Saturday, February 14, 2015

Hierarchies in faculty hiring networks

Short summary: top academic departments produce a disproportionate fraction of all faculty. The paper below finds that only 9 to 14% of faculty are placed at institutions more prestigious than their doctorate ... the top 10 units produce 1.6 to 3.0 times more faculty than the second 10, and 2.3 to 5.6 times more than the third 10.

For related data in theoretical high energy physics, string theory and cosmology, see Survivor: Theoretical Physics.
Systematic inequality and hierarchy in faculty hiring networks

Science Advances 01 Feb 2015: Vol. 1 no. 1 e1400005 DOI: 10.1126/sciadv.1400005

The faculty job market plays a fundamental role in shaping research priorities, educational outcomes, and career trajectories among scientists and institutions. However, a quantitative understanding of faculty hiring as a system is lacking. Using a simple technique to extract the institutional prestige ranking that best explains an observed faculty hiring network—who hires whose graduates as faculty—we present and analyze comprehensive placement data on nearly 19,000 regular faculty in three disparate disciplines. Across disciplines, we find that faculty hiring follows a common and steeply hierarchical structure that reflects profound social inequality. Furthermore, doctoral prestige alone better predicts ultimate placement than a U.S. News & World Report rank, women generally place worse than men, and increased institutional prestige leads to increased faculty production, better faculty placement, and a more influential position within the discipline. These results advance our ability to quantify the influence of prestige in academia and shed new light on the academic system.
From the article:
... Across the sampled disciplines, we find that faculty production (number of faculty placed) is highly skewed, with only 25% of institutions producing 71 to 86% of all tenure-track faculty ...

... Strong inequality holds even among the top faculty producers: the top 10 units produce 1.6 to 3.0 times more faculty than the second 10, and 2.3 to 5.6 times more than the third 10.

[ Figures at bottom show top 60 ranked departments according to algorithm defined below ]

... Within faculty hiring networks, each vertex represents an institution, and each directed edge (u,v) represents a faculty member at v who received his or her doctorate from u. A prestige hierarchy is then a ranking π of vertices, where πu = 1 is the highest-ranked vertex. The hierarchy’s strength is given by ρ, the fraction of edges that point downward, that is, πu ≤ πv, maximized over all rankings (14). Equivalently, ρ is the rate at which faculty place no better in the hierarchy than their doctorate. When ρ = 1/2, faculty move up or down the hierarchy at equal rates, regardless of where they originate, whereas ρ = 1 indicates a perfect social hierarchy.

Both the inferred hierarchy π and its strength ρ are of interest. For large networks, there are typically many equally plausible rankings with the maximum ρ (15). To extract a consensus ranking, we sample optimal rankings by repeatedly choosing a random pair of vertices and swapping their ranks, if the resulting ρ is no smaller than for the current ranking. We then combine the sampled rankings with maximal ρ into a single prestige hierarchy by assigning each institution u a score equal to its average rank within the sampled set, and the order of these scores gives the consensus ranking (see the Supplementary Materials). The distribution of ranks within this set for some u provides a natural measure of rank uncertainty.

Across disciplines, we find steep prestige hierarchies, in which only 9 to 14% of faculty are placed at institutions more prestigious than their doctorate (ρ = 0.86 to 0.91). Furthermore, the extracted hierarchies are 19 to 33% stronger than expected from the observed inequality in faculty production rates alone (Monte Carlo, P < 10−5; see Supplementary Materials), indicating a specific and significant preference for hiring faculty with prestigious doctorates.

Click for larger images.


mfm32 said...

An interesting approach with very cool results (i.e. they comport with intuition enough to be credible, but not enough to be boring).

I think their ranking methodology has a pretty serious flaw, however. I'll focus on CS, since that's the area I know best. The problem is that the p measure of hierarchy strength favors ranking highly those departments that produce fewer academic placements per faculty member. Consider a department that produces no academic placements whatsoever (e.g. because all the graduating students go to work at Google). That department's node in the multigraph will have only incoming edges, and it will never decrease p to rank such departments at the top of the hierarchy. High rankings for these departments increase the number of prestige-enhancing outgoing edges with no corresponding increase in the number of prestige-decreasing outgoing edges, because these departments by definition have no outgoing edges. In reality, though, producing very few academic placements relative to your faculty size is likely anticorrelated with prestige.

You can sort of see this phenomenon occurring in the CS rankings. Stanford has an enormous CS faculty, largely because of its 770 undergraduate majors. Its doctoral program is much smaller and has high attrition due to the many attractive non-academic opportunities for a Stanford PhD candidate in the Bay Area (so I hear and the department website seems to support). The result is a ton of faculty, comparatively few academic placements, and a consequent tendency toward higher ranking. The paper itself even points out a similar thing likely going on with Caltech, though it doesn't identify the cause. The authors remark, "Caltech ranks above 98.5% of other institutions but places fewer computer science faculty than 27 lower-ranked institutions" but attribute this anomaly to prestige. Yet Caltech's graduate CS program appears to have over 70 students according to its website, suggesting that Caltech isn't a highly prestigious boutique CS department. Instead, I'd suspect that something similar to Stanford is going on: relatively few academic placements but a big faculty to support a large contingent of undergraduate majors. Or, in the parlance of the paper, lots of incoming edges and very few outgoing edges.

steve hsu said...

Isn't 70 grad students on the small size for most CS departments? Even if CS is now the most popular major, Caltech can't have more than ~200 undergrads total in the program. The UG student body (and almost every department, in number of faculty relative to competitors) is quite small. (Smaller than most high schools!)

mfm32 said...

I think it's actually pretty big. Not the biggest, for sure, but Yale for instance admits about 8 new PhD students a year, which gives a total number of doctoral students of 20 - 30 depending on how long you think the average time to degree is. The article similarly suggests that Caltech may be in the ~68th percentile for size.

Maybe Caltech CS students are more likely to go into non-academic jobs or academic jobs in other fields (unclear how those count in the algorithm). Maybe it has to do with Caltech's CS department combining some applied math and traditional engineering fields as well, which could contribute to grad student leakage out of the CS academic ecosystem.

Blog Archive