sociologists and economists have focused on technological change, immigration rates, and de-unionization, deeper causes (such as those related to political institutions or social structures) remain largely unexplored.
• Why do so many cultural and social phenomena (such as the frequency of words in the English language, size of cities across the globe, and amount of wealth across individuals) follow power-law distributions when plotted by size (or frequency) and rank? Explanations have focused on preferential attachment (popularly articulated by Herbert Simon) and information efficiency costs (as outlined by Benoit Mandelbrot), but thus far we have no conclusive evidence for favoring any particular mechanism over others.
• How does culture (defined as values, norms, attitudes, and beliefs) result in different economic and political outcomes across groups? Since the time of Max Weber, the causal effect of culture on human behavior has baffled sociologists and other social scientists, in part because of the apparent intractability of measuring culture and clearly linking it to economic and political outcomes. As a result, answering this question is an open, fertile area of empirical and theoretical exploration.
• Why is the United States unusually politically conservative and religious compared to other developed countries? At least since Tocqueville sociologists, including the late Seymour Martin Lipset, have puzzled over why the United States has exhibited a kind of cultural "exceptionalism" (in the non-normative sense), with relatively high levels of religiosity and political conservatism. Although many explanations have been offered, a satisfactory account has remained stubbornly elusive.

The Limits of Formal Theory in Sociology

Sociologists and economists often disagree about the role of so-called "formal" theory in understanding social behavior. For the most part, sociologists are much more skeptical that mathematical models (with little reference to data) can clearly and accurately describe, explain, and predict how humans act, think, and feel. I take a middle-of-the-road position: such models of human behavior can be helpful for illuminating arguments, but often they are such crude approximations of reality that they can obscure what is actually going on. I'm reminded of Max Tegmark's brilliant article on the mathematical universe hypothesis, in which he claims that the universe is a giant mathematical structure. In fact, the disciplines can be understood in reference to derivations from known mathematical laws, as shown in this diagram:

The problem, as Tegmark suggests in this diagram, is that until we understand how to reconcile mathematically general relativity and quantum field theory, as well as how this reconciled theory is related to other fields in physics and related fields, mathematizing sociology will at best be a set of (possibly crude) approximations of reality.

Physics Envy

The NYT published an op-ed today by a pair of political scientists on "physics envy" by sociologists, economists, and political scientists. The authors mainly argue that theory can be useful even when it is wrong or unsupported by data, and briefly mention that data analysis is useful even if theoretical contributions are not obvious. I disagree with the former, but not the latter. For a similar view, see this post by the theoretical physicist Sean Carroll.

Irving Louis Horowitz

The eminent political sociologist died a few days ago, according to an obit in the NYT. Long ago I read, and took seriously, his book The Decomposition of Sociology, in which he argues (essentially) for more empirical analysis and less left-wing politics in sociology. Reflecting on his book, he neglects a fundamental, possible cultural contradiction: to the extent social reality exhibits facts consistent with liberalism and inconsistent with conservatism, empirical analysis will result in more liberal than conservative belief systems (but not values, since those cannot be proven "right" or "wrong" by scientific analysis). For example, evidence is accumulating that economic inequality (which is of little concern to most conservatives in the United States), has numerous deleterious effects, thus forcing conservatives either to hold beliefs inconsistent with the evidence (i.e., inequality is unrelated to deleterious effects) or alter their values (i.e., it is a "good" thing to have high rates of violence, low social mobility, and so forth).

Big Science and Sociology

I highly recommend this video featuring Dirk Helbing, a sociologist and erstwhile physicist who is (along with others) attempting to create a CERN-like society-simulating project for the social sciences by combining information from large data sets with simulated models of complex social systems:

Inequality: Everyone's Thinking About It

I ran into the following articles on inequality, which has not only been increasing structurally but culturally (in that more policy elites and journalists are discussing the topic openly). Here are some recent posts on inequality:

• Reuters is reporting findings from a group of researchers showing that Sweden has undergone an enormous increase in inequality, especially since the rise of the center-right in the political system. For those of us in the United States who look to Sweden as a model of development, in recent years even this country has regressed from the ideals of social democracy.
• Based on an online survey (with all the caveats about sampling procedures, of course), a group has surveyed wealthy Americans on their views on inequality. The biggest finding, which reinforces the importance of class-based analyses of electoral politics: among the wealthy there is a huge gap between self-identified Republicans and Democrats, with over 84% of the latter favoring policies taxing the rich while around 29% of the former.

Rethinking Tragedy and Success

The social theorist Alain de Botton presents a creative rethinking of the meaning of tragedy and success in a TED talk, shown here:

 

In essence, he argues that success needs to be rethought using insights from sociology, including an understanding of the limits of the ideal of a meritocratic society (since there is always random chance involved in social mobility), a deeper awareness of how failure as a concept involves particular beliefs and values (so that we can conclude that Hamlet is not a "loser" even though he "lost"), and a sensitivity to the fact that even when particular social and cultural distinctions appear to be irrelevant economic differences certainly are not (so that comparing oneself to Bill Gates rather than the Queen of England is just as absurd, even though the former wears "business casual").

Utility Theory as Naive Cultural Theory

Here's a fascinating presentation by the economist Steve Keen on utility theory and neoclassical economics. From the perspective of a cultural sociologist, what is of particular interest is that the utility theory underlying neoclassical economics has the appearance of a naive cultural theory. Specifically, the indifference curves that constitute supply and demand curves in neoclassical analysis are based on strong, disproved assumptions about how people value things in the world: first, completeness (i.e., that the individual knows their evaluative ranking of all combinations of things); second, transitivity (i.e., if thing A is valued to B, and B to C, then A is valued over C); third, non-satiation (i.e., more things are always valued to less); fourth, convexity (i.e., for each thing, additional value falls); fifth, structural independence from culture (i.e., what an individual values is independent of how much income the have); finally, no curse of dimensionality (i.e., information processing abilities are unlimited). No cultural theory  in sociology has even approached the disbelief required for these kinds of assumptions. Fortunately, some sociologists (for example Michael Hechter), have sought to correct this naive cultural theory, and have advocated eloquently and convincingly for a richer understanding of values in economic models of human behavior.

Big Data and the End of Theory?

An article in The Guardian gives appropriate caution to claims that data analysis (and only data analysis) is the solution for all or even most academic and research problems. As Max Weber observed in  his brilliant essay on objectivity in the social sciences, even the process of data analysis depends on values that cannot be empirically proven as right or wrong: "The 'objectivity' of the social sciences depends [..] on the fact that the empirical data are always related to those value-ideas which alone make them worth knowing and the significance of the empirical data is derived from these value-ideas. But these data can never become the foundation for the empirically impossible proof of the validity of the value-ideas."

Animating David Harvey

I found the addition of animation a clever way of augmenting the arguments by the sociologist David Harvey, who discusses the crises of capitalism here:

Clearly this was a time-consuming effort, so not many of these videos can be made easily. If there is a way to make animating lectures more automated (through, for instance, computerized animations) it would be very beneficial for helping students learn. You can find additional RSAnimate lectures here.

Daniel Bell, Master Sociologist

The NYT posted an excellent profile of my late friend Dan Bell, the master sociologist (and big thinker). Even though he was a big-thinking social theorist, I remember that Dan told me, emphatically in fact, that he was a quantitative sociologist! This makes sense, since his big books often included quantitative data of trend lines (which is in many ways advantageous over modeling the data and then focusing on the model parameters, such as regression coefficients or standard errors).

Top Ten Must-Have R Packages for Social Scientists

The political scientist Drew Conway has come up with a useful list of his ten "must-have" R packages for social scientists. I agree with him for the most part, and his list highlights the usefulness of R (vis-a-vis Stata) for social network analysis (see statnet/igraph) and graphics (see ggplot2). In some respects, his list also underscores the fact that R is arguably more suited for sociological data analysis than Stata, given the former's unique packages not only for social network analysis but also multilevel modeling and  a variety of non-parametric methods (including more recent forms of matching and classification techniques), which were especially popular in sociology before the "path analysis" revolution of the 1960s.

Multilevel and Longitudinal Modeling in Stata

For my "off-task" reading I recent perused an excellent book on multilevel and longitudinal modeling in Stata by Sophia Rabe-Hesketh and Anders Skrondal. The second edition (which I read) has been updated by including several chapters providing an overview of regression modeling and ANOVA (analysis of variance) as well as additional background information on models with nonlinear outcomes (e.g., logistic regression). The authors even include a self-test near the beginning of the book to ensure that readers can confidently progress through the rest of the material. The book has many great features, including ease of data accessibility (simply go to this website and you instantly have all the datasets used in the book), clarity of presentation, and numerous applied examples with accompanying Stata code. The only problem, which is not a problem with the book, is that multilevel modeling in Stata (as the authors note) can be rather slow, especially for nonlinear outcomes with many levels. (For this reason, when using nonlinear outcomes other statistical packages may be more desirable than Stata, such as R.) Yet overall the book is an excellent overview of an important class of statistical models, and can even be viewed as a way of take advantage of Stata beyond the realm of "econometric" approaches (which seems to be Stata's strength) and toward the realm of putatively more "sociologic" methods of data analysis, in which clustered data are viewed as something important in their own right rather than as statistical nuisances.

A Quantitative Tour of the Social Sciences

I just read "A Quantitative Tour of the Social Sciences," edited by Andrew Gelman and Jeronimo Cortina. I highly recommend the book for anyone who does quantitative research, including part-time quantitative analysts and ambitious undergraduates. The aim of the book is to expose the reader to the similarities and differences in quantitative thinking across five core social science disciplines: history (a welcome but oft neglected member of the social sciences), economics, sociology, political science, and psychology. The editors are unabashedly in favor of methodological pluralism, and present as diverse set of views as possible. What is notable about this volume is that for each discipline the authors have included exercises ranging from conceptual questions to hands-on data analyses. From my perspective, especially illuminating chapters include Andrew Gelman's thoroughly informative discussion of the application of game theory to trench warfare (in part because he discusses the criticisms of his paper as it went through peer review) and Jeronimo Cortina's overview of the potential outcomes model of causality (which, while familiar to more advanced readers, is presented with enviable clarity).

The chapters capture most of the differences among the disciplines in quantitative thinking. However, a few differences in mathematical modeling may be missed. In particular, likely reflecting an enduring interest in social context and interconnections among individuals, sociologists tend to use multilevel models and social network methods more frequently than other social scientists. As well, economists are much more likely to focus on trying to interpret observational data causally through the use of instrumental variables and, to a lesser extent, regression discontinuity design. Notwithstanding, overall this book is a welcome addition to the bookshelf of any scholar who does quantitative work.

The Relative Size of Things

Sociologists are often focused on different levels of phenomena; hence the attention paid by sociologists to the micro-macro problem (see James S. Coleman's "boat" showing linkages at various levels), Anthony Giddens' structuration theory (orienting social theory toward micro-macro concerns), and hierarchical linear models, otherwise known as multilevel models (in which the analyst models two or more levels of given social phenomena). Although dealing with biology and physics rather than sociology, both of the following hyperlinks help us to visualize the importance of how reality differs by various levels: cell size and scale (developed by scientists at the University of Utah) and Powers of Ten (created by IBM in the 1970s for the Museum of Science and Industry in Chicago). Cool stuff.

Multiple Imputation with Deletion

The sociologist Paul T. von Hippel has written a great article outlining how to deal with missing values when the Y's are also missing. Typically the gold standard for dealing with missing data has been multiple imputation, but he advocates multiple imputation with deletion (MID): that is, you use all cases for multiple imputation, but after imputing you delete those cases with imputed Y values. Somewhat surprisingly (because of the reduced sample size after excluding those cases with imputed Y values), MID usually leads to smaller standard errors; moreover, since the Y's are excluded from the analysis, MID is robust to problems with the imputation model. Check out von Hippel's informative paper here.