Gender-based homophily in collaborations across a ...

Gender-based homophily in collaborations across a

heterogeneous scholarly landscape

Carole LeeDepartment of PhilosophyUniversity of Washington

Metascience 2019 SymposiumStanford University

September 5-8

Joint work with:

Y. Samuel Wang

Business School

U Chicago

Elena Erosheva

Statistics; Center for Social Sciences and Statistics; Social Work

U Washington

Jevin West

Information School

U Washington

Carl Bergstrom

Biology

U Washington

Where do ideas come from?


Ideas come from people. . .


Different people have different forms of expertise.


We can create new ideas by combining folks with different forms of expertise into collaborative teams.


Collaborative teams are more likely than solo authors to create novel combinations of old ideas.

Combinations that are atypical and span a longer interdisciplinary distance have higher impact.

Uzzi, Brian, Satyam Mukherjee, Michael Stringer, & Ben Jones. "Atypical combinations and scientific impact." Science 342 (2013): 468-472. Larivière, Vincent, Stefanie Haustein, & Katy Börner. "Long-distance interdisciplinarity leads to higher scientific impact." Plos one 10 (2015): e0122565. Larivière, Vincent, Yves Gingras, Cassidy R. Sugimoto, and Andrew Tsou. "Team size matters: Collaboration and scientific impact since 1900." JASIST 66 (2015): 1323-1332.

How do teams self-assemble?

• Intellectual factors: expertise

• Instrumental factors: resources

• Social factors: respect, friendship, curiosity-seeking, fun

Katz, J. Sylvan, and Ben R. Martin. "What is research collaboration?." Research policy 26 (1997): 1-18.

Melin, Göran. "Pragmatism and self-organization: Research collaboration on the individual level." Research policy 29 (2000): 31-40.

Maglaughlin, Kelly L., and Diane H. Sonnenwald. "Factors that impact interdisciplinary scientific research collaboration: Focus on the natural sciences in academia." (2005).

Hara, Noriko, Paul Solomon, Seung-Lye Kim, and Diane H. Sonnenwald. "An emerging view of scientific collaboration: Scientists' perspectives on collaboration and factors that impact collaboration." Journal of the American Society for Information science and Technology 54 (2003): 952-965.

Collaboration involves social discretion

Does decreasing social distance increase collaboration?

• Homophily: Social similarly breeds connection.

• Gender homophily divides work environments, voluntary associations, and friendships.

McPherson, Miller, Lynn Smith-Lovin, and James M. Cook. "Birds of a feather: Homophily in social networks." Annual review of sociology 27 (2001): 415-444.

Kalleberg, Arne L., David Knoke, Peter V. Marsden, and Joe L. Spaeth, eds. Organizations in America. Sage, 1996.

McPherson, J. Miller, and Lynn Smith-Lovin. "Sex segregation in voluntary associations." American Sociological Review (1986): 61-79.

Ibarra, Herminia. "Homophily and differential returns: Sex differences in network structure and access in an advertising firm." Administrative science quarterly (1992): 422-447.

Ibarra, Herminia. "Paving an alternative route: Gender differences in managerial networks." Social psychology quarterly (1997): 91-102.

Collaborative teams and social distance

• Is there gender-based homophily in collaborations across the heterogeneous scholarly landscape at varying levels of granularity?

• Women are less likely to co-author and serve as first or last author

• Given professional advantages of collaboration, it’s important to understand how and under what conditions women collaborate

Question

Larivière, Vincent, Chaoqun Ni, Yves Gingras, Blaise Cronin, and Cassidy R. Sugimoto. "Bibliometrics: Global gender disparities in science." Nature News 504, no. 7479 (2013): 211.

West, Jevin D., Jennifer Jacquet, Molly M. King, Shelley J. Correll, and Carl T. Bergstrom. "The role of gender in scholarly authorship." PloS one 8, no. 7 (2013): e66212.

Data

• JSTOR, a repository of papers across the humanities, social sciences, and natural sciences

• We consider cited papers from 1960 onward

• 252,413 multi-author papers with 807,588 authorships (i.e., instances of co-authoring)

Hierarchical clustering

• Apply hierarchical implementation of the InfoMap network algorithm to the citation network on the JSTOR corpus

• This reveals the hierarchical structure of corpus through the efficient coding of random walks on the citation network

Rosvall, Martin, and Carl T. Bergstrom. "Maps of random walks on complex networks reveal community structure." Proceedings of the National Academy of Sciences 105, no. 4 (2008): 1118-1123.

Rosvall, Martin, and Carl T. Bergstrom. "Multilevel compression of random walks on networks reveals hierarchical organization in large integrated systems." PloS one 6, no. 4 (2011): e18209.


Status characteristics

Exchange networks

At the lowest level of clustering, each paper is grouped into one of 1,450 terminal fields which form the finest partition of the data.


Group interactions


Exchange networks

Each higher clustering forms progressively coarser partitions of the documents by aggregating terminal fields into the 280 composite fields.


Sociology of communication

Group interactions Role performance Conversation Motive


Exchange networks


Sociology

Sociology of family

Status, education, wages


Delinquency, deviance Religion Etc . . .



Exchange networks

At the top-level, we have 24 major fields.


Sociology

Sociology of family






Exchange networks

Hierarchical structure has up to 6 levels.


Sociology

Sociology of family






Exchange networks

At any level, papers in a common field are more connected via citations than to papers from neighboring fields.

Fields at finer levels of the hierarchy are more connected than fields at coarser levels.

Determining gender

• Gender inferred from first names (>95% certainty)

• 75.3% gender determined via Social Security records

• 12.6% determined via genderizeR (user profiles from social networks)

• 12.1% gender unknown and omitted from our analysis:

• 7.6% appear in neither data base

• 4.5% are used for males and females with > 5% certainty

• Rate of missingness compares favorably to previous studies

West, Jevin D., Jennifer Jacquet, Molly M. King, Shelley J. Correll, and Carl T. Bergstrom. "The role of gender in scholarly authorship." PloS one 8, no. 7 (2013): e66212.

Larivière, Vincent, Chaoqun Ni, Yves Gingras, Blaise Cronin, and Cassidy R. Sugimoto. "Bibliometrics: Global gender disparities in science." Nature News 504, no. 7479 (2013): 211.

Gender and authorship practices across fields

1960 1980 2000

12

34

56

7Av

g N

um o

f Aut

h

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

% o

f Mul

ti−au

thor

Pap

ers

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

femalesunestimated

% o

f aut

hor g

ende

r

Demography

1960 1980 2000

12

34

56

7Av

g N

um o

f Aut

h

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

% o

f Mul

ti−au

thor

Pap

ers

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

femalesunestimated

% o

f aut

hor g

ende

r

Ecology and evolution

1960 1980 2000

12

34

56

7Av

g N

um o

f Aut

h

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

% o

f Mul

ti−au

thor

Pap

ers

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

femalesunestimated

% o

f aut

hor g

ende

rEconomics

6 of 22

621

622

623

624

625

626

627

628

629

630

631

632

633

634

635

636

637

638

639

640

641

642

643

644

645

646

647

648

649

650

651

652

653

654

655

656

657

658

659

660

661

662

663

664

665

666

667

668

669

670

671

672

673

674

675

676

677

678

679

680

681

682

683

684

685

686

687

688

689

690

691

692

693

694

695

696

697

698

699

700

701

702

703

704

705

706

707

708

709

710

711

712

713

714

715

716

717

718

719

720

721

722

723

724

725

726

727

728

729

730

731

732

733

734

735

736

737

738

739

740

741

742

743

744

Y. Samuel Wang, Carole J. Lee, Jevin D. West, Carl T. Bergstrom, Elena A. Erosheva


1960 1980 2000

12

34

56

7Av

g N

um o

f Aut

h

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

% o

f Mul

ti−au

thor

Pap

ers

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

femalesunestimated

% o

f aut

hor g

ende

r

Radiation damage

1960 1980 2000

12

34

56

7Av

g N

um o

f Aut

h

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

% o

f Mul

ti−au

thor

Pap

ers

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

femalesunestimated

% o

f aut

hor g

ende

r

Sociology

1960 1980 2000

12

34

56

7Av

g N

um o

f Aut

h

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

% o

f Mul

ti−au

thor

Pap

ers

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

femalesunestimated

% o

f aut

hor g

ende

rVeterinary medicine

12 of 22

1365

1366

1367

1368

1369

1370

1371

1372

1373

1374

1375

1376

1377

1378

1379

1380

1381

1382

1383

1384

1385

1386

1387

1388

1389

1390

1391

1392

1393

1394

1395

1396

1397

1398

1399

1400

1401

1402

1403

1404

1405

1406

1407

1408

1409

1410

1411

1412

1413

1414

1415

1416

1417

1418

1419

1420

1421

1422

1423

1424

1425

1426

1427

1428

1429

1430

1431

1432

1433

1434

1435

1436

1437

1438

1439

1440

1441

1442

1443

1444

1445

1446

1447

1448

1449

1450

1451

1452

1453

1454

1455

1456

1457

1458

1459

1460

1461

1462

1463

1464

1465

1466

1467

1468

1469

1470

1471

1472

1473

1474

1475

1476

1477

1478

1479

1480

1481

1482

1483

1484

1485

1486

1487

1488



1960 1980 2000

12

34

56

7Av

g N

um o

f Aut

h

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

% o

f Mul

ti−au

thor

Pap

ers

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

femalesunestimated

% o

f aut

hor g

ende

r

Operations research

1960 1980 2000

12

34

56

7Av

g N

um o

f Aut

h

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

% o

f Mul

ti−au

thor

Pap

ers

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

femalesunestimated

% o

f aut

hor g

ende

r

Organizational and marketing

1960 1980 2000

12

34

56

7Av

g N

um o

f Aut

h

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

% o

f Mul

ti−au

thor

Pap

ers

1960 1980 2000

0.0

0.2

0.4

0.6

0.8

1.0

femalesunestimated

% o

f aut

hor g

ende

r

Philosophy


993

994

995

996

997

998

999

1000

1001

1002

1003

1004

1005

1006

1007

1008

1009

1010

1011

1012

1013

1014

1015

1016

1017

1018

1019

1020

1021

1022

1023

1024

1025

1026

1027

1028

1029

1030

1031

1032

1033

1034

1035

1036

1037

1038

1039

1040

1041

1042

1043

1044

1045

1046

1047

1048

1049

1050

1051

1052

1053

1054

1055

1056

1057

1058

1059

1060

1061

1062

1063

1064

1065

1066

1067

1068

1069

1070

1071

1072

1073

1074

1075

1076

1077

1078

1079

1080

1081

1082

1083

1084

1085

1086

1087

1088

1089

1090

1091

1092

1093

1094

1095

1096

1097

1098

1099

1100

1101

1102

1103

1104

1105

1106

1107

1108

1109

1110

1111

1112

1113

1114

1115

1116

9 of 22

Question

• Do males co-author with males (and females with females) more often than we would otherwise expect?

• We need to be careful about how we measure:

1. How often do males co-author w/ males (and females w/ females)?

2. Counterfactual: Is this more often than we would otherwise expect?

3. If yes, then we have behavioral homophily.

1. Tendency for same-gender authorships to co-author

• We measure homophily by computing the difference in risks:

• α = P(random co-author of random male is male) - P (random co-author of a random female is male)


• We measure homophily by computing the difference in risks:

• α = P(random co-author of random male is male) - P (random co-author of a random female is male)

• This measure is equivalent to:

• Pearson correlation of gender indicators for random co-authorship pairs

• Wright’s F Coefficient of Inbreeding when all papers have two authors

• Newman’s network-based assortativity coefficient in an appropriately weighted network

Bergstrom, Theodore C. "The algebra of assortative encounters and the evolution of cooperation." International Game Theory Review 5, no. 03 (2003): 211-228.

Wright, Sewall. "The genetical structure of populations." Annals of eugenics 15, no. 1 (1949): 323-354.

Bergstrom, T., M. Bergstrom, M. King, J. Jacquet, J. West, and S. Correll. "A note on measuring gender homophily among scholarly authors." (2016).

Wang, Y. Samuel, and Elena A. Erosheva. "On the relationship between set-based and network-based measures of gender homophily in scholarly publications." arXiv preprint arXiv:1610.09026 (2016).

Newman, Mark EJ. "Mixing patterns in networks." Physical Review E 67, no. 2 (2003): 026126.


Sociology

Sociology of family






Exchange networks


Sociology


Paper 1

Paper 8Paper 7Paper 6Paper 5

Paper 2 Paper 3 Paper 4


Paper 1



femalemale


P(co-author = male | author = male) = 3/4

P(co-author = male | author = female) = 3/10

α = 0.45

Paper 1



Question

1. How often do males co-author w/ males (and females w/ females)?

2. Counterfactual: Is this more often than we would otherwise expect?

1. To do this, we must account for:

1. Structural Homophily

2. Compositional Homophily

P(co-author = male | author = male) = 3/4

P(co-author = male | author = female) = 3/10

α = 0.45

Paper 1



2. Is this more often than we would otherwise expect?


Paper 1



Fix gender ratio, number of authorships, number of authorships per paper.


Paper 1



Randomly reassign authorships and measure counterfactual alpha value.

Measuring HomophilyDoc 1 Doc 2 Doc 3 Doc 4

Doc 5 Doc 6 Doc 7 Doc 8

Null Distribution of alpha

alpha

−1.0 −0.5 0.0 0.5 1.0

P−value: 0.035

Y. Samuel Wang Homophily in Co-authorships 08/11/2019 9 / 17


Structural homophily = Deviation of alpha from zero due to structural aspects (gender ratio, number of authorships, number of authorships per paper)


−1.0 −0.5 0.0 0.5 1.0

P−value: 0.035


Paper 1




−1.0 −0.5 0.0 0.5 1.0

P−value: 0.035


Paper 1



p value = proportion of α values generated from the null distribution which are greater than or equal to the observed value of α.

Small p-value implies that the observed α is unlikely to occur.

Sociology

Sociology of family






Exchange networks


Sociology


Sociology

Paper 1




Sociology

Paper 1




Each terminal field has different gender ratios, numbers of authorships, and numbers of authorships per paper.

Sociology


Fix gender ratio, number of authorships, number of authorships per paper within each terminal field.

Paper 1



Sociology

Paper 1




Randomly reassign authorships within terminal fields.

Compositional homophily = Deviation of alpha from the expected alpha under structural homophily that arises due to the tendency for authorships to co-author with those who are intellectually closer.


Compositional Homophily


Molecular Biology


Sociology


alphaComp

−1.0 −0.5 0.0 0.5 1.0

P−value: 1



−1.0 −0.5 0.0 0.5 1.0

P−value: 1

Field

Paper 1




−1.0 −0.5 0.0 0.5 1.0

P−value: 1

Field

Paper 1



Reversal due to gender imbalances and other structural differences across sub-populations:

• Simpson’s paradox (statistics)• Wahlund effect (population genetics)

• Generate counterfactuals:

• Assume authorships in the same terminal field are exchangeable

• Assume authorships in different terminal fields are less likely to swap and use citation flows to determine swap probabilities

• Use a Markov Chain Monte Carlo Metropolis Hastings sampler to generate counterfactuals

• 75,000 draws form null distribution after burn-in

• Compare counterfactual alpha values to observed alpha:

• Hypothesis test for all levels (terminal fields, composite fields, major fields)

• Use p-values adjusted by the Benjamini-Yuketieli procedure to control False Discovery Rate at 0.05

Testing procedure

Results: Behavioral homophily

• 84% of top fields

Top Level Fields

FieldObs / Exp

P-valueSignificant / Total

↵ FM Term CompJSTOR .11/.05 38.6/41.1 .00 124/1450 82/280Mol/Cell Bio .05/.01 38.2/39.8 .00 29/178 19/44Eco/Evol .06/.02 31.9/33.3 .00 17/257 15/56Economics .11/.02 18.7/20.8 .00 9/136 11/28Sociology .19/.07 38.5/44.2 .00 13/94 12/21Prob/Stat .09/.03 26/27.8 .00 1/90 2/23Org/mkt .16/.04 29/33.2 .00 8/68 3/4Education .16/.04 41.2/47.2 .00 12/42 6/10Occ Health .10/.02 41.7/45.5 .00 12/24 1/1Anthro .12/.03 38.5/42 .00 5/63 2/8Law .17/.08 29.7/32.9 .00 0/98 1/16History .16/.07 32.9/36.5 .00 0/49 1/6Phys Anthro .07/.01 34.7/36.8 .00 1/32 2/10Intl Poli Sci .09/.02 27.3/29.1 .03 0/34 0/2US Poli Sci .15/.07 25.2/27.4 .00 2/37 1/6Philosophy .10/.03 18.7/20.3 .03 0/45 0/8Math .04/.01 14.3/14.7 1.00 0/46 0/9Vet Med .09/.01 38.3/41.6 .00 7/19 1/2Cog Sci .18/.09 35.7/39.4 .00 4/14 3/3Radiation .09/.01 34/36.8 .00 3/14 1/5Demography .15/.06 40.3/44.4 .00 0/20 1/2Classics .07/.01 38.7/41.2 .27 0/35 0/8Opr Res .03/.00 16.6/17.1 .73 0/18 0/4Plant Phys .08/.02 29.1/31 .03 1/21 0/3Mycology .03/.01 36.8/37.5 1.00 0/16 0/1


Top Level Fields

FieldObs / Exp




Avg counterfactual

Observed

• 29% of composite fields

• 8% of terminal fields

Results: Behavioral homophilyTop Level Fields

FieldObs / Exp




Top Level Fields

FieldObs / Exp




• Trade-off between increasing testing power by aggregating data versus controlling for confounders by analyzing at a fine-grain level.

http://eigenfactor.org/projects/gender_homophily/

Visualization


How sensitive are our results to missing gender indicators?

• To evaluate, we impute gender for authorships under two scenarios:

• Low homophily: Impute each missing gender indicator at random according to the proportions of assigned genders in the authorship’s original terminal field. Assumes no behavioral homophily in the imputed data.

• High homophily: Impute each missing gender indicator at random according to the proportions of assigned gender in the original paper. If a paper contains only unassigned authorships, impute a single gender for all according to the proportions of assigned gender authorships for the terminal field. Assumes behavioral homophily since, by construction, papers with one or no assigned authorships are always gender homophilous.

• For each scenario, carry out 10 imputations and then repeat the entire sampling and testing procedures used for the main analysis.

• Original results:

• Top fields: 84%

• Composite fields: 28%

• Terminal fields: 8%

How sensitive are our results to missing gender indicators?

E. Sensitivity Analysis: Missing Gender Indicators. To evaluate how sensitive our main results are to the missing gender

indicators, we impute gender for authorships with missing gender indicators under two scenarios:

• Low homophily: Each authorship with a missing gender indicator is assigned a gender at random according to the

proportions of observed genders on its original terminal field. This procedure assumes that there is no behavioral

homophily in the imputed data because the imputed genders are conditionally independent given the terminal field. Thus,

it gives a reasonable lower bound on the homophily we might have observed given the full data.

• High homophily: Each authorship with a missing gender indicator is assigned a gender at random according to the

proportions of observed genders on its original paper. If the original paper contains only authorships with missing gender

indicators, we assign all authorships on the paper the same gender indicator which is drawn randomly according to the

proportions of observed genders for its original terminal field. Because papers with at most one assigned gender indicator

are homophilous by construction, this provides a reasonable upper bound on the homophily we might have observed

given the full data.

For each scenario, we carry out 10 imputations and then repeat the entire sampling and testing procedures used for the

main analysis. Table S8 gives the resulting percentages of terminal, composite, and top level fields with significant behavioral

homophily under the Benjamini-Yekutieli FDR procedure with – = .05 under the low and high homophily missing data

imputation scenarios. We observed that, on average, 7%, 25%, and 78% of terminal, composite, and top level fields exhibit

statistically significant respectively in the low homophily scenario; for the high homophily procedure the corresponding averages

are 54%, 82%, and 100%.

Table S8. Each column shows the percentage of fields which exhibit statistically significant homophily for each of the individual imputations

Terminal Composite TopMain Analysis 0.09 0.29 0.83Low Imputation 1 0.06 0.23 0.83Low Imputation 2 0.07 0.25 0.75Low Imputation 3 0.06 0.25 0.75Low Imputation 4 0.08 0.25 0.75Low Imputation 5 0.06 0.26 0.75Low Imputation 6 0.07 0.28 0.75Low Imputation 7 0.07 0.25 0.83Low Imputation 8 0.07 0.26 0.79Low Imputation 9 0.07 0.25 0.75Low Imputation 10 0.06 0.26 0.79Low Imputation Avg 0.07 0.25 0.78High Imputation 1 0.54 0.82 1.00High Imputation 2 0.53 0.82 1.00High Imputation 3 0.53 0.82 1.00High Imputation 4 0.53 0.82 1.00High Imputation 5 0.54 0.82 1.00High Imputation 6 0.53 0.81 1.00High Imputation 7 0.54 0.82 1.00High Imputation 8 0.54 0.83 1.00High Imputation 9 0.54 0.83 1.00High Imputation 10 0.54 0.82 1.00High Imputation Avg 0.54 0.82 1.00


2481

2482

2483

2484

2485

2486

2487

2488

2489

2490

2491

2492

2493

2494

2495

2496

2497

2498

2499

2500

2501

2502

2503

2504

2505

2506

2507

2508

2509

2510

2511

2512

2513

2514

2515

2516

2517

2518

2519

2520

2521

2522

2523

2524

2525

2526

2527

2528

2529

2530

2531

2532

2533

2534

2535

2536

2537

2538

2539

2540

2541

2542

2543

2544

2545

2546

2547

2548

2549

2550

2551

2552

2553

2554

2555

2556

2557

2558

2559

2560

2561

2562

2563

2564

2565

2566

2567

2568

2569

2570

2571

2572

2573

2574

2575

2576

2577

2578

2579

2580

2581

2582

2583

2584

2585

2586

2587

2588

2589

2590

2591

2592

2593

2594

2595

2596

2597

2598

2599

2600

2601

2602

2603

2604

21 of 22

Secondary analysis

• Fit logistic regression for all terminal fields where the outcome is whether there is statistically significant behavioral homophily

• Result: behavioral homophily has a statistically significant positive association with the proportion of females and terminal field size

• In economics, behavioral homophily was also found to be more prevalent in sub-fields with a higher proportion of females

• Homophily: as representation of women increases, more likely that same-gender individuals who are sufficiently compatible along key dimensions become available as co-authors

• Caveat: Larger field size and balanced gender representation increase power of testing procedure (i.e., ability to detect behavioral gender homophily).

Boschini, Anne, and Anna Sjögren. "Is team formation gender neutral? Evidence from coauthorship patterns." Journal of Labor Economics 25, no. 2 (2007): 325-365.

Conclusion

• We detect behavioral gender homophily in 84% of top fields, 29% of composite fields, and 8% of terminal fields

• Since behavioral gender homophily is endemic to even some of the smallest intellectual communities, it might only be mitigated by changing the cultural norms and perceptions that drive behavioral gender homophily within intellectual communities

Future work: Strategic value of gender homophily?

• Short-term: does gender homophily increase retention, productivity, and impact of female authors?

• Stereotype threat: presence of other women in male-stereotyped domains enhances confidence, performance, and motivation

• Long-term: do gender homophilous co-authorships lead to gender-homophilous intellectual communities? If so, does increasing the ratio of women in an intellectual community decrease its value/impact, just as increasing the ratio of women in an occupation decreases its prestige?

Murphy, Mary C., Claude M. Steele, and James J. Gross. "Signaling threat: How situational cues affect women in math, science, and engineering settings." Psychological science 18, no. 10 (2007): 879-885.

Stout, Jane G., Nilanjana Dasgupta, Matthew Hunsinger, and Melissa A. McManus. "STEMing the tide: using ingroup experts to inoculate women's self-concept in science, technology, engineering, and mathematics (STEM)." Journal of personality and social psychology 100, no. 2 (2011): 255.

Goldin, Claudia. "A pollution theory of discrimination: male and female differences in occupations and earnings." In Human capital in history: The American record, pp. 313-348. University of Chicago Press, 2014.

Future work: Fine-tuning methods

• Temporal aspects: Gender representation changes over time. Incorporate temporal info into the null distribution.

• Disambiguating authors: In terminal fields with few female authors, we may overestimate structural and compositional homophily (and underestimate behavioral homophily) by allowing multiple female authorships corresponding to the same author to be reassigned to the same paper.

Thank you

• For early discussions:

• Jennifer Jacquet, Molly King, Shelley Correll, & Ted Bergstrom

• Funders:

• Royalty Research Fund Grant #A118374, Elena Erosheva (PI) and Carole Lee (co-PI)

• NSF Grant #1735194, Jevin West (co-PI)

For more information

• Link to paper: http://arxiv.org/abs/1909.01284

• Visualization: http://eigenfactor.org/projects/gender_homophily/

• Code for analysis and plots: https://github.com/ysamwang/genderHomophily

• Data: Under license by JSTOR to the authors. Requests for raw data should be made to JSTOR directly.

http://arxiv.org/abs/1909.01284


https://github.com/ysamwang/genderHomophily

Size of each top level field

2. JSTOR Description

Table S1 shows the size of each of the 24 top level fields identified by the map equation. The values are calculated for all papers

published after 1959. Note that the table describes the data prior to the data cleaning procedure, so counts of authorships,

papers, terminal fields and composite fields shown here may di�er from those given in the main manuscript which refer to data

after the cleaning procedure. Specifically, Classics, Law, and Philosophy have entire terminal fields which are removed by the

cleaning procedure. Table S2 presents the structural characteristics of each top level field. For the multi-author columns, we

report the proportion amongst all authorships on a multi-author paper; e.g., all female authorships on multi-authored papers

divided by the total count of authorships on multi-authored papers. For the intraclass correlation (ICC) of individuals with

unimputed genders, we use the flAOV statistic from (1). This gives a measure of how unimputed authorships cluster by paper.

Anecdotally, unimputed authorships are often names which have been Romanized. Thus a high ICC may indicate homophily

by race or ethnicity.

Table S1. Size of each of the top level fields identified by the map equation hierarchical clustering

Authors Papers Terminal CompositeLabel (Count) (Count) Fields FieldsAnthropology 37588 30499 63 8Classical studies 10596 9061 37 8Cognitive science 15715 5553 14 3Demography 9653 5509 20 2Ecology and evolution 264853 116327 257 56Economics 95934 59096 136 28Education 40188 23065 42 10History 26449 24043 49 6Law 23974 19779 105 16Mathematics 18348 14125 46 9Molecular & Cell biology 382971 92528 178 44Mycology 7469 3679 16 1Operations research 13716 7780 18 4Organizational and marketing 34254 17963 68 4Philosophy 21738 19126 46 8Physical anthropology 29693 16703 32 10Plant physiology 9159 5436 21 3Political science - international 15283 11835 34 2Political science-US domestic 12581 7824 37 6Pollution and occupational health 50967 12359 24 1Probability and Statistics 37471 22094 90 23Radiation damage 14118 4215 14 5Sociology 57146 31662 94 21Veterinary medicine 17756 4796 19 2


249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

3 of 22

Structural characteristics of each field

Table S2. The structural characteristics of each top level field identified by the map equation hierarchical clustering. The “Prop Single-Author”columns display the proportion of papers (authorships) which are single-authored out of all papers (authorships). The “Single-author” (“Multi-Author”) column give the proportions of all authorships on single-authored (multi-authored) papers which were imputed a gender based onfirst name. F- Female; M- Male; U- Unimputed. The “ICC” column displays the intraclass correlation of unimputed authorships on multi-authorpapers.

Prop Single Author Single-Author Multi-AuthorLabel Papers Auth % F % M % U % F % M % U ICCAnthropology 0.86 0.70 0.27 0.63 0.10 0.28 0.61 0.12 0.10Classical studies 0.93 0.79 0.22 0.70 0.08 0.27 0.65 0.08 0.05Cognitive science 0.25 0.09 0.29 0.64 0.07 0.28 0.62 0.10 0.09Demography 0.57 0.32 0.24 0.61 0.15 0.30 0.53 0.16 0.11Ecology and evolution 0.37 0.16 0.14 0.79 0.08 0.20 0.70 0.11 0.10Economics 0.55 0.34 0.08 0.81 0.11 0.11 0.77 0.12 0.10Education 0.55 0.31 0.35 0.58 0.07 0.41 0.50 0.08 0.07History 0.92 0.84 0.24 0.70 0.06 0.23 0.69 0.08 0.05Law 0.85 0.70 0.17 0.78 0.06 0.22 0.71 0.06 0.05Mathematics 0.75 0.58 0.06 0.76 0.18 0.06 0.73 0.21 0.19Molecular & Cell biology 0.14 0.03 0.19 0.70 0.10 0.23 0.61 0.16 0.09Mycology 0.45 0.22 0.20 0.71 0.09 0.22 0.65 0.13 0.08Operations research 0.48 0.27 0.05 0.81 0.14 0.08 0.72 0.20 0.21Organizational and marketing 0.40 0.21 0.18 0.72 0.10 0.19 0.68 0.12 0.12Philosophy 0.89 0.78 0.09 0.82 0.08 0.10 0.78 0.11 0.12Physical anthropology 0.66 0.37 0.22 0.72 0.06 0.22 0.68 0.09 0.07Plant physiology 0.53 0.31 0.13 0.79 0.08 0.17 0.72 0.10 0.07Political science - international 0.78 0.60 0.16 0.74 0.10 0.17 0.73 0.10 0.08Political science-US domestic 0.57 0.35 0.17 0.76 0.07 0.18 0.75 0.07 0.05Pollution and occupational health 0.22 0.05 0.24 0.65 0.11 0.31 0.53 0.17 0.19Probability and Statistics 0.54 0.32 0.08 0.75 0.17 0.13 0.69 0.19 0.20Radiation damage 0.23 0.07 0.22 0.66 0.11 0.22 0.62 0.16 0.14Sociology 0.52 0.29 0.30 0.63 0.08 0.38 0.53 0.08 0.07Veterinary medicine 0.26 0.07 0.27 0.60 0.12 0.25 0.59 0.15 0.22

The plots below show how the following quantities have changed over time for each top level fields- average number of

authors per paper, proportion of papers with multiple authors, and the imputed gender proportions. The values are calculated

on the data before the data-cleaning procedure which removes authorship instances with unimputed genders.

4 of 22

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

465

466

467

468

469

470

471

472

473

474

475

476

477

478

479

480

481

482

483

484

485

486

487

488

489

490

491

492

493

494

495

496


C. Calculating and adjusting P-values. In a sampled configuration, if a field only contains authorships of a single gender, – is

undefined. When calculating a p-value, we consider this as – = 1. This approach is conservative because it increases p-values,

but in practice has very little e�ect on our results.

In the main manuscript, we control the false discovery rate at .05 with the Benjamini-Yekutieli procedure (5) which allows

for arbitrary dependence of the p-values, but is more conservative than the Benjamini-Hochberg procedure (6), which only

allows for certain types of positive dependence. Table S5 replicates the last 3 columns of Table 1 of the main manuscript using

the Benjamini-Yekutieli procedure with an FDR of .005 as well as the Benjamini-Hochberg procedure with FDR rates of .05

and .005.

Table S5. Main results using different FDR procedures. “BY” indicated Benjamini-Yekutieli and “BH” indicates Benjamini-Hochberg.

BY; Rate = .005 BH; Rate = .005 BH; Rate = .05Field P-value Term Comp P-value Term Comp P-value Term CompJSTOR .00 68/1450 65/280 .00 114/1450 81/280 .00 261/1450 125/280Mol/Cell Bio .00 16/178 18/44 .00 28/178 19/44 .00 53/178 29/44Eco/Evol .00 7/257 13/56 .00 14/257 15/56 .00 43/257 25/56Economics .00 4/136 8/28 .00 8/136 11/28 .00 25/136 17/28Sociology .00 9/94 9/21 .00 12/94 12/21 .00 26/94 14/21Prob/Stat .00 0/90 1/23 .00 1/90 2/23 .00 7/90 7/23Org/mkt .00 5/68 3/4 .00 6/68 3/4 .00 15/68 3/4Education .00 6/42 4/10 .00 10/42 6/10 .00 17/42 6/10Occ Health .00 8/24 1/1 .00 12/24 1/1 .00 15/24 1/1Anthro .00 2/63 1/8 .00 5/63 2/8 .00 8/63 2/8Law .00 0/98 0/16 .00 0/98 1/16 .00 1/98 4/16History .00 0/49 0/6 .00 0/49 1/6 .00 1/49 1/6Phys Anthro .00 1/32 2/10 .00 1/32 2/10 .00 6/32 3/10Intl Poli Sci .03 0/34 0/2 .00 0/34 0/2 .00 3/34 0/2US Poli Sci .00 0/37 0/6 .00 2/37 1/6 .00 4/37 3/6Philosophy .03 0/45 0/8 .00 0/45 0/8 .00 5/45 0/8Math 1.00 0/46 0/9 .16 0/46 0/9 .16 2/46 0/9Vet Med .00 5/19 1/2 .00 7/19 1/2 .00 8/19 2/2Cog Sci .00 2/14 3/3 .00 4/14 3/3 .00 7/14 3/3Radiation .00 3/14 1/5 .00 3/14 1/5 .00 5/14 3/5Demography .00 0/20 0/2 .00 0/20 0/2 .00 3/20 2/2Classics .27 0/35 0/8 .03 0/35 0/8 .03 1/35 0/8Opr Res .73 0/18 0/4 .09 0/18 0/4 .09 1/18 0/4Plant Phys .03 0/21 0/3 .00 1/21 0/3 .00 4/21 0/3Mycology 1.00 0/16 0/1 .27 0/16 0/1 .27 1/16 0/1


2233

2234

2235

2236

2237

2238

2239

2240

2241

2242

2243

2244

2245

2246

2247

2248

2249

2250

2251

2252

2253

2254

2255

2256

2257

2258

2259

2260

2261

2262

2263

2264

2265

2266

2267

2268

2269

2270

2271

2272

2273

2274

2275

2276

2277

2278

2279

2280

2281

2282

2283

2284

2285

2286

2287

2288

2289

2290

2291

2292

2293

2294

2295

2296

2297

2298

2299

2300

2301

2302

2303

2304

2305

2306

2307

2308

2309

2310

2311

2312

2313

2314

2315

2316

2317

2318

2319

2320

2321

2322

2323

2324

2325

2326

2327

2328

2329

2330

2331

2332

2333

2334

2335

2336

2337

2338

2339

2340

2341

2342

2343

2344

2345

2346

2347

2348

2349

2350

2351

2352

2353

2354

2355

2356

19 of 22

Readjust the Benjamini-Yekutieli procedure to control the false discovery rate at 0.005 instead of 0.05

Previous work

• Field-level:

• Economics: study of publications from cohort of 178 PhDs found women > 5x more likely than men to have female co-authors

• A study of 1,045,401 multi-authored papers finds gender homophily at what we’d characterize as the field level

• Sub-field studies:

• Economics: Study of 3,090 articles in the top three journals (1991-2002) found gender homophily at the sub-field level

McDowell, John M., and Janet Kiholm Smith. "The effect of gender-sorting on propensity to coauthor: Implications for academic promotion." Economic Inquiry 30, no. 1 (1992): 68-82.

AlShebli, Bedoor K., Talal Rahwan, and Wei Lee Woon. "The preeminence of ethnic diversity in scientific collaboration." Nature communications 9, no. 1 (2018): 5163.

Boschini, Anne, and Anna Sjögren. "Is team formation gender neutral? Evidence from coauthorship patterns." Journal of Labor Economics 25, no. 2 (2007): 325-365.

Structural versus compositional homophily

B. Comparison with Naive Approach. We can compare the expected value of – from the null distribution which accounts

for structural and compositional homophily (Eq. (2) in the main document) to the expected value of – from a naive null

distribution which only accounts for structural homophily. We construct a naive null distribution for each level l = 1, . . . , 6 in

the full hierarchical clustering by preserving all structure of (terminal or composite) fields with depth less than l, but treating

all fields of depth l as a terminal field. We then recalculate the swap probabilities pfa,fúa

given the citation flows, and then

run the sampler for 5,000 samples. We discard the first 1,000 as burn in and use the remaining 4,000 samples to calculate an

expected value and calculate p-values.

Columns labeled “Struct” provide the expected value of –, the expected number of female-male papers, the p-value for

behavioral homophily, and the number of significant composite fields under the null hypothesis of only structural (but not

compositional) homophily. Under only structural homophily, the expected – value is smaller than the expected – when also

preserving compositional homophily. In addition, the p-value decreases for all top-level fields when only considering structural

homophily. In many top-level fields, the number of composite fields with behavioral increases when only capturing structural

homophily and never decreases.

Table S4. Comparison of naive analysis only preserving structural homophily to main analysis.

– F M P-values Signif CompField Obs Exp Struct Obs Exp Struct Main Struct Main StructJSTOR .11 .05 .00 38.6 41.1 43.3 .00 .00 82/280 157/280Mol/Cell Bio .05 .01 .00 38.2 39.8 40.2 .00 .00 19/44 35/44Eco/Evol .06 .02 .00 31.9 33.3 34.0 .00 .00 15/56 33/56Economics .11 .02 .00 18.7 20.8 21.1 .00 .00 11/28 18/28Sociology .19 .07 .00 38.5 44.2 47.4 .00 .00 12/21 19/21Prob/Stat .09 .03 .00 26.0 27.8 28.6 .00 .00 2/23 12/23Org/mkt .16 .04 .00 29.0 33.2 34.7 .00 .00 3/4 4/4Education .16 .04 .00 41.2 47.2 49.2 .00 .00 6/10 9/10Occ Health .10 .02 .00 41.7 45.5 46.3 .00 .00 1/1 1/1Anthro .12 .03 .00 38.5 42.0 43.5 .00 .00 2/8 4/8Law .17 .08 .00 29.7 32.9 35.7 .00 .00 1/16 4/16History .16 .07 .00 32.9 36.5 39.1 .00 .00 1/6 2/6Phys Anthro .07 .01 .00 34.7 36.8 37.1 .00 .00 2/10 2/10Intl Poli Sci .09 .02 .00 27.3 29.1 29.8 .03 .00 0/2 1/2US Poli Sci .15 .07 .00 25.2 27.4 29.6 .00 .00 1/6 2/6Philosophy .10 .03 .00 18.7 20.3 20.8 .03 .00 0/8 0/8Math .04 .01 .00 14.3 14.7 14.9 1.00 .12 0/9 0/9Vet Med .09 .01 .00 38.3 41.6 42.0 .00 .00 1/2 2/2Cog Sci .18 .09 .00 35.7 39.4 43.3 .00 .00 3/3 3/3Radiation .09 .01 .00 34.0 36.8 37.3 .00 .00 1/5 4/5Demography .15 .06 .00 40.3 44.4 47.3 .00 .00 1/2 1/2Classics .07 .01 .00 38.7 41.2 41.7 .27 .01 0/8 0/8Opr Res .03 .00 .00 16.6 17.1 17.1 .73 .33 0/4 0/4Plant Phys .08 .02 .00 29.1 31.0 31.8 .03 .00 0/3 1/3Mycology .03 .01 .00 36.8 37.5 37.9 1.00 .60 0/1 0/1

18 of 22

2109

2110

2111

2112

2113

2114

2115

2116

2117

2118

2119

2120

2121

2122

2123

2124

2125

2126

2127

2128

2129

2130

2131

2132

2133

2134

2135

2136

2137

2138

2139

2140

2141

2142

2143

2144

2145

2146

2147

2148

2149

2150

2151

2152

2153

2154

2155

2156

2157

2158

2159

2160

2161

2162

2163

2164

2165

2166

2167

2168

2169

2170

2171

2172

2173

2174

2175

2176

2177

2178

2179

2180

2181

2182

2183

2184

2185

2186

2187

2188

2189

2190

2191

2192

2193

2194

2195

2196

2197

2198

2199

2200

2201

2202

2203

2204

2205

2206

2207

2208

2209

2210

2211

2212

2213

2214

2215

2216

2217

2218

2219

2220

2221

2222

2223

2224

2225

2226

2227

2228

2229

2230

2231

2232


Data reduction due to unimputed gender

3. Data Cleaning Procedures

For the main analysis, we impute gender indicators for authorships with first names that are used for a single gender with at

least 95% frequency in either the U.S. Social Security records or in the genderizeR database. We consider the gender indicator

to be missing for authorships that either do not appear in those databases or are not used with at least 95% frequency for

one gender. We subsequenty remove authorships with unimputed genders from our main analysis. This removal results in

some articles which originally had multiple authors becoming single author papers, which are excluded from the analysis.

The following table shows the proportion of authorships and papers which are lost solely due to unimputed genders. The

denominator only includes papers which have multiple authors which were published from 1960-2012. The % unimputed

column is the % of authors for which we do not impute a gender indicator. The % Lost column is the % of authors (or papers)

which are lost after removing the authorships with unimputed gender indicators and then removing the resulting single author

papers. For authorships, this percentage includes the authorships with unimputed genders.

Table S3. Data reduction due to unimputed gender indicators

Prop Authors with Authors PapersLabel Unimputed Gender Remaining Prop Lost Remaining Prop LostAnthropology 0.12 9326 0.17 3466 0.15Classical studies 0.08 1976 0.11 610 0.09Cognitive science 0.10 12510 0.13 3814 0.07Demography 0.16 5069 0.22 1930 0.17Ecology and evolution 0.11 192091 0.13 66152 0.08Economics 0.12 51691 0.19 22178 0.15Education 0.08 24356 0.12 9396 0.09History 0.08 3699 0.12 1596 0.11Law 0.06 6526 0.10 2765 0.09Mathematics 0.21 5319 0.31 2459 0.25Molecular & Cell biology 0.16 303761 0.18 73357 0.07Mycology 0.13 4828 0.17 1759 0.11Operations research 0.20 7217 0.28 3025 0.21Organizational and marketing 0.12 22299 0.18 9137 0.13Philosophy 0.11 3897 0.18 1770 0.15Physical anthropology 0.09 16463 0.12 5175 0.07Plant physiology 0.10 5388 0.14 2287 0.10Political science - international 0.10 5128 0.16 2247 0.14Political science-US domestic 0.07 7269 0.11 3068 0.09Pollution and occupational health 0.17 39703 0.18 8845 0.06Probability and Statistics 0.19 18763 0.27 7600 0.21Radiation damage 0.16 10710 0.18 2902 0.09Sociology 0.08 35858 0.12 13600 0.09Veterinary medicine 0.15 13741 0.17 3275 0.06Total 0.14 807588 0.16 252413 0.11


1489

1490

1491

1492

1493

1494

1495

1496

1497

1498

1499

1500

1501

1502

1503

1504

1505

1506

1507

1508

1509

1510

1511

1512

1513

1514

1515

1516

1517

1518

1519

1520

1521

1522

1523

1524

1525

1526

1527

1528

1529

1530

1531

1532

1533

1534

1535

1536

1537

1538

1539

1540

1541

1542

1543

1544

1545

1546

1547

1548

1549

1550

1551

1552

1553

1554

1555

1556

1557

1558

1559

1560

1561

1562

1563

1564

1565

1566

1567

1568

1569

1570

1571

1572

1573

1574

1575

1576

1577

1578

1579

1580

1581

1582

1583

1584

1585

1586

1587

1588

1589

1590

1591

1592

1593

1594

1595

1596

1597

1598

1599

1600

1601

1602

1603

1604

1605

1606

1607

1608

1609

1610

1611

1612

13 of 22

Gender-based homophily in collaborations across a ...

Documents

Transcript of Gender-based homophily in collaborations across a ...