Alex’s Adventures in Academia-land

Words, words, words
Intro

While I usually use this blog to work on casual pet projects, I wanted to take an opportunity to use the medium to discuss academic research. Writing is an instinctive mechanism for me to process my thoughts on a topic, but it is one that I use sparingly to discuss the meta-narrative of my own decisions and behavior. The impetus for this self-reflection is the following exciting news: I’ll be pursuing my PhD in economics at Harvard starting this fall! The decision has naturally prompted me to think about my adventures thus far in the academic sphere and the scope of my ambitions and interests.

Think of this as a more organized and open outlet for many of the words (written, spoken, and silently thought) that have bounced around my head throughout the (now 100% finished!) applications process. This post contains a mixture of excerpts from academic personal statements from PhD applications as well as even undergraduate ones (turns out the overwhelming majority of my college application essays involved math in some way, shape, or form).[1] The purpose of this piece is multi-pronged: I’m hoping to (Part I) introduce my interest in economics research on a personal level, (Part II) clearly outline research questions and topics that I have worked on, and (Part III) describe potential eventual research ambitions.[2]

Part I: The number friends

A framed piece of legal paper hung in my parents’ room for nearly a dozen years. The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 were etched onto the page. Each held a shade or two of color, leaked from a gifted box of gel pens, within its skinny outline. A speech bubble burst from each number so it could introduce itself or articulate feelings that might be beyond its self-quantification. ‘9’ philosophizes that “it is hard to be odd,” while ‘1’ grumbles over lonesomeness. Atop this paper is the simply written title “The Number Friends.”[3]

Many of my childhood memories are inseparably intertwined with numbers. Learning the exponents of 2 while poking my head into the ice cream freezer at our local deli. Multiplying numbers by wicking my finger against moisture on my grandmother’s 1980 Volvo. Calculating and writing up the winning percentages of baseball teams on the white board in our living room. (It’s an understatement to say that the 2000 subway series was an exciting time in my early life.) To cut to the chase, I was always fond of numbers. My numbers—those I played with as though they were a set of stuffed animals in my living room—hardly resemble those many people groan about—their dusty gray, corporate counterparts.

Despite my interest in the numbers that were stacked on top of each other to fill the standings in the sports section, I grew up ignoring a word that often found itself on adjacent pages of the inky paper— “economics.” The word always seemed to be coming from the lips of men in suits who carried leather briefcases and drank dark, serious coffees. It was a word that I did not associate with anything but Mr. Monopoly—that is, until my senior year of high school when I took an economics class for the first time. Carrying the weightless tools of microeconomics outside of the classroom, I quickly found myself internally modeling the grumpiness of my classmates based on the outside temperature, the day’s schedule type, the quality of their chosen lunch, and the morning delays (or, hopefully, lack thereof) on their regular subway line; explaining my teenage decisions to my parents by implicitly highlighting our very different utility functions; and even debating how one could “optimally” match up students for prom.[4] Imagine my joy in 2012 when Alvin E. Roth won the Economics Nobel for work that redesigned the mechanism for students to select into my exam high school (Stuyvesant High School[5])! The eventual knowledge that groundbreaking work in game theory and market design had implicitly played a role in my presence at that school and, accordingly, in my first foray into economics was incredibly exciting and inspiring. My innate adoration of mathematics and logic combined with my attention to the dynamics of the human world around me molded me into a young economist.[6]

Part IIa: Early research exposure

In my undergraduate studies, I eagerly continued formulating arguments and theories using the building blocks of microeconomic theory and began to seek out academic opportunities to explore these interests. In particular, my fondness for behavioral economics was solidified when I earned a job as a Research Assistant to Professor Sarah Jacobsen my junior year and discovered how assumptions of rational choice do not necessarily hold in human decision-making.  In helping evaluate the results of experimental economic studies, I was intrigued by the gap between seemingly concrete theory and the realities of human behavior.[7] I dived deeper into economics research by working on campus at Williams that following summer as a 1957 Research Fellow for Professor Yung Suk Lee, focusing on a project about the expansion of exam schools and opportunities to attain academic achievement. In this role, I used knowledge of exam cutoffs for admission into specialized New York exam schools and compared academic outcomes for students that were at the margin (both above and below cutoffs) to investigate the much-debated impact of these schools on later academic success. As well as exposing me to statistical methodologies such as regression discontinuity design, the summer taught me how to work independently and probe assumptions and logical frameworks at the core of well-respected studies.

Part IIb: Wine economics as senior thesis

At the end of my junior year, I was lucky enough to be awarded the Carl Van Duyne Prize in Economics and received funding to pursue a senior honors thesis; this opportunity was the catalyst for the start of my self-directed economics research. My project focused on the intersection of applied econometrics and behavioral economics and examined the dynamic response of prices in the wine market to wine critic reviews. Since consumers have often not experienced a given wine ex ante when considering what to buy, reviews and ratings of quality play a consequential role in shaping consumer and market dynamics. My fascination with this subject was derived from the knowledge that, though ratings measure quality, they also influence consumers independent of their accuracy; for this reason, my curiosity about how researchers could disentangle the concepts of hype and quality grew.

While other economists have studied similar topics, no previous work had defined hype and quality as unobserved concepts. Given the fact that I defined these two dimensions of a product as unobserved, a naive cross-sectional regression would not have sufficed in comparing the respective roles. Therefore, I instead used a panel structural vector autoregression methodology to approach this topic from a new angle. (For more on this method, see Pedroni 2013.) I exploited knowledge of the dynamics of an online wine community (CellarTracker) as well as the behavior of the consumer rating mechanism in order to construct short-run restrictions to identify structural shocks. Therefore, by combining both substantive knowledge of wine and the wine drinking community with statistical techniques, I was able to work on a novel approach to a continuously intriguing problem.

I continue to work with my advisor Professor Peter Pedroni on translating the concepts beyond the scope of wine to broader research pertaining to high-end goods. In fact, I’m going to the American Association of Wine Economists Meeting in Bordeaux to present on this in June![8] In preparing a paper for conference submission, we treat information from expert reviews of high-end goods as a part of a broader signal extraction problem tackled by consumers of such goods. (More to come on this soon…) During June 2015, I presented this ongoing work at the interdisciplinary Connected Life Conference at Oxford University, which fostered collaboration with computer scientists, sociologists, and other researchers.[9]

Part IIc: Working at the intersection of law and economics @ Stanford

Since graduating from Williams, I have worked with Professor John Donohue at Stanford Law School as a Research Fellow.[10] In this pre-doctoral role, I work on projects at the intersection of law and economics, with a particular focus on the economics of crime and related econometric and statistical methodologies. For instance, I got to play a large role in developing and reviewing the paper “The Empirical Evaluation of Law: The Dream and the Nightmare” (published in the Journal of American Law and Economics Review).[11] This paper charts the enormous advances in estimating causal effects of laws and policies in the past few decades and points out the frequency of conflicting studies on identical questions. Given the conflicting nature of many studies, it can be hard to know what should be believed and the media, think tanks, and others often exploit this difficulty to promote certain studies for private political or social agendas. Accordingly, in discussing the methodological soundness of various approaches, this article seeks to begin a discussion about how we want to manage the translation between research and media coverage especially when it comes to politically contentious topics.

On a related note, I am currently working on a project that uses a statistical technique called synthetic controls (see Abadie & Gardeazabal 2003 and Abadie, Diamond, & Hainmueller 2009) to look at the impact of right-to-carry laws on crime in the United States. The impact of right-to-carry gun laws on crime has been debated within both the academic community and the public sphere for decades. To address some of the inherent weaknesses of panel data models, we are using the aforementioned synthetic controls methodology, a methodology that generates counterfactual units by creating a weighted combination of similar (in terms of the pre-treatment period) control units. Panel data studies are often extremely sensitive to minor changes in choices of explanatory variables. Therefore, by working on new approaches to these sorts of questions, we seek out methods that generate robust results that have the potential to help guide policy decisions in pivotal areas, where slicing and dicing numbers can be done to fit virtually any policy agenda. The broader impacts of creating robust decision-making processes for analyzing the impact of controversial policies is one of the aspects of economics about which I am most passionate.

Part IIIa: Potential research ambitions in economics

During PhD visits, it is common to pitch your interests to professors. At the macro level (and using some slick economics jargon), I am most interested in behavioral economics, and applied microeconomics. Applied microeconomics is a lovably large umbrella term that easily contains both urban economics, and law and economics, and, therefore, the previous sentence adequately articulates both my interest in the effects of psychological/social/cognitive/emotional factors on decision making as well as the application of microeconomic theory to the study of crime, cities, law, and education. (That undoubtedly leaves space for a lot of potential research topics!)

While I have a number of continuing interests, such as the reputational influence of experts in networks as investigated in the wine project (in the behavioral realm), or economics of crime topics at Stanford, I believe one of the ripest and most important areas for economic research is actually a union of behavioral economics with the economics of crime. That is, further investigating how people find themselves participating in crime.

I am often struck by how often individuals, myself included, buy into illusions of choice. It is tempting to view one’s accomplishments as essentially a function of personal social/academic merit. This is especially true among the more privileged among us—those of us who grew up benefitting from the financial success of family members, the color of our skin, and overall, positive reenforcement in most facets of our lives. I became aware of the influence of environmental behavioral factors while observing my own behaviors in a school context. In high school, I was lucky enough to be a beneficiary of overwhelmingly positive forces (driven/ambitious peers and thoughtful/encouraging teachers). The profound influence of positive classrooms like my own can be easily seen in a recent study by Card and Giuliano. The study found that participation by “non-gifted” students in a “gifted” classroom lead to significant achievement gains for the minority students (gains of 0.5 standard deviations in reading/math). Incredibly, the authors did not attribute the gains to teacher quality or peer effects, but to “the effects to a combination of factors like teacher expectations and negative peer pressure that lead high-ability minority students to under-perform in regular classes but are reduced in a GHA classroom environment“!

While education topics are increasingly receiving a behavioral treatment in the literature (due in part to the ability to fashion experiments in classrooms and, potentially, due to the less politically contentious nature of education), the current state of the economics of crime is still deeply entrenched in Beckerian ideas of deterrence–criminals make cost-benefit calculations in their minds and then use these to inform decisions. This type of reasoning (which is not incorrect, as much as it is lacking in dimensions of the human experience) over the past decades has lead to piles and piles of papers trying to separate out the impact of sentence enhancements (seen around the time of the 1990’s crime decline) into an incapacitation effect (people are off the street in prison and thus incapable of committing crimes) and a deterrence effect (people are scared off of committing crimes because of the greater cost). What with our improved notions of behavioral mechanisms and the current well-deserved focus on incarceration levels, policies from the 1990’s (specifically, the 1994 crime bill), and interactions between police and disadvantaged communities, there is no doubt that further studies of the social interactions in crime networks (see the classic Glaeser 1996 paper) as well as environmental factors (think Reyes’ work on lead exposure) are warranted to better inform policy as well as our core human understanding of how peoples’ lives diverge so starkly. Illusions of choice are powerful (as well as enticing to those at the helm of the ship) and are accordingly worth a hefty dose of skepticism from the community at large. (There are many more ideas to develop and papers to cite in these paragraphs, but I’ll let this marinate as it is for the moment.)

On herd behavior in particular: I have no qualms in asserting that I have benefited immensely from herding behaviors that harm others who simply gained consciousness in a different social/economic environment. The same strains of herd behavior, which pulses through networks (those of academics, and those of drug traffickers alike), lead to disparate outcomes based on the starting point and environment in which they occur. 

Beyond behavior and crime, some other developing research interests on my eventual topic wishlist include:

Part IIIb: Things are about to get meta

On a somewhat meta note, I feel strongly about making economics research and, more generally, research that is data-driven replicable and accessible to the public. I believe that open sourcing datasets and code for projects not only facilitates how different projects can build off of one another but also encourages a more diverse group of individuals to explore quantitative methods.[12] By making work publicly accessible, researchers can challenge themselves to defend their ideas and assertions to any interested individuals, rather than limiting themselves to discussion in academic bubbles. I strongly believe that this renders research dynamics fundamentally more efficient, as public-facing projects allow for a faster and smoother exchange of ideas, which can lead to superior projects in the long-run. This sort of openness on the part of researchers often allows for great collaborations—my wonderful friend/public speaking inspiration Sarah Michael Levine and I originally bonded via Twitter (!) and then ended up writing a paper together on the shortcomings of mainstream data science when applied to social good projects (which we got to present at the Bloomberg Data for Good Exchange 2015). In my personal experience, making work and ideas available to a larger audience has led to a number of incredible opportunities to work with talented people on a range of captivating questions that engage the public and illustrate the fundamental creativity that is inherent to but often ignored in quantitative work.

Endnote

In reviewing this writing, I am acutely aware of the fact that I tend to over-narrativize my own experiences, injecting meaning into the twists and turns that may just be segments of a random walk. However, while there might not be some grand meaning in an individual’s path towards the degree that we call a PhD, I do strongly believe in the profound nature of social science research more generally—self-awareness is fundamentally human and our ability to study our own machinations is something that we find irresistible.[13] The letters we desire to have traipse behind our names are trivial in the long run, but the questions we ask in pursuit of them ultimately stem from the core of personhood—consciousness and the curiosity that comes with it.[14][15]

Footnotes

[1] Concretely describing motivations, processes, and goals for research is an element of communication in academia that I believe can be much improved by embracing non-traditional/technologically-driven mediums of discussion. So, why not take the time to try and practice communicating with the transparency and openness that I often crave from other researchers? (Warning: this is going to be long! I am working through caches of thoughts that have managed to build themselves into some pretty hefty structures over the years.)

[2] In thinking about that oft-cited 2 x 2 matrix that contains four quadrants dedicated to simple/complex ideas vs. simple/complex writing, the dream is to eventually make it into that slick complex ideas & simple writing quadrant.

[3] Oh, the trials and tribulations of being an only child… (“Some imaginary friends you never outgrow.”)

[4] Think utility maximization problems. If the application of mathematical concepts to questions of romance is interesting to you: check out the marriage problem.

[5] Go Vixens!/Go Phoenix!/Go Renegades! (The last one was a much needed improvement from the softball team’s previous mascot—the Chipmunks.)

[6] In this vein of personal narrative, see also Claudia Goldin’s “The Economist as Detective.”

[7] In technical terms, I ran paired t-test and signed-rank regressions in order to analyze a survey participant’s level of consistency in terms of his or her risk-taking decisions.

[8] Hopefully, I will soon have some slides that can help in communicating the relevant ideas.

[9] Check out the call for papers!

[10] I originally found out about Prof Donohue through reading Freakonomics (a commonly cited catalyst for people’s realization that economics can be clever and creative!) my sophomore year since the abortion and crime chapter is based on one of his articles “The Impact of Legalized Abortion on Crime” with Steven Levitt of UChicago.

[11] I saw the journal that contained this article (and my name typed within it) in the flesh a few weeks ago at Harvard before some meetings. That experience immediately quashed some hefty feelings of impostor syndrome.

[12] Papers, data, and methods should be available to the public rather than only available to those at institutions of higher education…or, even worse only available through asking nicely via email with shiny credentials. (Once, a professor I emailed once for data responded that he was retiring and moving across the country, so he had thrown out all his papers, and, thus, could not help me. I often feel more like an investigative reporter when tracking down data than an academic!)

[13] Research in this context should not be solely interpreted as academic research! In fact, I would argue that every individual conducts casual research in the day-to-day, while the PhD is an example of an institutionalized and formal medium for research.

[14] Listen to this recent episode of Radiolab for the following relevant quote and much more: “Consciousness—for some reason, for some reason one animal on the planet and only one that we can know seems to string into this very elaborate sense of self-awareness—we don’t know how it happened we don’t know why it happened it just did”

[15] Insightful discussions that stem from that very curiosity should not be limited to only those with a PhD. So, social network, let’s talk.


© Alexandra Albright and The Little Dataset That Could, 2016. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts, accompanying visuals, and links may be used, provided that full and clear credit is given to Alex Albright and The Little Dataset That Could with appropriate and specific direction to the original content.

The Curious Case of The Illinois Trump Delegates

Scatter Plots
Intro

This past Wednesday, after watching Hillary Clinton slow-motion strut into the Broad City universe and realizing that this election has successfully seeped into even the most intimate of personal rituals, I planned to go to sleep without thinking any more about the current presidential race. However, somewhere in between Ilana’s final “yas queen” and hitting the pillow, I saw David Wasserman’s FiveThirtyEight article “Trump Voters’ Aversion To Foreign-Sounding Names Cost Him Delegates.”

Like many readers I was immediately drawn to the piece’s fundamentally ironic implication that Trump could have lost delegates in Illinois due to the very racial resentment that he espouses and even encourages among his supporters. The possibility that this could be more deeply investigated was an energizing idea, which had already inspired Evan Soltas to do just that as well as make public his rich-in-applications-and-possibilities dataset. With this dataset in hand, I tried my hand at complementing the ideas from the Wasserman and Soltas articles by building some visual evidence. (Suffice it to say I did not end up going to sleep for a while.)

To contribute to the meaningful work that the two articles have completed, I will first quickly outline their scope and conclusions, and then present the visuals I’ve built using Soltas’ publicly available data. Consider this a politically timely exercise in speedy R scripting!

Wasserman’s FiveThirtyEight piece & Soltas’ blog post

In the original article of interest, Wasserman discusses the noteworthy Illinois Republican primary. He explains that,

Illinois Republicans hold a convoluted “loophole” primary: The statewide primary winner earns 15 delegates, but the state’s other 54 delegates are elected directly on the ballot, with three at stake in each of the state’s 18 congressional districts. Each campaign files slates of relatively unknown supporters to run for delegate slots, and each would-be delegate’s presidential preference is listed beside his or her name.

Given that the delegates are “relatively unknown,” one would assume that delegates in the same district who list the same presidential preference would earn similar numbers of votes. However, surprisingly, Wasserman found that this did not seem to be the case for Trump delegates. In fact, there is a striking pattern in the Illinois districts with the 12 highest vote differentials: “[i]n all 12 cases, the highest vote-getting candidate had a common, Anglo-sounding name” while “a majority of the trailing candidates had first or last names most commonly associated with Asian, Hispanic or African-American heritages.” These findings, while admittedly informal, strongly suggest that Trump supporters are racially biased in their delegate voting behaviors.

Soltas jumps into this discussion by first creating dataset on all 458 people who ran for Illinois Republican delegate spots. He merges data on the individuals’ names, districts, and candidate representation with a variable that could be described as a measure of perceived whiteness–the non-Hispanic white percentage of the individual’s last name, as determined from 2000 US Census data. The inclusion of this variable is what makes the dataset so exciting (!!!) since, as Soltas explains, this gives us an “objective measure to test the phenomenon Wasserman discovered.”

The article goes on to confirm the legitimacy of Wasserman’s hypothesis. In short, “Trump delegates won significantly more votes when they had “whiter” last names relative to other delegates in their district” and this type of effect does not exist for the other Republicans.

Visual evidence time

I now present a few visuals I generated using the aforementioned dataset to see Soltas’ conclusions for myself. First things first, it’s important to note that some grand underlying mechanism does not jump out at you when you simply look at the association between perceived whiteness and vote percentage for all of Trump’s Illinois delegates:

fig1

The above graph does not suggest any significant relationship between these two numbers attached to each individual delegate. This is because the plot shows delegates across all different districts, which will vote for Trump at different levels, but compares their absolute variable levels. What we actually care about is comparing voting percentages within the same district, but across different individuals who all represent the same presidential hopeful. In other words, we need to think about the delegates relative to their district-level context. To do this, I calculate vote percentages and whiteness measures relative to the district: the percentage point difference between a Trump delegate’s vote|whiteness percentage and the average Trump delegate vote|whiteness percentage in that district. (Suggestions welcome on different ways of doing this for visualization’s sake!)

fig2

Now that we are measuring these variables (vote percentage and whiteness measure) relative to the district, there is a statistically significant association beyond even the 0.1% level. (The simple linear regression Y~X in this case yields a t-statistic of 5.4!) In the end, the interpretation of the simplistic linear regression is that a 10 percentage point increase in a Trump delegate’s perceived whiteness relative to the district yields a 0.12 percentage point increase in the delegate’s vote percentage relative to the district. (I’m curious if people think there is a better way to take district levels into account for these visuals–let me know if you have any thoughts that yield a simpler coefficient interpretation!)

The last dimension of this discussion requires comparing Trump to the other Republican candidates. Given the media’s endless coverage of Trump, I would not have been surprised to learn that this effect impacts other campaigns but just was never reported. But, Wasserman and Soltas argue that this is not the case. Their claims are further bolstered by the following visual, which recreates the most recent Trump plot for all 9 candidates who had sufficient data (excludes Gilmore, Huckabee, and  Santorum):

fig3

It should be immediately clear that Trump is the only candidate for whom there is a positive statistically significant association between the two relative measures. While Kasich has an upward sloping regression line, the corresponding 95% confidence interval demonstrates that the coefficient on relative perceived whiteness is not statistically significantly different from 0. Employing the whiteness measure in this context allows us to provide quantitative evidence for Wasserman’s original intuition that this effect is unique to Trump–thus, “lend[ing] credibility to the theory that racial resentment is commonplace among his supporters.”

The role of perceptions of whiteness

Wasserman’s article has incited an outpouring of genuine interest over the past few days. The fascinating nature of the original inquiry combined with Soltas’ integration of a perceived whiteness measure into the Illinois delegate dataset provides a perfect setting in which to investigate the role racial resentment is playing in these particular voting patterns, and in the election on the whole.

Code

My illinois_delegates Github repo has the R script and csv file necessary to replicate all three visuals! (We know data, we have the best data.)


© Alexandra Albright and The Little Dataset That Could, 2016. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts, accompanying visuals, and links may be used, provided that full and clear credit is given to Alex Albright and The Little Dataset That Could with appropriate and specific direction to the original content.

 

How I Learned to Stop Worrying and Love Economics

Words, words, words
Intro

Many months ago, in October, the Economics Nobel prize was awarded to Angus Deaton. Beyond experiencing sheer joy at having beaten my friend Mike at predicting the winner, I also was overwhelmed by the routine, yearly backlash against the discipline in the form of articles shared widely across any and all social networks. Of particular interest to me this year was the Guardian’s piece “Don’t let the Nobel prize fool you. Economics is not a science.” The dialogue surrounding this article made me incredibly curious to investigate my own thoughts on the discipline and its place in the realm of “the sciences.” In a frenzy of activity that can only be accurately explained as the result of a perfect storm of manic energy and genuine love for an academic topic, I wrote up a response not only to this article, but also to my own sense of insecurity in studying a discipline that is often cut down to size by the public and other academics.

In my aforementioned frenzy of activity, I found myself constantly talking with Mike (in spite of my status as the superior Nobel forecaster) about the definition of science, hierarchies of methodologies for causal inference, the role of mathematics in applied social science, and our own personal experiences with economics. Eventually, I linked the Guardian article to him in order to explain the source of my academic existential probing. As another economics researcher, Mike had a similarly strong reaction to reading the Guardian’s piece and ended up writing his own response as well.

So, I am now (albeit months after the original discussion) using this space to post both responses. I hope you’ll humor some thoughts and reactions from two aspiring economists.

Alex responds

I developed a few behavioral ticks in college when asked about my major.  First, I would blurt out “Math” and, after a brief pause of letting the unquestioned legitimacy of that discipline settle in, I would add “and Econ!”–an audible exclamation point in my voice. I had discovered through years of experience that the more enthusiastic you sounded, the less likely someone would take a dig at your field. However, nonetheless, I would always brace myself for cutting criticism as though the proofs I attempted to complete in Advanced Microeconomics were themselves the lynchpin of the financial crisis.

In the court of public opinion, economics is often misunderstood as the get-rich-quick major synonymous with Finance. The basic assumptions of self-interest and rationality that the discipline gives its theoretical actors are stamped onto its practitioners and relabeled as hubris and heartlessness. Very few students are seeking out dreamy economics majors to woo them with illustrations of utility functions in which time spent together is a variable accompanied by a large positive coefficient. (The part where you explain that there is also a squared term with a negative coefficient since the law of diminishing marginal utility still applies is not as adorable. Or so I’ve been told.)

It can be hard to take unadulterated pride in a subject that individuals on all sides of the techie/fuzzy or quant/qual spectrum feel confident to discredit so openly. Economics is an outsider to many different categories of academic study; it is notably more focused on quantitative techniques than are other social sciences but its applications are to human phenomena, which rightfully ousts it from the exclusive playground of the hard sciences. I admit I have often felt awkward or personally slighted when accosted by articles like Joris Luyendijk’s “Don’t let the Nobel prize fool you. Economics is not a science.” which readily demeans contributions to economics simply by both appealing to the unsexiness of technical jargon and by contrasting these with the literature and peace prizes:

Think of how frequently the Nobel prize for literature elevates little-known writers or poets to the global stage, or how the peace prize stirs up a vital global conversation: Naguib Mahfouz’s Nobel introduced Arab literature to a mass audience, while last year’s prize for Kailash Satyarthi and Malala Yousafzai put the right of all children to an education on the agenda. Nobel prizes in economics, meanwhile, go to “contributions to methods of analysing economic time series with time-varying volatility” (2003) or the “analysis of trade patterns and location of economic activity” (2008).

While comparing strides in economic methods to the contributions of peace prize recipients is akin to comparing apples to dragon fruit, Luyendijk does have a point that “[m]any economists seem to have come to think of their field in scientific terms: a body of incrementally growing objective knowledge.” When I first starting playing around with regressions in Stata as a sophomore in college, I was working under the implicit assumption that there was one model I was seeking out. My different attempted specifications were the statistical equivalent of an archeologist’s whisks of ancient dust off of some fascinating series of bones. I assumed the skeleton would eventually peek out from the ground, undisputedly there for all to see. I assumed this was just like how there was one theorem I was trying to prove in graph theory–sure, there were multiple modes of axiomatic transport available to end up there, but we were bound to end up in the same place (unless, of course, I fell asleep in snack bar before I could really get there). I quickly realized that directly transplanting mathematical and statistical notions into the realm of social science can lead to numbers and asterisks denoting statistical significance floating around in zero gravity with nothing to pin them down. Tying the 1’s, 3’s, and **’s  down requires theory and we, as economic actors ourselves who perpetually seek optimal solutions, often entertain the fantasy of a perfectly complex and complete model that could smoothly trace the outline and motions of our dynamic, imperfect society.

However, it is exactly Luyendijk’s point that “human knowledge about humans is fundamentally different from human knowledge about the natural world” that precludes this type of exact clean solution to fundamentally human questions in economics–a fact that has and continues to irk me, if not simply because of the limitations of computational social science, then because of the imperfection and incompleteness of human knowledge (even of our own societies, incentives, and desires) of which it reminds me. Yet, as I have spent more and more time steeped in the world of economics, I have come to confidently argue that the lack of one incredibly complex model that manages to encapsulate “timeless truth[s]” about human dynamics does not mean models or quantitative methods have no place in the social sciences. Professor Dani Rodek, in probably my favorite piece of writing on economics this past year, writes that,

Jorge Luis Borges, the Argentine writer, once wrote a short story – a single paragraph – that is perhaps the best guide to the scientific method. In it, he described a distant land where cartography – the science of making maps – was taken to ridiculous extremes. A map of a province was so detailed that it was the size of an entire city. The map of the empire occupied an entire province.

In time, the cartographers became even more ambitious: they drew a map that was an exact, one-to-one replica of the whole empire. As Borges wryly notes, subsequent generations could find no practical use for such an unwieldy map. So the map was left to rot in the desert, along with the science of geography that it represented.

Borges’s point still eludes many social scientists today: understanding requires simplification. The best way to respond to the complexity of social life is not to devise ever-more elaborate models, but to learn how different causal mechanisms work, one at a time, and then figure out which ones are most relevant in a particular setting.

In this sense, “focusing on complex statistical analyses and modeling” does not have to be to “the detriment of the observation of reality,” as Luyendijk states. Instead, emulating the words of Gary King, theoretical reasons for models can serve as guides to our specifications.

In my mind, economics requires not just the capability to understand economic theory and empirics, but also the humility to avoid mapping out the entire universe of possible economic interactions, floating coefficients, and greek numerals. Studying economics requires the humility to admit that economics itself is not an exact science, but also the understanding that this categorization does not lessen the impact of potential breakthroughs, just maybe the egos of researchers like myself.

WHERE IS ECONOMICS?

via xkcd. WHERE IS ECONOMICS?

Mike responds

Economics is an incredibly diverse field, studying topics ranging from how match-fixing works among elite sumo wrestlers to why the gap between developed and developing countries is as large as it is. When considering a topic as broad as whether the field of economics deserves to have a Nobel prize, then, it is important to consider the entire field before casting judgment.

Joris Luyendijk, in his article “Don’t let the Nobel prize fool you. Economics is not a science,” directs most of his criticisms of economics at financial economics specifically instead of addressing the field of economics as a whole. We can even use Mr. Luyendijk’s preferred frame of analysis, Nobel prizes awarded, to see the distinction between finance and economics. Out of the 47 times the economics Nobel has been awarded, it was only given in the field of Financial Economics three times.  And in his article, Mr. Luyendijk only addresses one of these three Nobels. I would argue that since financial economics is but a small part of the entire economics field, even intense criticism of financial economics should not bring the entire economics field down with it.

A closer look at the Nobels awarded in financial economics reveals that the award is not “fostering hubris and leading to disaster” as Mr. Luyendijk claims. The first Nobel awarded in financial economics was presented in 1990, for research on portfolio choice and corporate finance and the creation of the Capital Asset Pricing Model (CAPM). Far from causing financial contagion, to which Mr. Luyendijk hints the economics Nobel prize has contributed, optimal portfolio theory examines how to balance returns and risk, and CAPM provides a foundation for pricing in financial markets. More recently, the 2013 Nobel was again awarded in financial economics, for advances in understanding asset pricing in the short and long term, applications of which include the widely used Case-Shiller Home Price Index.

The second Nobel awarded for financial economics, to Merton and Scholes in 1997, does deserve some criticism, though. However, I would argue that the Black-Scholes asset pricing model gained traction long before the 1997 Nobel Prize, and continues to be used long after the collapse of the hedge fund Merton and Scholes were part of, because of its practical usefulness and not because of any legitimacy the Nobel prize might have endowed it with. The quantification of finance would have happened with or without the Nobel prize, and I find it hard to believe that the existence of the economics Nobel prize causes profit-driven financiers to blindly believe that the Black-Scholes formula is a “timeless truth.”

So if economics is not finance, then what is it? I would argue that an identifying feature of applied economics research is the search for causality. Specifically, much of economics is a search for causality in man-made phenomena. To model human behavior in a tractable way requires making assumptions and simplifications. I have to agree with Mr. Luyendijk that economics needs to be more forthright about those assumptions and limitations – economists may be too eager to take published findings as “timeless truths” without thinking about the inherent limitations of those findings.

Failing to realize the limitations of such findings can come back to bite. For example the Black-Scholes model assumes that securities prices follow a log-normal process, which underestimates the probability of extreme events, such as the ones that led to the collapse of Long-Term Capital Management. But the failure of some to pay attention to well-known limitations of important findings should not diminish economics as a whole.

Applied economics is also distinct from other social sciences in that it attempts to apply the tools of the hard sciences to human problems. I agree with Alex and Mr. Luyendijk that knowledge about the physical and human worlds is inherently different. The heterogeneity of human behavior creates messy models, and these models require the creation of new mathematical and statistical methods to understand them. This “mathematical sophistication” that Mr. Luyendijk bemoans is not just math for math’s sake, it is using tools from the hard sciences to explain real-world phenomena (and what’s wrong with pure math anyways?).

Despite the occasional messy solution, the ideal study in applied economics is still a controlled experiment, as it is in many hard sciences. In the human world, however, this experimental ideal is difficult to implement. Much of applied economics thus relies on quasi-experimental methods, trying to approximate experiments with observational data by finding natural experiments, for example, when controlled experiments are not feasible. Still other branches of economics use actual economic experiments, such as randomized control trials (RCTs). The idea behind economics RCTs is the same as that behind clinical drug trials, where people are randomly separated into treatment and control groups to test the effect of an intervention. RCTs have become increasingly popular, especially in development work, over the past decade or so. Given Mr. Luyendijk’s concern about how divorced from the real world economics has become, he would be impressed by the amount of practical, detailed planning required to successfully implement RCTs, and be taken aback by how different this fieldwork is from the academics spending all day thinking of complex and impractical models that he envisions.

A Nobel prize in economics will probably be awarded for advances in the methodology and applications of RCTs, the closest economics can come to the hard sciences that Mr. Luyendijk so reveres, sometime in the next decade. What will he say then?

Endnote

Mike and I were Research Assistants at Williams College together during summer 2013. Mike is currently on a Fulbright in China working with Stanford’s Rural Education Action Program, which conducts RCTs in rural China. We are both happy to hear any feedback on the linked articles and our responses, as we are both genuinely interested in thinking through where economics (and computational social sciences on the whole) should belong in scientific dialogue.


© Alexandra Albright and The Little Dataset That Could, 2016. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts, accompanying visuals, and links may be used, provided that full and clear credit is given to Alex Albright and The Little Dataset That Could with appropriate and specific direction to the original content.

This Post is Brought to You by the National Science Foundation

Nightingale Graphs, Stacked Area Charts, Stacked Bar Charts, Treemaps
Intro

I have officially finished applying for my PhD. While the application process included many of the same elements that I had previously encountered as a fresh-faced* 17-year-old (think standardized testing without the #2 pencils and lots more button clicking), I am no longer applying as a (relatively) blank slate–a future liberal arts student who will float and skip between disciplines until being neatly slotted into a major. Instead, we PhD applicants have already zeroed in on a particular area of study–in my case, economics. Consequently, each PhD discipline is unlikely to exhibit the same carefully crafted demographics boasted in the pie charts that plaster undergraduate brochures across the country to provide tangible evidence for optimistic, bolded statements about diversity. In formulating responses to a slew of university-specific prompts about diversity in “the sciences,” I grew curiouser and curiouser about two particular questions: What do demographic compositions look like across various PhD disciplines in the sciences? & Have demographic snapshots changed meaningfully over time?

As I continued working to imbue a sense of [academic] self into pdfs composed of tightly structured Times New Roman 12 point font, I repeatedly found myself at the NSF open data portal, seeking to answer these aforementioned questions. However, I would then remind myself that, despite my organic urge to load rows and columns into R Studio, I should be the responsible adult (who I know I can be) and finish my applications before running out to recess. Now that the last of the fateful buttons have been clicked (and a sizable portion of my disposable income has been devoured by application fees and the testing industrial complex), I’m outside and ready to talk science!**

NSF data and sizes of “the sciences”

In this post, I am focusing on the demographics of science PhD degrees awarded as they pertain to citizenship and race/ethnicity, but not gender. In an ideal world, I would be able to discuss the compositions of PhD fields as broken into race/ethnicity-gender combinations, however, the table that includes these types of combinations for US citizens and permanent residents (Table 7-7) only provides the numbers for the broader categories rather than for the desired discipline-level. For instance, social science numbers are provided for 2002-2012 without specific numbers for economics, anthropology, etc. This approach, therefore, would not allow for an investigation into the main topic of interest, which is the demographic differences between the distinct disciplines–there is too much variety within the larger umbrella categories to discuss the fields’ compositions in this way. Therefore, I limit this discussion to demographics with respect to citizenship and race/ethnicity and, accordingly, use Table 7-4 “Doctoral degrees awarded, by citizenship, field, and race or ethnicity: 2002–12” from the NSF Report on Women, Minorities, and Persons with Disabilities in Science and Engineering*** as my data source.

Before getting into the different PhD science fields and their demographics, it’s worth noting the relative sizes of these disciplines. The following treemap depicts the relative sizes of the sciences as defined by NSF data on doctoral degrees awarded in 2012:

treemap2

The size of each squarified rectangle represents the number of degrees awarded within a given field while the color denotes the field’s parent category, as defined by the NSF. (Note that some studies are, in fact, their own parent categories. This is the case for Biological Sciences, Psychology, Computer Sciences, and Agricultural Sciences.) In the upcoming discussion of demographics, we will first discuss raw numbers of degrees earned and the relevant demographic components but will then pivot towards a discussion of percentages, at which point remembering the differences in size will be particularly helpful in piecing together the information into one cohesive idea of the demographics of “the sciences.”****

A decade of demographic snapshots: PhD’s in the sciences

The NSF data specifies two levels of information about the doctoral degrees awarded. The first level identifies the number of degree recipients who are US citizens or permanent residents as well as the number who are temporary residents. Though “[t]emporary [r]esident includes all ethnic and racial groups,” the former category is further broken down into the following subgroups: American Indian or Alaska Native, Asian or Pacific Islander, Black, Hispanic, Other or unknown, and White. In our first exploration of the data, we specify the raw number of degrees awarded to individuals in the specific ethnic and racial categories for US citizens and permanent residents as well as the number awarded to temporary residents. In particular, we start the investigation with the following series of stacked area charts (using flexible y-axes given the vastly different sizes of the disciplines):

raw_plot

In this context and for all following visualizations, the red denotes temporary residents while all other colors (the shades of blue-green and black) are ethnic and racial subsets of the US citizens and permanent residents. By illustrating the raw numbers, this chart allow us to compare the growth of certain PhD’s as well as seeing the distinct demographic breakdowns. While overall the number of science PhD’s increased by 39% from 2002 to 2012, Astronomy, Computer Science, Atmospheric sciences, and Mathematics and statistics PhD’s clearly outpaced other PhD growth rates with increases of 143%, 125% 84%, and 80%, respectively. Meanwhile, the number of Psychology PhD’s actually decreased from 2002 to 2012  by 8%. While this was the only science PhD to experience a decline over the relevant 10-year period, a number of other disciplines grew at modest rates. For instance, the number of Anthropology, Sociology, and Agricultural Sciences PhD’s experienced increases of 15%, 16%, and 18% between 2002 and 2012, which pale in comparison to the vast increases seen in Astronomy, Computer Science, Atmospheric sciences, and Mathematics and statistics.

While it is tempting to use this chart to delve into the demographics of the different fields of study, the use of raw numbers renders a comprehensive comparison of the relative sizes of groups tricky. For this reason, we shift over to visualizations using percentages to best get into the meat of the discussion–this also eliminates the need for different y-axes. In presenting the percentage demographic breakdowns, I supply three different visualizations: a series of stacked area graphs, a series of nightingale graphs (essentially, polar stacked bar charts), and a series of straightforward line graphs, which despite being the least exciting/novel are unambiguous in their interpretation:

percent_area

perc_nightingale

perc_line

One of my main interests in these graphs is the prominence of temporary residents in various disciplines. In fact, it turns out that Economics is actually quite exceptional in terms of its percentage of temporary residents, which lingers around 60% for the decade at hand and is at 58% for 2012. (In 2012, out of the remaining 42% that are US citizens or permanent residents, 70% are white, 11% are asian or pacific islander, 3% are black, 3% are hispanic, 0% are american indian or alaskan native, and 13% are other or unknown.) Economics stands with Computer science, Mathematics and statistics, and Physics as one of the four subjects in the sciences for which temporary residents made up a higher percentage of the PhD population than white US citizens or permanent residents consistently from 2002 to 2012. Furthermore, Economics is also the science PhD with the lowest percentage of white US citizens and permanent residents–that is, a mere 30%.  In this sense, the field stands out as wildly different in these graphs from its social science friends (or, more accurately, frenemies). On another note, it is also not hard to immediately notice that Psychology, which is not a social science in the NSF’s categorization, is so white that its nightingale graph looks like an eye with an immensely overly dilated pupil (though anthropology is not far behind on the dilated pupil front).

Also readily noticeable is the thickness of the blue hues in the case of Area and ethnic studies–an observation that renders it undeniable that this subject is the science PhD with the highest percentage of non-white US citizens and permanent residents. Following this discipline would be the other social sciences Anthropology, Sociology, and Political science and public administration, as well as the separately categorized Psychology. However, it is worth noting that the ambiguity of the temporary residents’ racial and ethnic attributes leaves much of our understanding of the prominence of various groups unclear.

Another focal point of this investigation pertains to the time dimension of these visuals. When homing in on the temporal aspect of these demographic snapshots, there is a discouraging pattern–a lack of much obvious change. This is especially highlighted by the nightingale graphs since the polar coordinates allow the 2012 percentages to loop back next to the 2002 percentages and, thus, facilitate for a simple start-to-end comparison. In most cases, the two points in time look incredibly similar. Of course, this does not necessarily mean there has been no meaningful change. For instance, there have been declines in the percentage of white US citizens and permanent residents in the subjects Area and ethnic studies, Psychology, Sociology, Anthropology, and Political science and public administration, which have then been offset by increases in other groups of individuals. However, the picture is incredibly stagnant for most of the disciplines, especially the hard sciences and the unusually quantitative social science of economics. In pairing the stagnant nature of these demographic snapshots with consistent calls for greater faculty diversity in the wake of campus protests, it is clear that there is a potential bottleneck since such lagging diversity in PhD disciplines can directly contribute to a lack of diversity at the faculty-level.

Endnote

When the public discusses the demographics and diversity of “the sciences,” 1.5 dozen disciplines are being improperly blended together into generalized statements. To better understand the relevant dynamics, individuals should zero in on the discipline-level rather than refer to larger umbrella categories. As it turns out according to our investigation, the demographic breakdowns of these distinct subjects are as fundamentally different as their academic methodologies–methodologies which can be illustrated by the following joke that I can only assume is based on a true story:

As a psychological experiment, an engineer, a chemist, and a theoretical economist are each locked in separate rooms and told they won’t be released until they paint their entire room. They are each given a can of blue paint which holds about half the paint necessary to paint the room and then left alone. A few hours later the psychologist checks up on the three subjects.

(1) The engineer’s walls are completely bare. The engineer explains that he had worked out that there wasn’t enough paint to cover all the walls so he saw no point in starting.

(2) The chemist’s room is painted in faded, streaky blue. “There wasn’t enough paint, so I diluted it,” she explains.

(3) In the economist’s room, the floor and the ceiling are completely blue, and there’s a full can of paint still sitting on the floor. The experimenter is shocked and asks how the economists managed to paint everything. The economist explains, “Oh, I just painted the rational points.”

And with an unwavering appreciation for that bit, I hope to be one of the ~20-30 (who knows?) % of white US citizens/permanent residents in the economics PhD cohort of 2021.

PS-Happy 2016 everyone!

Footnotes

* I had yet to take a driving test at a DMV. I did this successfully at age 21. But, I will not drive your car.

** The NSF divides subjects up into S&E (science and engineering) and non-S&E categories. In this context, I am only discussing the subjects that fall under the umbrella of science. It would be simple to extend the approach and concept to the provided numbers for engineering.

*** This table explains that the exact source for this information is: National Science Foundation, National Center for Science and Engineering Statistics, special tabulations of U.S. Department of Education, National Center for Education Statistics, Integrated Postsecondary Education Data System, Completions Survey, 2002–12.

**** In particular, the tiny size of the group of History of Science PhD’s allows for much more variability year-to-year in terms of demographics. Only 19-34 degrees were given out on an annual basis from 2002-2012. In this case, size of the program is responsible for the wildly evident changes in demographic composition.

Code

Data and R scripts necessary to replicate visualizations are now up on my github! See the NSF_Demographics repo. Let me know if you have any questions or issues with the R script in particular.

Further directions for work
  • Create gif of treemap using years 2002-2012 to replace the static version for just 2012
    • Or use a slider via some D3 magic
  • Follow-up by comparing the gender compositions
  • Look into the development and change history of the US Office of Management and Budget for racial and ethnic categories
    • Just curious as to the timeline of changes and how categorization changes affect our available data

© Alexandra Albright and The Little Dataset That Could, 2016. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts, accompanying visuals, and links may be used, provided that full and clear credit is given to Alex Albright and The Little Dataset That Could with appropriate and specific direction to the original content.

Which U.S. State Performs Best in the New Yorker Caption Contest?

Choropleths

I wrote about this topic with Bob Mankoff for the New Yorker.

You can read the piece here

And you can see how the visuals were made here!

It builds off of my previous work on the New Yorker Caption contest. (New visuals, new data, and edits from real editors!) Many, many thanks to Bob for giving me access to troves of fascinating data as well as making great edits and alterations to this piece (including the addition of my new favorite phrase “nattering nabobs”).

Bonus cartoon of surprising relevance given Alaska’s success in terms of caption win rate:

Daily Cartoon for Tuesday, September 1st via The New Yorker

Daily Cartoon for Tuesday, September 1st via The New Yorker. We figure Alaska’s wins and submissions to the contest will decline if it comes to this…

Endnote

Code and raw data for replicating these choropleths are available at my NYer_Choropleths Github repo. An R Notebook on this is also available here. Also, thanks to Sarah Levine for using her QGIS knowledge to help me tame maps of the US.


© Alexandra Albright and The Little Dataset That Could, 2016. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts, accompanying visuals, and links may be used, provided that full and clear credit is given to Alex Albright and The Little Dataset That Could with appropriate and specific direction to the original content.

EDUANALYTICS 101: An Investigation into the Stanford Education Space using Edusalsa Data

Heat Maps, Histograms, Scatter Plots, Treemaps
Update [4-18-16]: Thanks to Stuart Rojstaczer for finding an error in my grade distribution histograms. Just fixed them and uploaded the fixed R script as well. Such is the beauty of internet feedback!
Note: This is the first in a series of posts that I am putting together in partnership with Edusalsa, an application based at Stanford that seeks to improve how college students explore and choose their courses. Our goal in these posts is to take advantage of the unique data collected from students’ use of the application in order to learn more about how to model and discuss the accumulation and organization of knowledge within the Stanford community as well as within the larger, global education space. (You can read the post here too.)
Course Syllabus

You are frozen in line. This always happens. You don’t know whether to pick the ENGLISH, PHYSICS with double CS combo that you always order or whether to take a risk and try something new. There are thousands of other options; at least a hundred should fit your strict requirements and picky tastes…Hey, maybe you’d like a side of FRENCH! But now you don’t even know what you should get on it; 258, 130, or 128. You are about to ask which of the three goes best with ENGLISH 90 when you wake up.

You realize you missed lunch… and you need to get out of the library.

Complex choices, those with a large number of options (whether in a deli or via online course registration), often force individuals to make choices haphazardly. In the case of academics, students find themselves unable to bulldoze their way through skimming all available class descriptions, and, accordingly, pick their classes with the help of word of mouth and by simply looking through their regular departments offerings. However, it is undoubtably the case that there are ways to improve matching between students and potential quarterly course combinations.

In order to better understand how one could improve the current course choice mechanism, one must first better understand the Stanford education space as well as the myriad of objects (courses, departments, and grades) and actors (students and Professors) that occupy it. The unique data collected from students’ use of Edusalsa provides an opportunity to do just this. In this post, organized in collaboration with the Edusalsa team, we will use this evolving trove of data to discuss three overarching questions: [1] How can we measure the interest surrounding, or the popularity of, a course/department? (In conjunction with that question, what should we make of enrollment’s place in measuring interest or popularity?) [2] What is the grade distribution at Stanford, on the whole as well as on the aggregate school-level? [3] How do students approach using new tools for course discovery?

[1] How can we measure the interest surrounding, or the popularity of, a course/department?

One of the first areas of interest that can be examined with the help of Edusalsa’s data is Stanford student interest across courses and departments. Simply put, we can use total views on Edusalsa, aggregated both by course and by department, as a proxy for for interest in a course/popularity of a course. [See technical footnote 1 (TF1)] In order to visualize the popularity of a collection of courses and departments, we use a treemap structure to illustrate the relative popularities of two sets of academic objects; (1) all courses that garnered at least 20 views, and (2) all departments that garnered at least 30 views: [TF2]

course_tree

dept_tree

The size of the rectangles within the treemap corresponds to the number of endpoints while the darkness of the color corresponds to the estimated enrollment by quarter for classes and entire departments. We notice that, at the course-level, the distribution of colors throughout the rectangles seems disorganized over the size dimension. In other words, there does not seem to be a strong relationship between enrollment and views at the course level. On the other hand, from a cursory look at the second graph, the department treemap seems to illustrate that courses with larger aggregate enrollments (that is, the sum of all enrollments for all classes in a given department) have more views.

What should we make of enrollment’s place in measuring interest or popularity?

While these particular treemaps are useful for visually comparing the number of views across courses and departments, they do not clarify what, if any, is the nature of the relationship between enrollment and views for these two subsets of all courses and departments. [TF2] Due to the treemaps’ analytic shortcomings, we address the legitimacy of our previous intuitions about the relationship by simply regressing views on enrollment at both the course- and department-level. See below for the relevant plot at the course-level:

course_scatter

The coefficient on enrollment in the simple linear regression model, represented by the blue line in the above plot, while positive, is not statistically significant. We can also see this is the case when considering the width of the light green area above (the 99% confidence interval) and the more narrow gray area (the 95% confidence interval), as both areas comfortably include an alternative version of the blue regression line for which the slope is 0. The enrollment variable’s lack of explanatory power is further bolstered by the fact that, in this simple regression model framework, enrollment variation only accounts for 1.3% of the variation in views.

We now turn to the department-level, which seemed more promising from our original glance at the association between colors and sizes in the relevant treemap:

dept_scatter

In this case, the coefficient on enrollment in this model is statistically significant at the 0.1% level and communicates that, on average, a 1,000 person increase in enrollment for a department is associated with an increase of 65 views on Edusalsa. The strength of the association between enrollment and views is further evidenced by the 95% and 99% confidence intervals. In fact, the explanatory power of the enrollment variable in this context is strong to the point that the model accounts for 53.9% of variation in Edusalsa views. [TF3]

Theory derived from the comparison of course-level and department-level relationships

The difference between the strength of enrollment’s relationship with views at the course and at the department level is clear and notable. I believe that this difference is attributable to the vast heterogeneity in interest across courses, meaning there is extreme variance in terms of how much interest a course garners within a given department. Meanwhile, the difference in interest levels that is so evident across courses disappears at the department-level, once all courses are aggregated. This observation potentially serves as evidence of a current course search model in which students rigidly search within specific departments based on their requirements and fields of study, but then break up their exploration more fluidly at the course-level based on what they’ve heard is good or which classes look the most interesting etc. While the students know what to expect from departments, courses can stand out via catchy names or unique concepts in the description.

More possible metrics, and way more colors…

There are a few other metrics beyond views and enrollment that we might be interested in when trying to assess or proxy for interest surrounding a course or department. In order to compare some of these alternative metrics across various departments we present the below heat map, which serves to relatively compare a set of six metrics across the top 15 departments by enrollment size:

heat

While we have discussed enrollment before, I also include number of courses in the second column as an alternative measurement of the size of the department. Rather than defining size by number of people who take classes in the department, this defines size by the number of courses the department offers. The darker greens of CEE, Education, and Law illustrate that these are the departments parenting the most courses.

Another new metric in the above is the fifth column, a metric for number of viewers, which refers the number of unique individuals who visited a course page within a department. The inclusion of this measurement allows us to avoid certain individuals exerting improperly large influence over our measures. For example, one person who visits Economics course pages thousands of times won’t be able to skew this metric though she could skew the views metric significantly. Note that the columns for number of views and number of viewers are very similar, which indicates that, beyond some individuals in EE, departments had individuals viewing courses at similar frequencies.

The last new concept we introduce in the heat map is the notion of normalizing by enrollment, seen in columns four and six, so as to define metrics that take into account the size of the Stanford population that is already involved with these departments. Normalizing views and viewers in this way makes a large impact. Most notably, CS is no longer the dominant department, and instead shares the stage with other departments like Psychology, MS&E, MEE, etc. This normalized measure could be interpreted to proxy for the interest outside of the core members of the department (eg-majors and planned majors), in which case Psychology is certainly looking interesting to those on the outside looking in.

[2] What is the grade distribution at Stanford, on the whole as well as on the aggregate school-level?

The second topic that we cover in this post pertains to that pesky letter attached to a course–that is, grades. Our obtained data included grade distributions by course. [TF4] We use this data to build the frequency distribution for all grades received at Stanford. The following histogram illustrates that the most commonly received grade during the quarter was an A while the median grade was an A- (red line) and the mean grade was a 3.57 (blue line):

stanford_dist

While this visual is interesting in and of itself since it presents all Stanford course offerings solely by grade outcomes, it would also be meaningful to compare different subsets of the Stanford education space. In particular, we choose to use a similar technique to compare grading distributions across the three schools at Stanford–the School of Humanities & Sciences, the School of Engineering, and the School of Earth, Energy and Environmental Sciences–in order to see whether there is any notable difference across the groups:

school_dist

The histograms for the three schools present incredibly similar distributions–to the extent that at first I thought I mistakenly plotted the same school’s distribution three times. All three have medians of A- and the means are span a narrow range of 0.08; the means are 3.52, 3.60, and 3.58 for the Humanities & Sciences, Engineering, and Earth Sciences schools, respectively. [TF5]

[3] How do students approach using new tools for course discovery?

Since we have discussed views and other metrics both across classes and departments, it is worth mentioning what the Edusalsa metrics look like over individual users. Specifically, we are curious how many times unique users view courses through Edusalsa. In examining this, we are inherently examining the level of “stickiness” of the site and the aggregated view of how users interact with new course tools. In this case, the stickiness level is low, as illustrated below by both (i) a quickly plunging number of unique individuals as the number of course views grows, and (ii) a linear decline of number of unique individuals as the number of course views grows when using a log-log plot. [TF6]

stick

The negative linear relationship between the log transformed variables in the second panel (evidenced by the good fit of the above blue line) is indicative of the negative exponential form of the relationship between number of course views and number of unique individuals. [TF7]  This simply indicates that, as is the case with most new applications, so-called stickiness is low. It will be interesting to see whether this changes given the new addition of the ability to create an account.

School’s out (for summer)

Our key insights in this post lie in the depths of section [1], which discussed

evidence of a current course search model in which students rigidly search within specific departments based on their requirements and fields of study, but then break up their exploration more fluidly at the course-level

With evolving data collection, we will continue to use Edusalsa data in order to learn more about the current course search model as well as the specific Stanford education space. Future steps in this line of work will include analyzing the dynamics between departments and the courses that populate them using network analysis techniques. (There is a slew of possible options on this topic: mapping out connections between departments based on overlap in the text of course descriptions, number of cross-listings, etc.)

There is ample room for tools in the education space to help students search across conventional departments, rather than strictly within them, and understanding the channels that individuals most naturally categorize or conceptualize courses constitutes a large chunk of the work ahead.

Technical footnotes
  1. Edusalsa views by course refers to the number of times an invidual viewed the main page for a course on the site. Technically, this is when the data.url that we record includes the suffix “/course?c=DEPT&NUM” where DEPT is the department abbreviation followed by the number of the course within the department. Views aggregated by department is equivalent to the sum total of all views for courses that are under the umbrella of a given department.
  2. We only illustrate courses with at least 20 views and departments with at least 30 views in order that they will be adequately visible in the static treemap. Ideally, the views would be structured in an interactive hierarchical tree structure in which one starts at the school level (Humanities & Sciences, Engineering, Geosciences) and can venture down to the department level followed by the course level.
  3. Though it might seem as though Computer Science is an outlier in this dataset whose omission could fundamentally alter the power of the simple regression model, it turns out even after omitting CS the coefficient on enrollment remains significant at the 0.1% level while the R^2 remains high as well at approximately 0.446.
  4. The grade distribution data is self-reported by Stanford students over multiple quarters.
  5. While the distributions are very similar aggregated over the school level, I doubt they would be as similar at the smaller, more idiosyncratic department-level. This could be interesting to consider across similar departments, such as ME, EE, CEE, etc. It could also be interesting to try and code all classes at Stanford as “techie” or “fuzzy” a la the quintessential Stanford student split and see whether those two grade frequency distributions are also nearly identical.
  6. We found that ID codes we use to identify individuals can change over people in the long-run. We believe this happens rarely in our dataset, however, it is worth noting nonetheless. Due to this caveat, some calculations could be over- or underestimates of the their true values. For instance, the low stickiness for Edusalsa views could be overestimated as some of the users who are coded as distinct people are the same. Under the same logic, in the heat table, the number of viewers could be an overestimate.
  7. The straight line fit in a log-log plot indicates a monomial relationship form. A monomial is a polynomial with one term–i.e. y=ax^n–appear as straight lines in log-log plots such that n and a correspond to the slope and intercept, respectively.
Code and replication

All datasets and R scripts necessary to recreate these visuals are available at my edusalsa Github repo!


© Alexandra Albright and The Little Dataset That Could, 2016. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts, accompanying visuals, and links may be used, provided that full and clear credit is given to Alex Albright and The Little Dataset That Could with appropriate and specific direction to the original content.

The Multidimensional Success of Pixar Films Visualized

Bubble Charts
Get the popcorn

Last Wednesday, as I watched the letter “I” flattened by a familiar sweaky little lamp, I found myself, for the first time in half a decade, about to enter a new Pixar universe. I hadn’t seen a Pixar film in theaters since Toy Story 3—a movie revolving around a boy’s departure to college that was released the same summer my high school graduate cohort and I were also due to leave behind plush bunnies and Hess trucks in pursuit of profound academic knowledge…and a few beers. Now, five years later, I was watching Inside Out, another movie that felt meaningfully-timed due to its release around my one-year anniversary of college graduation. As time has passed since those four years of accelerated, electric activity, we are all left wondering which memories will inevitably roll down into the dusty abyss of lost moments and which will solidify their spots as core memories, turning within our own mental Kodak Carousels.

This train of thought led me to ponder not only key moments in my own lifetime but also those in the Pixar feature film universe’s almost 20-year existence. Considering all 15 movies Pixar has created and released, are some doomed for the abyss of our collective memory while others are permanent pillars of the Pixar canon? In other words, how do the individual units within this manifold collection of films stack up against one another? Moreover, how can we visualize Pixar’s trajectory over the past two decades?

Pixar and metrics of success

In attempting to illustrate Pixar’s evolution over time, I am inclined to use “success” as a metric of interest. Pixar is considered wildly successful—but how do we define success given its multidimensional nature? Well, for one, success is often substantiated through winning awards. Even Pixar’s first movie, Toy Story, which was released in November 1995, proceeded to receive a Special Achievement Academy Award for being the first feature-length computer-animated film, and this was years before the introduction of the Best Animated Film Academy Award in 2001. In fact, since the latter’s inception, Pixar has won the award for Best Animated Film 7 out of 14 years, despite only releasing films in 11. Other meaningful metrics of success include quality ratings, such as those maintained by Rotten Tomatoes and IMDb, and… of course, money. Thus, in tracing out Pixar’s success, we consider three dimensions of success: award victories (Best Animated Film Academy Award wins), quality ratings (we treat Rotten Tomatoes % Fresh as a measure of critical acclaim and IMDb ratings as a measure of public acclaim), and commercial success (Opening Weekend Gross). (We use opening weekend gross since there is not yet a final box office number for Inside Out.)

A path lined with multidimensional success

In order to map out Pixar’s trajectory, we plot all 15 movies released by Pixar using differing colors and sizes of data points in order to represent all three aforementioned dimensions of success. In this graph, the main focus of interest is the % Fresh Rotten Tomatoes rating, which specifies what percentage of critic reviews’ were positive. (Note: we truncate the y-axis in order to better emphasize the evolution of quality over time.) This metric accurately separates out those regularly cited as subpar Pixar movies: Cars, Cars 2, Brave, and Monsters University. We use locally weighted scatterplot smoothing (“loess”) to fit a curve to the dataset, thus charting the movement of % Fresh over time. The loess curve shows us that Pixar took a dip in critical acclaim between 2010 and 2015–what with the release of Cars 2, Brave, and Monsters University–however, Inside Out’s release has tugged the loess curve back up to pre-2011 levels!

pix1

In this sense, Inside Out marks a return to the Pixar of emotive toys and robots—not to mention the most sob-inducing 4 minutes in all of animated film history. The above plot also illustrates Pixar’s success at the Oscars, with films depicted by blue points as Best Animated Film Academy Award winners. Lastly, in terms of opening weekend gross, we can see that despite being on the lower end of quality ratings, the disappointing movie grouping of Cars, Cars 2, Brave, and Monsters University did not make less money during opening weekend than other films. In fact, in comparing these four films to the other 5 films released since 2005, the average opening weekend gross is actually larger—$79.46 million rather than $75.78 million.

Pivoting from a measure of critical acclaim to a measure of public acclaim in the quality realm, we now plot the same dimensions of success as defined before but we substitute IMDb scores for the Rotten Tomatoes % Fresh metric. This set of scores also suggests mediocrity in Cars, Cars 2, Brave, and Monsters University—however, it also puts A Bug’s Life in the same subpar quality category. Again, we use a loess regression line to exhibit the movement in quality ratings of Pixar movies over time. As was the case before, this line also provides evidence of a return to the old Pixar.

pix2

However, there is one element to note about the nature of IMDb scores–that is, they are often higher when a film is just out. This is because the first people to see and rate films are the hardcore fans, which therefore contributes to a “hype effect,” superficially inflating the aggregate rating. (Speaking of hype and quality discussions…) This could potentially be an issue in currently measuring the public acclaim of Inside Out, as its rating will likely fall to WALL-E / Up levels as months pass.

Despite this particular caveat, the graph still serves as evidence of an improvement in Pixar film quality following its recent senior slump (~ ages 15-18)–an improvement that is fitting since, in a few months, we will be able to welcome Pixar to the world of 20-somethings, the beginning of a new decade in which we are content to forget about the mishaps of adolescence.

Roll the credits

In short, Pixar has faltered in its adolescence, sometimes producing movies that fail to depict the nuanced emotions that color the memories organized within our seemingly endless stockpiles of human experiences. However, just like the wonderfully colored marbles of memories in the Pixar universe, these fifteen films exist within the collective memory as works of art that are, no doubt, greater than the sum of their tangible metrics of success. If Joy herself were to project my memory of Toy Story in the headquarters of my brain, I would not see a small black data point—I would see “Andy” written on the bottom of Woody’s boot and feel something that is beyond a simple, neat linear combination of joy and melancholy—something beyond my or Pixar’s capacity for visualization… Something you can’t even see with 3-D glasses.

«Visualization update»

Thanks to discussion of the aforementioned graphs in the /r/dataisbeautiful universe, I have been made acutely aware of improvements that should be made to my visualizations. In particular, there are two issues from my previous work that are worth quickly addressing:

  1. In my original visualizations, area is scaled non-linearly with the opening weekend gross data. This was a rookie mistake on my part, especially considering that one of the first things the Wikipedia “Bubble chart” article explains is that, “if one chooses to scale the disks’ radii to the third data values directly, then the apparent size differences among the disks will be non-linear and misleading.” As /u/FlailingMildly explained, “It looks to me like the diameter of the points scales with opening weekend gross (110 looks roughly twice as wide as 50). However, our brain doesn’t look at diameter, it looks at area. So the 110 looks more than four times as large as the 50.” 
  2. The blue lines from the original graphs are loess curves, or locally weighted scatterplot smoothings. I reasoned that this choice of smoothing was acceptable as an exploratory feature since the original paper that developed loess explains that: “The first [major use of this local-fitting methodology] is simply to provide an exploratory graphical tool.” However, I knew it could be argued that this curve is over-fitted and better for the purposes of prediction than for conceptual modeling. In the end, individuals on the subreddit came to the conclusion that, in this particular case, the loess curves are not useful since the graph is easy to read without any type of smoothing method. In short, the overarching consensus was that this type of curve is best used for smoothing noisy data–a category to which my Pixar csv file definitely does not belong!

In order to address these genuine issues, I made two quick changes to the previous graphs: (1) I scaled opening weekend box office gross to the area of the circles rather than to their radii, and (2) I excluded the blue loess curves. See the new graphs here:

pix1.1

pix1.2

Lastly, I also present a similarly constructed graph with a y-axis corresponding to Metacritic scores (to add another quality metric into the mix):

pix1.3

Code

Data and R scripts needed to recreate all the included visualizations are available via my Pixar GitHub repo!


© Alexandra Albright and The Little Dataset That Could, 2016. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts, accompanying visuals, and links may be used, provided that full and clear credit is given to Alex Albright and The Little Dataset That Could with appropriate and specific direction to the original content.