Quantitative Sociology

[gilbertrollins]

Can anyone enlighten me on what sociologists mean when they talk about quantitative and mathematical sociology?

Mathematical anything would seem to imply logical derivations based on assumptions. Game theory. Graph theory. And their spinoffs in social sciences, networks and computational simulations. Do I safely categorize "mathematical sociology" as "mathematical social theory?"

That work, however is not quantitative, as in it doesn't measure quantities, only suggests directions variables lean and interact. So is "quantitative sociology" sociology which leverages advanced statistical analyses? That would be on the empirical end, and very different from mathematical theory (though probably not mutually exclusive in authorship trends).

Edited October 19, 2012 by econosocio

[jacib]

Your talk about this makes me first of all want to suggest by the economist Dierdre McClusky's book The Secret Sins of Economics. I widely recommend it to people interested in both quantitative and qualitative work; it's about economics but many of the things apply equally to sociology. It's also put out by my favorite press: Prickly Paradigm. Best of all, PDFs are available FREE and it's like 60 pages. Summary here (I know one doesn't normally say this about an academic book, but warning: that review contains spoilers).

Regardless, I'm no expert, and I'm not sure I fully understand your question, but let me answer as best I can.

Most quantitative sociology uses variable-based statistics. "Mathematical sociology" is often, as far as I can tell, just a catch-all term for sociology that uses numbers and computation but doesn't use variable-based statistics. To put it another way, you need a computer to do mathematical sociology but you can't do (most of) it on STATA. It's not only simulations and game-theory. Even though a lot of it doesn't use variables, I think most people still think of it as "quantitative" (in that it uses computers and not traditional "qualitative" methods) but I've gotten into debates with colleagues about whether most social network analysis is "quantitative", which inevitably leads to questions about whether we can just bracket things crudely "quantitative" and "qualitative" (for the record, my answer is yes to both). The point is, I don't think mathematical sociology necessarily has to do with assumptions going into the project. Sure, mathematical sociology uses a lot of simulations, but data mining is, as far as I understand, also an important part of mathematical sociology and it's obviously (hugely) empirical, though, I should add, most of the interesting data mining stuff I've seen doesn't really use variables, at least not like most sociology uses them. Check out the culturomics stuff for example: mathematical, empirical, but also not based on assumptions like you're worried about or using conventional variables.

We talked about induction and deduction literally years ago on the board and someone posted a link to this powerpoint. I don't think that powerpoint is 100% accurate, but it's a useful place to start (only the first few slides are relevant, and you can also just check on wikipedia). Is this what your question is really about, "Is mathematical sociology all deductive, or are there inductive mathematical sociologists?" I'd say the answer is no.

Demographers are interested in "counting things", largely, and aren't as interested necessarily in causal explanations. Almost all other quantitative sociologists are interested in causal explanations (at least the good ones) so they need, as it were, theory. As far as I can tell, lot of the important theories in stat/inequality come out of quantitative findings. It's empirical, it's theoretical, and it's mostly inductive (there are, of course, a lot of assumptions that go into any research project, but I don't think those are the ones you're talking about). Economics is similarly based on assumptions but that doesn't make it "mere theory"; in that case, though, the assumptions matter in a different way because the theory is deductive. Durkheim's Suicide is of course social theory, empirical, and inductive. Social theory can be inductive or deductive; it can be based on quantitative evidence or qualitative evidence (or, in some cases, show no evidence--DiMaggio and Powell's "the Iron Cage Revisited" is a great example of theory that included no evidence when it was published. It is a very well respected paper). All subfields of sociology (besides maybe orthodox demography) creates new and critiques existing social theory.

I might be misinterpreting you, but the difference you're talking about seem to be more the differences between "induction" and "deduction". Take social networks stuff as an example; it can rely on simulations, but it can also rely on very empirical data (either with variables or without). Similarly, I read a lot of qualitative political science which is very deductive (rational choice). I'd say there's deductive and inductive work all over. I just read a great article that covers, among other things, ethnography and rational choice (a kind of deductive thinking)--I can have read the the (excellent) Chandra article, but this whole issue is devoted to the subject. Sociology of religion also weirdly got hung up on rational choice for a while. One of the best books by a sociologist on nationalism is deductive. A lot of gender stuff is deductive (not rational choice, but I'd say equally deductive). Everything using Marxism is obviously deductive and based on assumptions, but that doesn't mean it can't also be based on empirics (my colleague just cited Erik Olin Wright as an example of a rigorously empirical Marxist). You'll see deduction even in social movements literature (everytime you see someone cite Olson 1965, for example).

If I completely missed the boat on your question, my apologies, but, yeah, I'd say, there's probably more deductive thinking in mathemtical sociology than most sociology, but no, by no means is mathemtical sociology exclusively deductive nor, I feel obliged to add, is it the only place deduction is used in sociology.

[RefurbedScientist]

I won't add much to jacib's characteristically comprehensive response.

I see two ways in which mathematical sociology might differ from quantitative methods. The first is formal logic or formal theory, which uses mathematical notation to show causal relationships between variables that may or may not have measurable values or quantities. It's all about postulates and predictions, logically derived. This kind of theory building seems to be a small niche in sociology. Here's one prof who does this sort of work.

Then I see the fields the OP mentioned, like graph theory, simulations, etc. These are essentially computational methods that do not rely on statistics or probability per se. That is, social network analysis uses a lot of computation and math to calculate certain measures like centrality, but these measures don't have much meaning independent of the analysis. Graph theory gives a value do relationships, but it's all sort of a stand-in or proxy measurement for something qualitative (e.g. location in a social network).

Then there's people in sociology who more closely resemble statisticians, but who shape the development of new statistical methods toward application in social science. Kenneth Bollen at UNC, for example. We don't usually think of these people as mathematical sociologists, but they're doing a lot more math than your average quantitative methodologist who just does regression analyses all day.

[gilbertrollins]

Thanks for all the links. I'm not familiar with the terms "inductive" and "deductive" outside my mathematics courses, so I don't get the usage above. Maybe that's my fault for not having a foundational base in philosophy.

I don't understand how "rational choice" is deductive, as juxtaposed with other behavioral theories. In a rational choice framework we assume agents face costs and benefits accruing to their actions (which not always and not even usually accrue to pecuniary interest), and maximize their welfare based on them. In a structural framework we assume agents are compelled by the path dependencies and mechanics of the social frame. Both of those approaches rely on assumptions and definitions of behavior, come to conclusions and (hopefully) test them, no? Is that not deductive both ways, then?

My OP wasn't clear. That's what I get for trying to be fancy. My question is more so, how much of network theory in sociology takes a priori form in mathematical proofs, like Damon Centola's work and other economists on graphs and games? How much empirical work uses multivariate and descriptive statistics against interpretive and ethnographic methods? And on a scale 1-10, how hot under the collar is the quant v. qual debate in sociology, if much at all?

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[gilbertrollins]

Oh. I just looked at that powerpoint. If you're talking about working from theory down to empirics, vis a vis starting with a look at the data and working back to theory, arguably a majority of the application of rational choice in sociology started from an inductive approach. Demographers saw people having less kids as their incomes went up which seemed backwards, reasoned that the opportunity cost of time was going up commensurate to income increase, and that children were less productive as labor inputs in technologically advanced societies. So too with Religion -- Smith was the the first one to point out that state supported monopolies of religion allows religions to charge people higher prices in terms of subscription (think Crusades and Suicide Bombing). Becker's work on crime maybe started more from a theoretical perspective.

In any case, I'm saying a lot about what very little I know of rational choice in sociology so feel free to correct.

[jacib]

Rational choice work is all considered "deductive" in sociology, as far as I know, in that you already kind of know the answer before you ask the questions. People maximize utility. People are rational actors. Competition breeds lower costs. Monopolies let you charge higher costs. A lot of sociologists I know (the inductive ones) start with a bunch of data and their first question is just "Whoa, what the hell is going on here?" Like, you should really, really understand the difference before you apply to sociology departments, just because I worry you might be unhappy. Like, we look at things like "racial prejudice" and we're not going like "Okay, in what situations is racism rational", but rather, "In what situations, does discrimination occur?" and ideally "What interventions can we put in place to decrease racial discrimination?" There aren't a priori assumptions about the actors. It's late, so I feel like I'm not explaining well and perhaps that's a poorly chosen example but like... it's just a very different way of going about things.

I mostly know rational choice from (qualitative) political scientists, not economists, so forgive me if you think I'm giving it the short shrift. But a lot of people would disagree with that kind of rational choice explanation of the crusades or suicide bombing (rat choice is pretty marginal in sociology, about as popular as the Marxian stuff, maybe more marginal, depending on what population you're talking about, but in top departments, probably about equal). Maybe, it's not that the monopolies allowed states to charge higher costs, but that people really believed that stuff, for example. Off the top of my head, a critic might point to things like Aum Shin Rikyo in perhaps the least monopolistic religious state or suicide bombing in pluralistic Iraq where there also wasn't a state monopoly or countless other examples. The rat choice explanation is not based on sufficient evidence, they might argue, but on certain a prioris that don't explain the action as well as other models. Instead, the cirtic might point to issues around identity (in the case of Iraq--there are actually good, convincing rational choice arguments in the ethnic violence literature) or meaning (in the case of Aum, it's pretty clear they did believe the world was going to end) or status or whatever else being the primary motivator based on evidence and then built upwards. Is that clear? I feel like it might not be but if someone cares, maybe they'll pick up.

Sociology, even economic sociology, is really different from economics, and it'd probably do some good to familiarize yourself with the literature and approaches before you apply. I think you're still in school so presumably have access to all the wonderful articles on Google Schoolar but I'd really recommend you start reading a bunch of sociology before you apply. I guess you're interested in networks? Go to the Annual Review of Sociology, and just type in Networks. Read minimally the Stovel and Shaw piece called "Brokerage" and the Pachuki and Breiger piece called "Cultural Holes: Beyond Relationality in Social Networks and Culture". I am not a social networks guy, but I can tell you those are two hot issues in the networks literature right now. Krippner and Alvarez's "Embeddedness and the Intellectual Projects of Economic Sociology", the "Birds of a Feather: Homophily in Social Networks" article, Duncan Watts's 2004 article, and "Statistical Models for Social Networks" (I haven't heard anything about this last one, but like I said, I'm not a social networks guy) would be the next set to read. You should really familiarize yourself with the literature, in just that you should understand how sociological arguments are framed. Are these the kind of conversations you want to have for the next 30 years?

"Strong correlations like this seem compelling, but mean nothing without a testable hypothesis on behavior and stated preferences, especially at such a macro scale." That's often not really what we do. We don't often think in terms of "preferences" or (in some cases) testable hypotheses. In one class, we read one early article by this famous guy, and the professor teaching it was like "I know him, and I know that's he's embarassed about this article beause it uses formal hypothesis testing (H1, H2, H3...etc), and he's kind of like now 'Oh, what was I thinking back then? I was so young!'". But go to a soc talk and go to an econ talk--I would wager that in the econ talk, the speaker is interrupted a lot more often during the talk, and the soc speaker is brutalized only after they finish presenting. Why? It's not because econ professors are ruder and more voracious and the sociology professors are low key and polite, but because the way they're working. Econ profesors are making a different set of assumptions and their theory has a different relationship to the data. The problems you pointed to with Culturomics stuff are the kind of things that sociologists wouldn't really have. The two "basic assumption" that I've heard sociologists raise with that stuff is around the representativeness of the sample and what meanings we can say these words have divorced from their context. Those are the issues I remember people talking about. This statement "[it] lacks basic assumptions on behavior to get tested is as I see the major problem with the project" really makes me think you should read more sociology, because you're going to be seeing a lot of "major problems" if you go to graduate school in it. I just get the sense that you don't know what you're trying to get yourself into. I don't mean to be rude, but when you say "most corpus and sociolinguistics lack consistent, well defined assumptions on behavior to test as well" makes me think you just won't fit in in a sociology department, even (or maybe especially) one with a heavy load of economic sociologists.

For those still reading, I don't think the qual/quant debate is hot at all right now in sociology. Those fights have died down. It's often more "parallel play" than perfect synthesis between the two, but "mixed methods" is the new watch word, for sure. Mario Small has a good annual review about that for anyone interested. Most people I know are just interested in getting data appropriate for the question.

Consider reading C. Wright Mills's the Sociological Imagination. I've never read it (shame, shame) but it's the book that people really recommend for "What is it that sociologists do?" But like, you got to know, economic sociology is not economics with less rigorous math. As far as I can tell, we honestly don't talk about preferences in the same way you think we do (as far as I know--as with all of this, I could be wrong and over generalizing) and I have a feeling for stuff about institutions and norms that you want to do, you might be better served in an econ (or poli sci) department not a sociology department. But like honestly, in your case, I'd describe what you want to do to the professors you want to work with via email and see how they react. Tell them you're switching fields and ask them if this is something that you could work on with them in their departments (I did this when I was switching fields as I was applying--it was useful). But before doing that, though, try talking to professors at your current school about your plans (in soc, poli sci, and econ).

Demographers, as far as I know, wouldn't really say "opportunity costs", "labor inputs", or "seemed backwards".

[faculty]

I will echo jacib's tough love. To put it another way, be sure that you're moving from economics to sociology not because you don't seem to fit in economics, but because there's something specific that speaks to you in sociology. In other words, you're not repelled, but drawn in. That sentiment is not only imporant to convey in your statement and materials, but in your reasons for applying.

Sociology programs are full of students who weren't sociology undergraduates and/or who pursued graduate work in other disciplines. From my experience, these cross-overs end up flourishing or struggling, with few falling in between. The ones who struggle are the ones who wonder why we sociologists don't see the world like their old discipline. They throw out obscure references during seminars and argue that sociologists have it all wrong. They pay more attention to how everything fits with their prior understanding rather than appreciate it in its own right. This perspective amplifies the perpetual graduate student problem of missing forest for the trees. If these students stick around, they choose to do work that is less sociological and become less easy to mentor and less marketable in the long run. The ones who flourish have similar backgrounds, but they see sociology as a new approach and a new perspective. They thoughtfully take in what it has to offer, appreciating that it has its own history, assumptions, goals, and strengths. They use their former reading as background reading, not foundational work. In other words, they don't try to fit sociology on top of their previous knowledge, but let the two co-exist. With this orientation, once they have sociology under their belt, these students can merge the two disciplines and generate innnovative, important questions, methods, and understandings. They are often the superstars.

It's not that I don't think that a sociology program is for you, but think hard about why you want to pursue sociology over economics (or something else).

[gilbertrollins]

I'm on my way out the door and will reply in greater detail, but Erez and Jean Michelle aren't sociologists. They're applied statisticians, and early in their careers at that. What I said about their project might be naive, or misguided by my narrow undergraduate training, had my sentiments not been drawn from the incredible criticism of their project they drew from linguists, of whom have fully four corpus linguistics journals - not a paper in one of them cited.

I've read Sociological Imagination. I've also read a good deal of economic sociology.

If my begging for "specific, well defined assumptions about behavior to test" sounded like a haughty, veiled criticism which really meant "lacks a mathematical rational actor model which the data can then be run through econometric multivariate analysis in order to establish its fit to a production function or static equilibrium," it wasn't. And it's really not my lack of reading in sociology, methodology, and philosophy of science broadly that's to blame for the misinterpretation, though the reverse instance may be true in how you interpreted my statement.

[gilbertrollins]

I will echo jacib's tough love. To put it another way, be sure that you're moving from economics to sociology not because you don't seem to fit in economics, but because there's something specific that speaks to you in sociology. In other words, you're not repelled, but drawn in. That sentiment is not only imporant to convey in your statement and materials, but in your reasons for applying.

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C) To elevator my thesis and why it fits with concerns in sociology, my claim is that long-run preference intransitivity (inconsistency -- i.e. people change their minds about what they like) allowed people to be persuaded that markets and innovation were a good thing. There is broad (if not coming to the same conclusions about the beneficence of markets) support for that idea in the sociological literature on Progress. And indeed it's fundamentally a Hegelian claim about the influence of ideas on social forms.

Forgive me for thinking that my work on the formation of social norms and mores, search for microfoundations of macrosocial outcomes, and experience in doing comparative historical empirics on the early modern era don't fit into the aims of swaths of sociological research in historical and economic sociology. THE major complaint about economics in economic sociology is that preferences aren't a consistent and stable set which can then be maximized with respect to a constraint function (prices and budgets). Their claim is that preferences are embedded in social structure. And most of the work in networks seems to try to get an idea of what that structure actually looks like and how it affects the formation of opinions/preferences. Hence my interest in networks, one of the very few fruitful cross-over areas where there's any talk beyond open hostility and dismissal left between economists and sociologists.

Beyond preferences I'm interested in technology, as it's the foundation of economic growth even according to economists -- again correct me if I've misidentified technology to be a hot topic in sociology. My claim on technology is that it's the result of a collective action problem, which is not just anethema to a majority of work in economics, but of course at the center of the analysis of social change in sociology.

But the concern that I haven't done enough reading on my research interests, and potentially lack enough of an open mind to absorb the lessons of a graduate education in methods I already prefer is noted.

This statement, "rational choice work is all considered "deductive" in sociology, as far as I know, in that you already kind of know the answer before you ask the questions," reeks of profound ignorance not just of what deduction is (you're claiming that all deductive reasoning is tautological), but even a cursory reading of any economics outside blanket dismissals of its methods as merely the reproduction of neoliberal doctrine.

Economists constantly look at data to see "gee what the hell is going on here?" and that, what you are calling inductive method of research is why the discipline has made progress in the last fifty years. Take for instance Robert Fogel's work on slavery. Doug North's work on institutions. Coase on institutions. Becker on family. Demographers on population data that didn't fit Malthusian predictions. And on. And that's how I came to a sociological perspective on my research on language, preferences, social norms, and technology re: the Industrial Revolution and economic growth.

Jacib's fourth paragraph is just one assertion or another, proceeding roughly as such: "You say X. You haven't read enough sociology." If you'd like to provide some substantive contrast to how sociological thinking differs from what I was saying, other than that context matters (yes, that is the whole point of Pragmatics, another whopper the Culturomics guys missed), and that statistical hypothesis testing has problems (yes, a measure merely of the signal-to-noise ratio in data says very little about the theoretical and social significance of the size of the coefficient), feel free. I was talking broadly about formalizing consistent, generalizable hypotheses about social mechanics and testing them with data. You've got quite a larger audience than me or even economists to argue against if you see gross negligence in that methodological approach.

And since your a soc of religion guy, and have such a naive view of economics, you may want to read Eli Berman's Radical Religious, and Violent: The New Economics Of Terrorism. Neither Adam Smith nor Berman nor economists broadly have ever claimed people do not believe the things they do -- the argument is that people face an ecology of costs and benefits (wait! context?) which delimit their choices. Maybe the Federalist papers are wrong. Maybe the degree of competition among institutions is a useless variable in social analysis because economists are a bunch of arrogant imperialists. I seriously doubt either, though.

That said, the methods in economics lack a very serious look at norms, institutions, and collective action outside some game theoretical work which barely provides testable hypotheses anyway, and are really just very fancy looking interpretive stories. So I thought I might transition to a social science which is more dedicated to empirical foundations and open to my interests in its main stream.

[gilbertrollins]

Smiley is an unintentional artifact of typing "B" ")"

[jacib]

I'm sending you a response as a personal message because I think it'll be easier than having this play out on the boards, but I thought I'd just clarify that I suggested that networks and markets stuff because you were asking, "Is networks research like ____?", and I don't know the fullest answer to that, so I suggested the best stuff I could, the Annual Reviews (it's pretty safe advice, in general). They'll give a clearer (and fairer) sense than I can of what's going on. Sorry, honestly, if that wasn't clear and I sounded like a pedantic D. I didn't mean to be scolding or demean you by saying "Read this, then let's talk". I was trying to give you a better answer to your initial question because I had thought you were asking more about networks stuff, and I at least know what are hot topics in networks (and less about what's going on in economic sociology, I just know the name Krippner is hot and I like her work that I've seen). Apologies if that didn't come through (which would be a failure on my part, not yours).

I have actually coincidentally read (parts of) that Eli Berman book you're talking about. He's got a good thing online for people wanting to use that book as a course book, too, which is nice, I like when authors do that. I know some of his other work work. I think I'm going to actually going to use his paper on Orthodox Jews for one of the projects that I'm working, because I think it's a good paper, though I didn't like that book on terrorism as much.

Edited October 22, 2012 by jacib

[gilbertrollins]

No apologies necessary. How we went from me asking about the proliferation of mathematical proofs and statistics in different subfields of sociology to my putative naivete of the methods and models attending to the research I've been working on for two years, I don't know.

In case this discussion can still be a benefit to the viewers at home, I get the impression that something like half of sociology cohorts are full of people coming from other disciplines (though probably very few from economics, as these candidates will typically go over to political science if they're not happy with econ proper). And @faculty is absolutely right that sociology adcoms aren't merely looking for orphans from other disciplines who have confused research goals and nothing better than hackneyed essays about the methodological shortcomings of their home discipline to sell themselves. But I would venture that subset of students would have struggled anywhere -- these people sound like they more had a problem absorbing material at a professional level and applying it creatively and novelly, though may have done quite well for themselves acing material that was spoon fed to them in their home discipline as undergraduates. That they came from other disciplines probably makes them more salient examples -- but uncreative, and unpersuasive research from people who don't manage to transcend their BA training in another discipline aren't any more scientifically useful than people who don't transcend their BA training in sociology -- and probably fare just as poorly on the job market.

That said, considering the abysmal stereotypes of sociology one gets in the economics department, please do stop to consider that someone considering a transition who can speak even half way competently about disciplinary intersections and frictions, probably has considered his decision and former research, with some appropriate gravity. Especially if he shows up asking rather particular questions about sociological methodology.

All links and suggestions are completely appreciated. Thanks.