One of the things that makes me so happy about having joined the Broadstreet crew is how often my fellow contributors write about topics that I—the lone sociologist of the bunch—get really excited about. The obvious examples here are space and networks, which have been my main focus over my last couple of posts. For this post, I want to do something slightly different—I want to talk about the role of network analysis in the study of culture. This post is inspired not only by Jared Rubin’s excellent primer on network analysis in historical research, but Tracy Dennison’s thoughtful remarks regarding the challenges associated with isolating, defining, and measuring culture in historical settings. I want to talk about these themes from the perspective of sociology, where the study of networks and culture have become closely tied due in no small part to the pioneering efforts of the late, great John Mohr, whose legacy was firmly cemented with the publication of Measuring Culture earlier this year.
Though he was trained at Yale, Mohr was undeniably a descendant of the Harvard School of network analysis by way of his mentors. These included, among other people, Scott Boorman and Paul DiMaggio, both of whom were students of Harrison White, founder of the Harvard School. As I mentioned in an earlier post, much of the work that emerged out of this tradition was historical in nature. Yet while other folks were busy examining the relationship between patron-client networks and the rise of the state, Mohr used network analysis to examine the cultural foundations of welfare provision in New York City in the late 19th and early 20th centuries. What set Mohr’s research apart was not so much its subject matter or its general approach to network analysis, but the nature of the underlying data. Insofar as it is comprised of observed connections between individual actors, there is little ambiguity about the fact that a patronage network is a network, in even the most colloquial sense of the term. Mohr’s central insight was that we could understand culture and measure meaning structures by treating words as if they were a network.
As part of his early work, Mohr applied this approach to help understand the cultural logic of relief practices, as articulated in the New York City Charity Directory. First appearing in 1883, the Directory was published intermittently by the New York City Charity Organization Society until 1897, at which point it became an annual publication. Looking at the descriptions of the organizations included in the directory, one can identify which types of people received which types of relief from which types of organizations. For the purposes of this discussion, our central focus will be on the relationship between types of people and types of relief. To put it in somewhat fancier terms, we will focus on the coupling of identities and tasks or, fancier still, the duality of categories and practices. The intuition behind this approach is that the moral order of relief is revealed by the practical affordances associated with the various social identities recognized within the field of social welfare. The result is a dual order in the sense that we can draw distinctions between people based on the types of relief that they receive in the same way that we can draw distinction between types of relief based on the types of people to which they apply.
This is a lot to swallow. To help provide a fixed point of reference, we will think about this in terms of the individuals receiving welfare. In his 1994 piece on discourse roles in the 1907 New York City Charity Directory, Mohr includes a table depicting the relief practices associated to different categories of people. We can treat this table as a two-mode network in which individuals are linked to one another through the services that they receive. Using the raw data from the original paper, I was able to create the network in question, as shown below. The labels—which are taken right from the paper—are a bit complicated, so I would urge you to check out the article if you want to make sense of them all. A little more than half of the labels contain both an abbreviated description and a modifier. In the case of categories, these modifiers refer to gender (M = male, F = female, NG = ungendered). In the case of practices, these modifiers refer to the type of organization (S = state, SR = state-supported religious, SN = state-supported non-profit, N = non-profit, R = religious, C = church).
The lines in the graph indicate which types of people received which types of services. For example, if you squint hard enough, you can see that whereas high status men (HISTAT_M) and working men (WORKMEN) both received asylum from non-profit charities, high-status men, much like other high-status individuals, also received asylum from religious organizations (ASYLUM_R) as well. Looking at the general pattern of connections, there are three general features that stand out. The first feature is the division of categories and practices within the main component that results from the unique position of ungendered immigrants (IMMIG_NG), who were seen as being eligible for a large number of services, while also being excluded from a large number, giving the appearance of a sharp divide among the set of relief practices. The second feature is the presence of a small a secondary component organized around the male and female tramps (TRAMP_M and TRAMP_F, respectively), both of whom were either provided work or sent to jail at the hands of the state. The third and final feature is the set of isolated nodes in the upper right-hand corner. These points represent relief practices that were part of the general repertoire of welfare provision during this period but were not observed in the 1907 directory.
While there is a discernible structure to this graph, I would be lying if I didn’t own up to its hairball-like quality. The graph can, however, be further simplified to reveal a more general pattern of relationships. This is where theory and method come together to produce a coherent framework for the analysis of meaning structures. Within Mohr’s theoretical framework, cultural signifiers such as “solider” and “widow” mean the same thing to the extent that they are afforded the same types of relief. In the language of network analysis, this translates into saying that signifiers are synonymous to the extent that they are structurally equivalent. We can measure the degree of structural equivalence between any given pair of signifiers or categories by measuring the degree of similarity between their respective tie profiles. This can be done in a number of ways, perhaps the simplest of which is to calculate the pairwise correlation between the row or columns of the original two-mode data matrix. Whether you look at rows or columns depends on which mode you are interested in. In this case, we are interested in categories, which happen to be the columns in the binary data matrix provided in table 3 of the original paper.
Once we have constructed an initial correlation matrix measuring the degree of structural equivalence between each pair of categories, we can simplify the original two-model graph by sorting the categories in question into groups or blocks of structurally equivalent signifiers and then depicting the pattern of ties between blocks. The simplified representation of the graph is known as a blockmodel. Following Mohr, I used the CONCOR algorithm (which I implemented myself) to sort each category into one of eight blocks. The algorithm capitalizes on the fact that if you start taking the correlation of correlations, you will eventually get a matrix comprised solely of 1s and -1s. You can then separate the 1s from the -1s and start all over, dividing each of the submatrices. Insofar as it partitions the data into increasingly smaller groups, CONCOR works in the much the same way as hierarchical clustering. As Mohr describes at some length, a notable feature of this process is that a pair of categories can be assigned to the same block even if the initial correlation between them is low. This is a reflection of the fact that categories are being sorted into blocks by repeatedly taking the correlation of correlations, which means that categories belonging to the same block are similarly similar in their relationship to other categories vis-à-vis relief practices. It may be hard to see, but this is, in effect, an indirect method of assigning categories to blocks such that categories belonging to the same block are similarly tied to structurally equivalent relief practices, which are now unfortunately hidden as a result of having converted the original two-mode data into a one-mode network comprised of correlations.
I originally intended to use this data to work towards a two-mode blockmodel, but that is clearly going to have to wait for another post. For now, let’s check out a recreation of Mohr’s main result (with some slight modifications in presentation). Looking at the figure below, you can see not only how categories were assigned to blocks, but how the blocks relate to one another. Following Mohr, a pair of blocks is said to be tied if the average correlation between members of the two blocks is higher than the average correlation across the correlation matrix as a whole. While there is no way that I can do justice to Mohr’s interpretation in the space remaining, it is worth highlighting that after all of that mathematical manipulation, we can describe the differences between the positions in theoretically meaningful ways. Not only can we differentiate between domains based on the distinction between achieved versus ascribed status, we can also identify a clear role structure within each domain. Moreover, the roles in question can be described in terms of the degree of moral ambiguity associated with them.
The general pattern described here should look deeply familiar to anyone who has read Theda Skocpol’s Protecting Soldiers and Mothers, which examines the political origins of the 19th century welfare state in the United States. As Mohr’s work shows, notions of deservingness were not simply out there in the ether; rather, they were deeply embedded in the classificatory practices of welfare organizations that were collectively trying to make sense of the meaning of welfare provision and its relationship to the social order. While not alone, there is little doubt that Mohr was at the forefront of the revolution in text analysis in the social sciences. By his own account, it took more than 10,000 lines of SAS code to transform the raw text from the New York City Welfare Directories into usable network data! It should come as no surprise that Mohr would later embrace methods such as topic modeling. But for those of us who spent years admiring his work, it is hard to look at some of these techniques and not immediately think about blockmodels, Galois lattices, or multiple correspondence analysis.
This is more than just nostalgia. I recently did a directed reading with a graduate student, which included a week on word embedding. The student commented that the piece we read reminded her of Mohr’s work, which led to a discussion about the connection between the idea of structural equivalence and the identification of synonyms in text data. Word embedding is a thoroughly relational technique. Indeed, early variants of this approach involved using singular value decomposition to decompose a word-by-context matrix. This is not a far cry from the methods used by Mohr. The basic idea behind word embedding is that words can be represented as vectors in a multidimensional space, such that the distance between any given pair of words is a reflection of their propensity to be used synonymously. Words that appear next to each other in this space do not necessarily appear together in the underlying text, so much as they appear alongside other similar words. This is the same thing as a saying that words are synonymous to the extent that they occupy structurally equivalent position in relationship to other words. You can see hints of this idea in the evolution of Mohr’s work on welfare provision, which began by talking about structural equivalence between categories, before moving on to synonymy and the duality of categories and practices. This is all to say that the next time you fire up Python to calculate a cosine similarity, you should spend a minute thinking about John Mohr and all that he gave us.