The graph above recently appeared as part of Scott Walker’s Twitter feed. Presumably, the idea is to suggest that under Walker’s leadership, Wisconsin has done better than the country as a whole when it comes to unemployment, though an alternative version of the ad makes it somewhat more personal, using the same basic figures to suggest that Walker—a Republican presidential candidate—is outperforming sitting Democratic president Barack Obama. In these ads, the Walker campaign repeatedly highlights the fact that the unemployment rate in Wisconsin is lower than the national average. Note, however, that the unemployment rate in Wisconsin was already lower than the national average when Walker took office. In other words, Walker inherited a good labor market. If we want to measure Walker’s effect on the Wisconsin economy, we need to look at changes in the unemployment rate over time.
In network analysis, blockmodels provide a simplified representation of a more complex relational structure. The basic idea is to assign each actor to a position and then depict the relationship between positions. In settings where relational dynamics are sufficiently routinized, the relationship between positions neatly summarizes the relationship between sets of actors. How do we go about assigning actors to positions? Early work on this problem focused in particular on the concept of structural equivalence. Formally speaking, a pair of actors is said to be structurally equivalent if they are tied to the same set of alters. Note that by this definition, a pair of actors can be structurally equivalent without being tied to one another. This idea is central to debates over the role of cohesion versus equivalence.
In practice, actors are almost never exactly structural equivalent to one another. To get around this problem, we first measure the degree of structural equivalence between each pair of actors and then use these measures to look for groups of actors who are roughly comparable to one another. Structural equivalence can be measured in a number of different ways, with correlation and Euclidean distance emerging as popular options. Similarly, there are a number of methods for identifying groups of structurally equivalent actors. The
equiv.clust routine included in the
sna package in R, for example, relies on hierarchical cluster analysis (HCA). While the designation of positions is less cut and dry, one can use multidimensional scaling (MDS) in a similar manner. MDS and HCA can also be used in combination, with the former serving as a form of pre-processing. Either way, once clusters of structurally equivalent actors have been identified, we can construct a reduced graph depicting the relationship between the resulting groups.
Yet the most prominent examples of blockmodeling built not on HCA or MDS, but on an algorithm known as CONCOR. The algorithm takes it name from the simple trick on which it is based, namely the CONvergence of iterated CORrelations. We are all familiar with the idea of using correlation to measure the similarity between columns of a data matrix. As it turns out, you can also use correlation to measure the degree of similarity between the columns of the resulting correlation matrix. In other words, you can use correlation to measure the similarity of similarities. If you repeat this procedure over and over, you eventually end up with a matrix whose entries take on one of two values: 1 or -1. The final matrix can then be permuted to produce blocks of 1s and -1s, with each block representing a group of structurally equivalent actors. Dividing the original data accordingly, each of these groups can be further partitioned to produce a more fine-grained solution.
Insofar as CONCOR uses correlation as a both a measure of structural equivalence as well as a means of identifying groups of structurally equivalent actors, it is easy to forget that blockmodeling with CONCOR entails the same basic steps as blockmodeling with HCA. The logic behind the two procedures is identical. Indeed, Breiger, Boorman, and Arabie (1975) explicitly describe CONCOR as a hierarchical clustering algorithm. Note, however, that when it comes to measuring structural equivalence, CONCOR relies exclusively on the use of correlation, whereas HCA can be made to work with most common measures of (dis)similarity.
Since CONCOR wasn’t available as part of the
igraph libraries, I decided to put together my own CONCOR routine. It could probably still use a little work in terms of things like error checking, but there is enough there to replicate the wiring room example included in the piece by Breiger et al. Check it out! The program and sample data are available on my GitHub page. If you have
devtools installed, you can download everything directly using R. At the moment, the
concor_hca command is only set up to handle one-mode data, though this can be easily fixed. In an earlier version of the code, I included a second function for calculating tie densities, but I think it makes more sense to use
concor_hca to generate a membership vector which can then be passed to the
blockmodel command included as part of the
#REPLICATE BREIGER ET AL. (1975) #INSTALL CONCOR devtools::install_github("aslez/concoR") #LIBRARIES library(concoR) library(sna) #LOAD DATA data(bank_wiring) bank_wiring #CHECK INITIAL CORRELATIONS (TABLE III) m0 <- cor(do.call(rbind, bank_wiring)) round(m0, 2) #IDENTIFY BLOCKS USING A 4-BLOCK MODEL (TABLE IV) blks <- concor_hca(bank_wiring, p = 2) blks #CHECK FIT USING SNA (TABLE V) #code below fails unless glabels are specified blk_mod <- blockmodel(bank_wiring, blks$block, glabels = names(bank_wiring), plabels = rownames(bank_wiring[])) blk_mod plot(blk_mod)
The results are shown below. If you click on the image, you should be able to see all the labels.
This is a guest post by Matt Sundquist. Matt studied philosophy at Harvard and is a Co-founder at Plotly. He previously worked for Facebook’s Privacy Team, has been a Fulbright Scholar in Argentina and a Student Fellow of the Harvard Law School Program on the Legal Profession, and wrote about the Supreme Court for SCOTUSblog.com.
Emailing code, data, graphs, files, and folders around is painful (see below). Discussing all these different objects and translating between languages, versions, and file types makes it worse. We’re working on a project called Plotly aimed at solving this problem. The goal is to be a platform for delightful, web-based, language-agnostic plotting and collaboration. In this post, we’ll show how it works for ggplot2 and R.
A first Plotly ggplot2 plot
Let’s make a plot from the ggplot2 cheatsheet. You can copy and paste this code or sign-up for Plotly and get your own key. It’s free, you own your data, and you control your privacy (the set up is quite like GitHub).
install.packages("devtools") # so we can install from github library("devtools") install_github("ropensci/plotly") # plotly is part of the ropensci project library(plotly) py <- plotly("RgraphingAPI", "ektgzomjbx") # initiate plotly graph object library(ggplot2) library(gridExtra) set.seed(10005) xvar <- c(rnorm(1500, mean = -1), rnorm(1500, mean = 1.5)) yvar <- c(rnorm(1500, mean = 1), rnorm(1500, mean = 1.5)) zvar <- as.factor(c(rep(1, 1500), rep(2, 1500))) xy <- data.frame(xvar, yvar, zvar) plot<-ggplot(xy, aes(xvar)) + geom_histogram() py$ggplotly() # add this to your ggplot2 script to call plotly
Here is how we added a fit and can edit the figure:
Your Rosetta Stone for translating figures
py <- plotly("ggplot2examples", "3gazttckd7") figure <- py$get_figure("MattSundquist", 1339) str(figure)
That routine is possible from other languages and any plots. You can share figures and data between a GUI, Python, R, MATLAB, Julia, Excel, Dropbox, Google Drive, and SAS files.
Three Final thoughts
- Why did we build wrappers? Well, we originally set out to build our own syntax. You can use our syntax, which gives you access to the entirety of Plotly’s graphing library. However, we quickly heard from folks that it would be more convenient to be able to translate their figures to the web from libraries they were already using.
- Thus, Plotly has APIs for R, Julia, Python, MATLAB, and Node.js; supports LaTeX; and has figure converters for sharing plots from ggplot2, matplotlib, and Igor Pro. You can also translate figures from Seaborn, prettyplotlib, and ggplot for Python, as shown in this IPython Notebook. Then if you’d like to you can use our native syntax or the GUI to edit or make 3D graphs and streaming graphs.
- We’ve tried to keep the graphing library flexible. So while Plotly doesn’t natively support network visualizations (see what we support below), you can make them with MATLAB and Julia, as Benjamin Lind recently demonstrated on this blog. The same is true with maps. If you hit a wall, have feedback, or have questions, let us know. We’re at feedback at plot dot ly and @plotlygraphs.
This is a guest post by Randy Zwitch (@randyzwitch), a digital analytics and predictive modeling consultant in the Greater Philadelphia area. Randy blogs regularly about Data Science and related technologies at http://randyzwitch.com. He’s blogged at Bad Hessian before here.
For those of you with WordPress blogs and have the Jetpack Stats module installed, you’re intimately familiar with this chart. There’s nothing particularly special about this chart, other than you usually don’t see bar charts with the bars shown superimposed.
I wanted to see what it would take to replicate this chart in R, Python and Julia. Here’s what I found. (download the data).
With Season 6 of RuPaul’s Drag Race in the books and the new queen crowned, it’s time to reflect on how our pre-season forecasts did. In February I posted a wiki survey asking who would win this season before the first episode had aired. I posted this to reddit’s r/rupaulsdragrace, Twitter, and Facebook, and it generated an impressive 15,632 votes for 435 unique user sessions. Which means the average survey taker did a little under 36 pairwise comparisons.
The plot below shows the results. The x-axis is the score assigned by the All Our Ideas statistical model and can be interpreted that, if “idea” 1 (or, in this case, queen 1) is pitted at random against idea 2, this is the chance that idea 1 will win. The color is how close the wiki survey got to the actual rank. The more pale the dot, the closer. Bluer dots mean the wiki survey overestimated the queen, while redder dots mean it underestimated them.
So how did the wiki survey do? Not terrible. Courtney Act was a clear frontrunner and had a lot of star power to carry her to the end. Bianca was a close second in the wiki survey and finally outshone her when it came to the final. These two are relatively close to each other in score. This was actually the first season in which two queens never had to lipsync. Ben DeLaCreme is ranked third in the survey, although she came in fifth. Little surprise she was voted Miss Congeniality.
After that, it gets interesting. Milk was ranked four by the survey, but came in 9th on the show. I’m thinking her quirkiness may have given folks the impression that she could go much further than she actually did. Adore, one of the top three, comes in fifth on the survey, rather close to her friend Laganja.
April Carrion and Kelly Mantle were expected to go far, but got the chop relatively early on. Darienne was a dark horse in this competition, ending up in fourth place when pre-season fans thought she’d be middling.
Lastly, Joslyn and Trinity are the biggest success stories of season 6. They had a surprising amount of staying power when folks thought they wouldn’t make it out of the first month.
So what can we learn from this? Well, for one, for a more or less staged reality show, I’m somewhat impressed by how well these rankings came out. Unlike using wiki surveys for sports forecasting, we have no prior information on contestants from season to season. Prior seasons give us no information about contestants (unless you consider something like “drag lineages”, e.g. Laganja is Alyssa Edwards’s drag daughter). All information comes from the domain expertise of drag aficionados. Courtney and Bianca were already widely regarded drag stars in their own right before the competition. Although this didn’t seem to be the case with other seasons, it seems like there was a strong Matthew effect at work this time. Is this the new normal as more well-known queens start competing?
Last week’s post on the metal collaboration network brought attention largely to the “giant component”–the largest subgraph in a network where all actors have at least one path to all other actors. In large networks, even sparse ones, giant components typically emerge and include the majority of actors in the network. While focusing on the giant component follows conventional practice while analyzing small world networks, perhaps worthwhile information can be inferred from actors outside of the giant component.
A few months ago I started listening to Tomahawk, a band described on Wikipedia as “an experimental alternative metal/alternative rock supergroup.” Beyond the quality of their music, I found myself intrigued by the musical background of their members. In addition to Tomahawk, their other bands include acclaimed groups such as Faith No More, Helmet, the Melvins, Fantômas, and the Jesus Lizard. Mike Patton alone has been affiliated with at least fifteen bands. Continue reading
As mentioned in a previous post, Alex Hanna and I had the opportunity to teach last week at the Higher School of Economic’s International Social Network Analysis Summer School in St. Petersburg. While last year’s workshop emphasized smaller social networks, this year’s workshop focused on online networks. For my part, I provided an introductory lecture to social network analysis along with four labs on the subject of R and social network analysis.
The introduction to social network analysis began with an historical overview, followed by outlining which concepts constitute a social network. The remaining portions review subjects relating to subgraphs, walks, centrality, cohesive subgroups, along with major research subjects in the field. Setting aside the substantive interest in networks, the first lab covered basic R usage, objects, and syntax. Admittedly, this material was relatively dryer, though necessary to make the most of the network analysis software in R. We followed this introduction to R with an introduction to R’s social network analysis software. This second lab introduces the class to the different network packages within R, reading data, basic measurements brought up in the introductory lecture, and visualization. The third R SNA lab was on the subject of graph-level indices, random graphs, and Conditional Uniform Graph tests. Both the second and third labs were conducted primarily using the igraph package. The fourth and final lab of the course was on the subject of exponential random graph modeling. For this lab, we walked through tests for homophily and edgewise-shared partner effects using data on both our Twitter hashtag (#SNASPb2013) as well as US political blogs.
The slides include scripts that download and read the data used within all lab examples.
I’ve hosted PDFs of all the slides on Google Drive.
There have been repeated calls for “space” in many fields of social science (all links are behind paywalls, sorry):
- Demography: (Voss 2007)
- Sociology: (Gieryn 2000)
- Epidemiology: for an early critical review (Jacquez 2000)
- Geography: obviously geographers were into space before it was cool. A couple of pieces I like are Doreen Massey’s book, For Space and O’Sullivan (2006) for a review of GIS.
- Anthropology: the proceedings of a conference including a piece by Clifford Geertz, Senses of Place (1996). Though what I’m writing here has less to do with the space/place debate.
These are nice papers about what the authors think should be new research agendas, bu I think social sciences need to stop calling for space and start “playing” with space. Let me explain…
This idea started when fellow Bad Hessian, Alex Hanna, suggested that I read a paper about spatio-temporal models of crime in Chicago. We are in the same writing group. Alex has suffered through many presentations of a paper I’m writing about crime in Chicago. Chicago? Crime? I mean these have to be related papers, right? So I gave it a quick read:
Seth R. Flaxman, Daniel B. Neill, Alex J. Smola. 2013. Correlates of homicide: New space/time interaction tests for spatiotemporal point processes. Heinz College working paper, available at: http://www.heinz.cmu.edu/faculty-and-research/research/research-details/index.aspx?rid=483
…and it’s a really great paper! Flaxman reviews three standard measures for spatial and temporal independence and then proposes a new measure that can simultaneously test for spatio-temporal dependence. The measures are validated against real crime data from Chicago. On the other hand, it’s also completely useless for my project. I mean, I stuck it in a footnote, but I can’t engage with it in a substantively meaningful way because my paper is about the Modifiable Areal Unit Problem and the good ol’ MAUP is fundamentally about polygons — not points. The MAUP occurs because a given set of points can be aggregated into any number of different polygon units, and the subsequent results of models, bivariate relationships, or even hot spot analysis might change based on the aggregation method.
This means that Flaxman’s approach and my approach are not comparable because they each rest on different assumptions about how to measure distance, social interaction, and spatial dependence. They’re based on different spatial ontologies, if you will. But back to the main argument of this post: could we play around with the models in Flaxman, the models I’m making, plus some other models in order to test some of the implications of our ideas of space? Here are some hypothetical hypotheses….
Isotropy. Isotropy means that effects are the same in every direction. For example, weather models often take into account anisotropy because of prevailing wind direction. As Flaxman mentions at the end of the paper, alternative distance measures like Manahatten distance could be used. I would take it a step further and suggest that distance could be measured across a trend surface which might control for higher crime rates on the south side of Chicago and in the near-west suburbs. Likewise, spatial regression models of polygon data can use polynomial terms to approximate trend surfaces. Do the additional controls for anisotropy improve model fit? Or change parameter estimates?
Spatial discontinuities. A neighborhood model posits — albeit implicitly and sort of wishy-washy — that there could be two locations that are very close as the crow flies, but are subject to dramatically different forces because they are in different polygons. These sharp breaks might really exist, e.g. “the bad side of the tracks”, red-lining, TIFF funding, empowerment zones, rivers, gated suburbs. Or they might not. Point process models usually assume that space is continuous, i.e. that there are no discontinuities. Playing around with alternative models might give us evidence one way or another.
Effect decay. In spatial regression models like I’m using, it’s pretty normal to operationalize spatial effects for contiguous polygons and then set the effect to zero for all higher order neighbors. As in the Flaxman paper, most point models use some sort of kernal function to create effect estimates between points within a given bandwidth. These are both pretty arbitrary choices that make spatial effects too “circular”. For exmple, think of the economic geographies of interstate exchanges in middle America. You’ll see fast food, big box retail, gas stations, car dealerships, hotesls, etc. at alomst every interchange. Certainly there is a spatial pattern here but it’s not circular and it’s not (exponentially, geometrically, or linearly) decaying across distance. Comparisons between our standard models — where decay is constrained to follow parametric forms — and semi-parametric “hot spot” analyses might tell us if our models of spatial effects are too far away from reality.
Ok. Those sound like valid research questions, so why not just do that research and publish some results? As I see it, spatial work in social sciences usually boils down to two main types of writing. First, there are the papers that aren’t terribly interested in the substantive research areas, and are more about developing statistical models or testing a bunch of different models with the same data. Here are some examples of that type:
- (Dormann et al 2007) undertake a herculean task by explicating and producing R code for no less than 13 different spatial models.
- (Hubbard et al 2010) compare GEE to mixed models of neighborhood health outcomes.
- (Tita and Greenbaum 2009) compare a spatial versus a spatio-social network as weighting matrices in spatial regression.
The problem with this approach is that the data is often old, simplified data from well-known example datasets. Or worst yet, it is simulated data with none of the usual problems of missing data, measurement error, and outliers. At best, these papers use over simplified models. For example, there aren’t any control variables for crime even when there is a giant body of literature about the socio-cultural correlates of spatial crime patterns (Flaxman and I are both guilty of this).
The second type of research would be just the opposite: interested in the substantive conclusions and disinterested in the vagaries of spatial models. They might compare hierchical or logistic regressions to the spatial regressions, but very rarely go in depth about all the possible ways of operationalizing the spatial processes they’re studying. And when you think about it, you can’t blame them because journal editors like to see logical arguments for the model assumptions used in a paper – not an admission that we don’t know anything about the process under study and a bunch of different models all with slightly different operationalizations of the spatial process. But here’s the thing: we don’t actually know very much about the spatial processes at work! And we have absolutely no evidence that the spatial processes for, say, crime are also useful in other domains like educational outcomes, voting behavior, factory siting, human pathogens, or communication networks.
Thus, we don’t need more social science papers that do spatial models. We need (many) more social science papers that do multiple, incongruent spatial models on the same substantively rich datasets. I think it’s only by modeling, for example, crime as an isotropic point process, a social network with spatial distance between nodes, and a series of discrete neighborhood polygons can we start to grasp if one set of assumptions about space is more/less accurate and more/less useful. In case you couldn’t tell, I’m a big fan of George Box’s famous quote. This is the slightly longer version:
“Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful.” (Box & Draper 1987, 74)
Good luck, and go play!
[Update, 2013-07-22: I changed the citation to the Flaxman paper, as it is now a working paper in his department at Carneige Mellon University.]
R users know it can be finicky in its requirements and opaque in its error messages. The beginning R user often then happily discovers that a mailing list for dealing with R problems with a large and active user base, R-help, has existed since 1997. Then, the beginning R user wades into the waters, asks a question, and is promptly torn to shreds for inadequate knowledge of statistics and/or the software, for wanting to do something silly, or for the gravest sin of violating the posting guidelines. The R user slinks away, tail between legs, and attempts to find another source of help. Or so the conventional wisdom goes. Late last year, someone on Twitter (I don’t remember who, let me know if it was you) asked if R-help was getting meaner. I decided to collect some evidence and find out.
Our findings are surprising, but I think I have some simple sociological explanations.