tie strength, embeddedness & social influence: a large ...web.mit.edu/sinana/www/msta14.pdf ·...

Social Influence and Tie Characteristics

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Tie Strength, Embeddedness & Social Influence:

A Large-Scale Networked Experiment

Technical Appendix

Sinan Aral

MIT Sloan School of Management

[email protected]

Dylan Walker

Boston University School of Management

[email protected]

Descriptive Statistics

Table A1: Descriptive Statistics of Covariates for Individuals and their Peers

Individuals (i)

[n=7730] Peers (j)

[n=1296202] Male

868 134866

Female 1867 172406

Gender undefined 4995 988930

Age (0-18) 458 63063

Age (18-23) 343 65606

Age (23-31) 439 62176

Age (>31) 960 69100

Age undefined 5530 1036257

Single 513 65410

Relationship 255 39536

Engaged 70 9494

Married 485 33561

Its Complicated 38 4775

Relationship Status Undefined 6369

1143426

mailto:[email protected]

mailto:[email protected]


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Table A2: Descriptive Statistics of Covariates for Ties

Num Min 1st Quartile Median Mean 3rd Quartile Max

Hometown (same) 13225 - - - - - -

Hometown (different) 25971 - - - - - -

Hometown (undefined) 1257006 - - - - - -

Current town (same) 2911 - - - - - -

Current town (different) 7088 - - - - - -

Current town (undefined) 1286203 - - - - - -

College (same) 1433 - - - - - -

College (different) 12666 - - - - - -

College (undefined) 1282103 - - - - - -

Num. common affiliations - 0 0 0 0.009457 0 2

Num. common pages - 0 0 0 0.6213 0 655

Num. common groups - 0 0 0 0.3018 0 185

Num. photos together - 0 0 0 0.1575 0 452

Num. common friends - 0 1 6 14.02 18 837

Degree (of user i) - 1 43 98 167.7 197 4992

Number notifications

received (by j) - 0 0 0 0.03216 0 6

Facebook Application Details

Figure A1 displays the front page of an example Facebook application that is similar to the one that we

studied and is representative of the view a user sees when using the application. Figure A2 displays the

notification inbox, where a Facebook user may view and click on notifications delivered to her inbox. The

notification inbox is private and only visible to users logged into their Facebook accounts. It is not visible

to peers visiting other users’ profile pages.


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Figures A1 (left) and A2 (right)

Model Results

Table A3: Full Estimates from the Cox Proportional Hazards Model of Influence

z Pr(>|z|)

CI

Lower .95

CI

Upper .95

Treatment (

# Notifications 1.684494 5.389723 0.080309 20.975 < 2e-16 4.60476 6.3085

Spontaneous Adoption of i (

Age (0-18) .268952 1.308592 0.18174 1.48 0.138906 0.91645 1.8685

Age (18-23) -0.57042 0.56529 0.276804 -2.061 0.03933 0.32859 0.9725

Age (23-31) -0.18764 0.828914 0.266578 -0.704 0.481506 0.49158 1.3977

Age (>31) -0.021 0.979215 0.174338 -0.12 0.904104 0.69579 1.3781

Male 0.045045 1.046075 0.191168 0.236 0.813718 0.71919 1.5215

Female 0.159938 1.173438 0.150431 1.063 0.287692 0.8738 1.5758

Single -0.22938 0.795026 0.174942 -1.311 0.189797 0.56425 1.1202

Relationship -0.21854 0.80369 0.262786 -0.832 0.405617 0.48018 1.3452

Engaged -0.32077 0.725594 0.450332 -0.712 0.476288 0.30017 1.7539

Married -0.35325 0.7024 0.190385 -1.855 0.063531 0.48365 1.0201

Its Complicated -0.09331 0.91091 0.428421 -0.218 0.827583 0.39337 2.1093

Spontaneous Adoption of j (


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Age (0-18) -0.05414 0.947302 0.142402 -0.38 0.703815 0.7166 1.2523

Age (18-23) 0.000206 1.000206 0.152298 0.001 0.998921 0.74208 1.3481

Age (23-31) -0.39789 0.671739 0.180174 -2.208 0.02722 0.47188 0.9562

Age (>31) 0.487589 1.628385 0.132142 3.69 0.000224 1.25683 2.1098

Male 0.392264 1.480328 0.125287 3.131 0.001743 1.15801 1.8924

Female 0.756543 2.130897 0.109676 6.898 5.27E-12 1.71872 2.6419

Single 0.163878 1.178071 0.140326 1.168 0.242873 0.8948 1.551

Relationship -0.10779 0.897817 0.187971 -0.573 0.566349 0.62114 1.2977

Engaged -0.39365 0.674588 0.366943 -1.073 0.283364 0.32862 1.3848

Married 0.319573 1.37654 0.167534 1.908 0.056454 0.99125 1.9116

Its Complicated -0.58725 0.555856 0.549704 -1.068 0.285387 0.18926 1.6326

Spontaneous (Preference) Adoption of tie i- j (

Hometown (same) 0.386861 1.472352 0.256799 1.506 0.131945 0.89007 2.4356

Hometown (different) -0.33028 0.718724 0.236089 -1.399 0.161826 0.45248 1.1416

Current town (same) -0.75802 0.468593 0.722129 -1.05 0.293855 0.11379 1.9296

Current town (different) 0.657508 1.929977 0.341757 1.924 0.054367 0.98775 3.771

College (same) -1.00886 0.364633 1.127244 -0.895 0.370797 0.04003 3.3218

College (different) -0.26611 0.766351 0.352884 -0.754 0.450781 0.38375 1.5304

Num. common affiliations -0.20043 0.818376 0.328813 -0.61 0.542149 0.4296 1.559

Num. common pages 0.006641 1.006663 0.000951 6.986 2.83E-12 1.00479 1.0085

Num. common groups 0.032985 1.033535 0.00441 7.48 7.45E-14 1.02464 1.0425

Num. photos together 0.014124 1.014224 0.001834 7.702 1.34E-14 1.01059 1.0179

Num. common friends 0.007649 1.007678 0.000761 10.05 < 2e-16 1.00618 1.0092

Influence (

Age (0-18) -0.32031 0.725928 0.149929 -2.136 0.032648 0.5411 0.9739

Age (18-23) 0.172528 1.188305 0.174764 0.987 0.323542 0.84366 1.6737

Age (23-31) -0.06347 0.938506 0.299367 -0.212 0.832105 0.52193 1.6876

Age (>31) 0.148318 1.159882 0.198598 0.747 0.455167 0.7859 1.7118

Male 0.133022 1.142276 0.16452 0.809 0.418774 0.82743 1.5769

Female -0.20393 0.815522 0.139504 -1.462 0.143795 0.62043 1.072

Single 0.235396 1.265409 0.216139 1.089 0.276113 0.82842 1.9329

Relationship -0.09242 0.911721 0.262322 -0.352 0.724597 0.54522 1.5246

Engaged -0.01265 0.98743 0.311268 -0.041 0.967583 0.53648 1.8174

Married 0.650194 1.915912 0.153836 4.227 2.37E-05 1.4172 2.5901

Its Complicated -0.28242 0.753959 0.300552 -0.94 0.347391 0.41833 1.3589

Susceptibility (

Age (0-18) 0.113955 1.120702 0.098007 1.163 0.244943 0.92484 1.358

Age (18-23) -0.20161 0.81741 0.10981 -1.836 0.066353 0.65913 1.0137

Age (23-31) -0.0975 0.907105 0.084742 -1.151 0.249931 0.76829 1.071

Age (>31) -0.17758 0.83729 0.087427 -2.031 0.042232 0.70544 0.9938

Male -0.20719 0.812865 0.066524 -3.115 0.001842 0.7135 0.9261


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Female -0.35571 0.700675 0.068325 -5.206 1.93E-07 0.61286 0.8011

Single 0.313367 1.368024 0.105858 2.96 0.003074 1.1117 1.6834

Relationship 0.255853 1.291562 0.172659 1.482 0.138382 0.92076 1.8117

Engaged 0.725132 2.065003 0.221963 3.267 0.001087 1.33655 3.1905

Married -0.00476 0.99525 0.140076 -0.034 0.972882 0.75631 1.3097

Its Complicated 0.774685 2.169909 0.294186 2.633 0.008455 1.21907 3.8624

Influenced Adoption of tie i- j (

Hometown (same) 0.016988 1.017134 0.227245 0.075 0.940407 0.65155 1.5879

Hometown (different) 0.317388 1.373535 0.168374 1.885 0.059428 0.98746 1.9106

Current town (same) 0.828517 2.28992 0.309416 2.678 0.007413 1.24866 4.1995

Current town (different) -1.14863 0.31707 0.669876 -1.715 0.086401 0.0853 1.1786

College (same) 2.146397 8.55398 0.838897 2.559 0.01051 1.65233 44.2832


Num. common affiliations 0.813058 2.254792 0.374014 2.174 0.029715 1.08329 4.6932

Num. common pages 0.003098 1.003103 0.002323 1.334 0.182296 0.99855 1.0077

Num. common groups 0.007395 1.007423 0.005746 1.287 0.198085 0.99614 1.0188

Num. photos together -0.00229 0.997708 0.003061 -0.75 0.453433 0.99174 1.0037

Num. common friends 0.006295 1.006315 0.001621 3.883 0.000103 1.00312 1.0095

Notes: This table reports parameter estimates, hazard ratios, z-scores, confidence intervals and P-values for the Influence Cox

proportional hazards model that estimate the impact of a user’s tie attributes (tie strength and embeddedness) on his hazard to

influence peers to adopt and on the hazard that his peers will spontaneously adopt, while controlling for individual influence and

susceptibility associated with the individual attributes: age, gender or relationship status. Goodness of fit and model likelihood

test statistics include: Concordance=0.832 (SE=0.009); Likelihood ratio test = 1797 on 67 degrees of freedom (p=0); Wald test

statistic = 3489 on 67 degrees of freedom (p=0); Logrank statistic = 20640 on 67 degrees of freedom (p=0) ; Robust Logrank

statistic = 411 (p=0)

Tables Displaying Robustness Checks Described in Section 6

Table A4: Variance Inflation Factors for model covariates

Individuals (i) Peers (j)

Age (0-18) 1.444275 1.4005

Age (18-23) 1.398194 1.393997

Age (23-31) 1.389676 1.392614

Age (>31) 1.553357 1.428591

Male 2.063772 2.034803

Female 1.979811 2.012696

Single 1.283196 1.198001

Relationship 1.213176 1.161256


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Engaged 1.072233 1.05444

Married 1.304241 1.15382

Its Complicated 1.052785 1.013733

Ties (i-j)

Hometown (same) 1.128576

Hometown (different) 1.192135

Current town (same) 1.031938

Current town (different) 1.062374

College (same) 1.02606

College (different) 1.034407

Num. common affiliations 1.093833

Num. common pages 1.181538

Num. common groups 1.195172

Num. photos together 1.025678

Num. common friends 1.086174

Table A5: Estimates from the Cox Proportional Hazards Model of Influence with Number of Common

Friends Omitted

z Pr(>|z|)

CI

Lower .95

CI

Upper .95

Treatment (

# Notifications 1.72297 5.601137 0.080553 21.389 < 2e-16 4.7831 6.5591


Age (0-18) 0.306627 1.358834 0.18089 1.695 0.090057 0.95322 1.937

Age (18-23) -0.52914 0.589112 0.269395 -1.964 0.04951 0.34745 0.9989

Age (23-31) -0.18685 0.829571 0.262678 -0.711 0.476889 0.49575 1.3882

Age (>31) -0.06175 0.940119 0.172581 -0.358 0.720496 0.67032 1.3185

Male -0.00983 0.990223 0.192972 -0.051 0.959392 0.67838 1.4454

Female 0.144999 1.156039 0.149689 0.969 0.332709 0.8621 1.5502

Single -0.20142 0.81757 0.170732 -1.18 0.238105 0.58506 1.1425

Relationship -0.20417 0.815321 0.261335 -0.781 0.434644 0.48852 1.3607

Engaged -0.33759 0.71349 0.45492 -0.742 0.458039 0.29252 1.7403

Married -0.33678 0.714065 0.189587 -1.776 0.075668 0.49245 1.0354

Its Complicated -0.13793 0.871157 0.438951 -0.314 0.753344 0.36852 2.0594



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Age (0-18) -0.00095 0.999049 0.141861 -0.007 0.994651 0.75655 1.3193

Age (18-23) -0.00567 0.99435 0.15307 -0.037 0.970473 0.73662 1.3422

Age (23-31) -0.44217 0.642638 0.181052 -2.442 0.014596 0.45067 0.9164

Age (>31) 0.439796 1.55239 0.132179 3.327 0.000877 1.19809 2.0115

Male 0.401254 1.493697 0.126208 3.179 0.001476 1.16636 1.9129

Female 0.785479 2.193458 0.110666 7.098 1.27E-12 1.76575 2.7248

Single 0.218679 1.244432 0.139673 1.566 0.11743 0.94641 1.6363

Relationship -0.08341 0.919977 0.18826 -0.443 0.657737 0.63611 1.3305

Engaged -0.37436 0.687731 0.365811 -1.023 0.306136 0.33577 1.4086

Married 0.33398 1.396515 0.1673 1.996 0.045902 1.0061 1.9384

Its Complicated -0.5717 0.564565 0.550128 -1.039 0.298707 0.19206 1.6595


Hometown (same) 0.48575 1.625394 0.250805 1.937 0.052774 0.9942 2.6573




College (same) -1.01429 0.36266 1.135805 -0.893 0.37185 0.03915 3.3597




Num. common groups 0.038259 1.039001 0.003952 9.682 < 2e-16 1.03098 1.0471


Influence (

Age (0-18) -0.26729 0.765454 0.145414 -1.838 0.066047 0.57563 1.0179

Age (18-23) 0.156882 1.169858 0.169591 0.925 0.354933 0.83903 1.6311

Age (23-31) -0.14608 0.864091 0.293515 -0.498 0.618707 0.48609 1.536

Age (>31) 0.126702 1.135078 0.197099 0.643 0.520332 0.77136 1.6703

Male 0.196348 1.21695 0.161604 1.215 0.224368 0.88657 1.6704

Female -0.2354 0.790258 0.13386 -1.759 0.078658 0.60789 1.0273

Single 0.491077 1.634075 0.188406 2.606 0.009148 1.12954 2.364

Relationship -0.11488 0.891472 0.253723 -0.453 0.650704 0.54217 1.4658

Engaged 0.068316 1.070703 0.317359 0.215 0.829562 0.57482 1.9944

Married 0.658964 1.932788 0.146586 4.495 6.94E-06 1.45014 2.5761

Its Complicated -0.29936 0.741294 0.296934 -1.008 0.313377 0.41423 1.3266

Susceptibility (

Age (0-18) 0.111341 1.117776 0.099216 1.122 0.261774 0.92024 1.3577

Age (18-23) -0.16863 0.844822 0.103534 -1.629 0.10337 0.68966 1.0349

Age (23-31) -0.10223 0.902823 0.082723 -1.236 0.216537 0.76769 1.0617

Age (>31) -0.18837 0.828306 0.085913 -2.193 0.028337 0.69994 0.9802

Male -0.23542 0.790239 0.065373 -3.601 0.000317 0.69521 0.8983

Female -0.36988 0.690816 0.065898 -5.613 1.99E-08 0.60711 0.7861


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Single 0.318101 1.374516 0.103771 3.065 0.002174 1.12155 1.6845

Relationship 0.332346 1.394236 0.154361 2.153 0.031315 1.03025 1.8868

Engaged 0.738243 2.092256 0.21676 3.406 0.00066 1.36807 3.1998

Married -0.00587 0.994146 0.136731 -0.043 0.965748 0.76044 1.2997

Its Complicated 0.742831 2.101877 0.304151 2.442 0.014594 1.15801 3.8151


Hometown (same) 0.020837 1.021056 0.217414 0.096 0.923646 0.66679 1.5636




College (same) 2.155887 8.63555 0.828914 2.601 0.009299 1.70105 43.8392



Num. common pages 0.006154 1.006173 0.002161 2.847 0.004408 1.00192 1.0104




proportional hazards model with number of common friends omitted as a test of the robustness of our main findings. It estimate

the impact of a user’s tie attributes (tie strength) on his hazard to influence peers to adopt and on the hazard that his peers will

spontaneously adopt, while controlling for individual influence and susceptibility associated with the individual attributes: age,

gender or relationship status. Goodness of fit and model likelihood test statistics include: Concordance=0.837 (SE=0.009); Like-

lihood ratio test = 1708 on 65 degrees of freedom (p=0); Wald test statistic = 3324 on 65 degrees of freedom (p=0); Logrank

statistic = 20506 on 65 degrees of freedom (p=0) ; Robust Logrank statistic = 407 (p=0)

Table A6a: Estimates from the Cox Proportional Hazards Model of Influence with Control for Network De-

gree

z Pr(>|z|)

CI

Lower .95

CI

Upper .95

Added Controls

Network Degree (of i) -5.71E-04 9.99E-01 3.06E-04 -1.866 0.062032 0.99883 1

Treatment (

# Notifications 1.61E+00 4.99E+00 8.59E-02 18.713 < 2e-16 4.21427 5.9007


Age (0-18) 2.78E-01 1.32E+00 1.79E-01 1.55 0.121233 0.92912 1.8754

Age (18-23) -5.96E-01 5.51E-01 2.81E-01 -2.124 0.033644 0.31774 0.9549

Age (23-31) -1.94E-01 8.24E-01 2.68E-01 -0.725 0.468695 0.48765 1.3916

Age (>31) 8.95E-03 1.01E+00 1.91E-01 0.047 0.96257 0.69428 1.4664

Male -1.37E-02 9.86E-01 1.86E-01 -0.074 0.94125 0.68461 1.4211

Female 8.47E-02 1.09E+00 1.51E-01 0.56 0.575149 0.80947 1.4633

Single -1.57E-01 8.55E-01 1.80E-01 -0.869 0.384704 0.6004 1.2173

Relationship -1.82E-01 8.34E-01 2.60E-01 -0.697 0.485808 0.5006 1.3895

Engaged -3.22E-01 7.25E-01 4.42E-01 -0.728 0.466397 0.30445 1.7243

Married -3.42E-01 7.10E-01 1.98E-01 -1.733 0.083084 0.48209 1.0458


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Its Complicated 1.40E-01 1.15E+00 3.98E-01 0.353 0.724327 0.52783 2.5078


Age (0-18) -5.41E-02 9.47E-01 1.41E-01 -0.384 0.701209 0.71863 1.2488

Age (18-23) -1.21E-02 9.88E-01 1.51E-01 -0.08 0.936149 0.73531 1.3275

Age (23-31) -4.26E-01 6.53E-01 1.80E-01 -2.367 0.017926 0.4587 0.9293

Age (>31) 4.54E-01 1.57E+00 1.31E-01 3.464 0.000531 1.21771 2.0344

Male 2.93E-01 1.34E+00 1.31E-01 2.243 0.024898 1.0377 1.7324

Female 6.33E-01 1.88E+00 1.15E-01 5.513 3.53E-08 1.50351 2.3578

Single 1.93E-01 1.21E+00 1.41E-01 1.372 0.169989 0.92055 1.599


Engaged -3.77E-01 6.86E-01 3.67E-01 -1.026 0.304755 0.33378 1.4093

Married 3.33E-01 1.39E+00 1.67E-01 1.987 0.046945 1.0045 1.9358

Its Complicated -5.44E-01 5.81E-01 5.50E-01 -0.988 0.322914 0.19758 1.7063


Hometown (same) 3.73E-01 1.45E+00 2.60E-01 1.434 0.151476 0.87227 2.4169

Hometown (different) -2.81E-01 7.55E-01 2.41E-01 -1.163 0.244656 0.47052 1.212

Current town (same) -7.62E-01 4.67E-01 7.21E-01 -1.057 0.290535 0.11352 1.9179

Current town (different) 6.80E-01 1.97E+00 3.45E-01 1.97 0.048833 1.00349 3.8833

College (same) -9.42E-01 3.90E-01 1.12E+00 -0.838 0.401789 0.04305 3.5275

College (different) -2.60E-01 7.71E-01 3.56E-01 -0.73 0.465685 0.38382 1.5498

Num. common affiliations -1.37E-01 8.72E-01 3.28E-01 -0.416 0.677504 0.45846 1.6601

Num. common pages 6.30E-03 1.01E+00 9.97E-04 6.319 2.64E-10 1.00435 1.0083

Num. common groups 3.56E-02 1.04E+00 4.86E-03 7.314 2.60E-13 1.02638 1.0461

Num. photos together 1.41E-02 1.01E+00 1.91E-03 7.358 1.86E-13 1.01039 1.018

Num. common friends 7.68E-03 1.01E+00 9.74E-04 7.886 3.11E-15 1.00579 1.0096

Influence (

Age (0-18) -3.13E-01 7.31E-01 1.50E-01 -2.086 0.03695 0.54506 0.9812

Age (18-23) 1.80E-01 1.20E+00 1.75E-01 1.026 0.304887 0.84894 1.6881

Age (23-31) -5.13E-02 9.50E-01 2.99E-01 -0.172 0.863611 0.52894 1.7061

Age (>31) 1.28E-01 1.14E+00 2.01E-01 0.636 0.524861 0.7662 1.6855

Male 1.37E-01 1.15E+00 1.64E-01 0.833 0.405009 0.83118 1.581

Female -1.81E-01 8.34E-01 1.40E-01 -1.298 0.194117 0.63453 1.0967

Single 2.22E-01 1.25E+00 2.18E-01 1.018 0.308505 0.81469 1.9122


Engaged -4.19E-03 9.96E-01 3.13E-01 -0.013 0.989302 0.53979 1.8371

Married 6.46E-01 1.91E+00 1.56E-01 4.138 3.50E-05 1.40465 2.5892


Susceptibility (

Age (0-18) 1.09E-01 1.12E+00 9.79E-02 1.111 0.266429 0.92024 1.3509

Age (18-23) -1.92E-01 8.26E-01 1.09E-01 -1.752 0.079704 0.66646 1.0229


9

Age (23-31) -8.24E-02 9.21E-01 8.61E-02 -0.957 0.33846 0.77784 1.0902

Age (>31) -1.69E-01 8.45E-01 8.69E-02 -1.943 0.052036 0.71231 1.0015

Male -1.78E-01 8.37E-01 6.79E-02 -2.626 0.00865 0.73231 0.9558

Female -3.15E-01 7.30E-01 7.01E-02 -4.493 7.01E-06 0.63615 0.8373

Single 3.01E-01 1.35E+00 1.07E-01 2.827 0.004698 1.09679 1.6654

Relationship 2.46E-01 1.28E+00 1.71E-01 1.445 0.148584 0.91586 1.787

Engaged 7.07E-01 2.03E+00 2.23E-01 3.165 0.00155 1.30888 3.1416

Married 4.57E-03 1.01E+00 1.39E-01 0.033 0.973746 0.76509 1.319




Hometown (different) 2.95E-01 1.34E+00 1.71E-01 1.724 0.084751 0.96033 1.8802

Current town (same) 8.28E-01 2.29E+00 3.09E-01 2.679 0.007379 1.24906 4.1971

Current town (different) -1.15E+00 3.16E-01 6.77E-01 -1.701 0.088992 0.08397 1.1918

College (same) 2.12E+00 8.33E+00 8.35E-01 2.539 0.01113 1.62136 42.8262


Num. common affiliations 7.72E-01 2.16E+00 3.75E-01 2.059 0.039457 1.03796 4.5095

Num. common pages 3.14E-03 1.00E+00 2.32E-03 1.353 0.175928 0.99859 1.0077

Num. common groups 6.73E-03 1.01E+00 5.53E-03 1.217 0.2236 0.9959 1.0177

Num. photos together -2.41E-03 9.98E-01 2.97E-03 -0.812 0.41664 0.9918 1.0034

Num. common friends 6.71E-03 1.01E+00 1.70E-03 3.955 7.64E-05 1.00339 1.0101


proportional hazards model with network degree of user (i) added as an additional control as a test of the robustness of our main

findings. It estimates the impact of a user’s tie attributes (tie strength and embeddedness) on his hazard to influence peers to

adopt and on the hazard that his peers will spontaneously adopt, while controlling for individual influence and susceptibility as-

sociated with the individual attributes: age, gender or relationship status. Goodness of fit and model likelihood test statistics in-

clude: Concordance=0.838 (SE=0.009); Likelihood ratio test = 1850 on 68 degrees of freedom (p=0); Wald test statistic = 3438

on 68 degrees of freedom (p=0); Logrank statistic = 20647 on 68 degrees of freedom (p=0) ; Robust Logrank statistic = 413

(p=0)

Table A6 b: Estimates from the Cox Proportional Hazards Model of Influence with Control for Network De-

gree (Raw and Interaction)

z Pr(>|z|)

CI

Lower .95

CI

Upper .95

Added Controls

Network Degree (of i) -0.00071 0.99929 0.000359 -1.979 0.047807 0.99859 1

# Notifications X Network

Degree (of i) 0.000743 1.000744 0.000212 3.506 0.000454 1.00033 1.0012

Treatment (

# Notifications 1.55824 4.750453 0.086808 17.95 < 2e-16 4.00723 5.6315


Age (0-18) 0.279203 1.322075 0.179708 1.554 0.12027 0.92958 1.8803

Age (18-23) -0.5945 0.551838 0.282046 -2.108 0.035047 0.31749 0.9592

Age (23-31) -0.19204 0.825271 0.268202 -0.716 0.473965 0.48787 1.396


10

Age (>31) 0.00811 1.008142 0.191029 0.042 0.966139 0.6933 1.466

Male -0.02302 0.977246 0.185888 -0.124 0.901458 0.67885 1.4068

Female 0.076389 1.079382 0.150986 0.506 0.612904 0.80289 1.4511

Single -0.15732 0.854427 0.179455 -0.877 0.380661 0.60107 1.2146

Relationship -0.1699 0.843753 0.261252 -0.65 0.515491 0.50564 1.408

Engaged -0.32612 0.721721 0.443856 -0.735 0.462501 0.30238 1.7226

Married -0.343 0.709637 0.198035 -1.732 0.083268 0.48136 1.0462

Its Complicated 0.17167 1.187286 0.401556 0.428 0.669007 0.54044 2.6083


Age (0-18) -0.05672 0.944861 0.141047 -0.402 0.687598 0.71665 1.2457

Age (18-23) -0.01197 0.988102 0.150685 -0.079 0.936686 0.73543 1.3276

Age (23-31) -0.42904 0.651132 0.180341 -2.379 0.017357 0.45726 0.9272

Age (>31) 0.447508 1.564408 0.131238 3.41 0.00065 1.2096 2.0233

Male 0.275834 1.317629 0.13187 2.092 0.036464 1.01753 1.7062

Female 0.612629 1.845276 0.116322 5.267 1.39E-07 1.46909 2.3178

Single 0.203489 1.225671 0.141224 1.441 0.149615 0.92932 1.6165

Relationship -0.05968 0.94207 0.188253 -0.317 0.751246 0.65139 1.3625

Engaged -0.37333 0.688441 0.36815 -1.014 0.310554 0.33458 1.4166

Married 0.337083 1.400856 0.167649 2.011 0.044363 1.00853 1.9458

Its Complicated -0.45686 0.63327 0.53192 -0.859 0.390403 0.22326 1.7962


Hometown (same) 0.376228 1.456779 0.260808 1.443 0.149147 0.87376 2.4288




College (same) -0.94643 0.388126 1.135289 -0.834 0.404482 0.04194 3.592






Num. common friends 0.007743 1.007773 0.001012 7.655 1.92E-14 1.00578 1.0098

Influence (

Age (0-18) -0.31772 0.727807 0.147367 -2.156 0.031085 0.54523 0.9715

Age (18-23) 0.169514 1.184728 0.170951 0.992 0.321396 0.84743 1.6563

Age (23-31) -0.06796 0.934298 0.289479 -0.235 0.814392 0.52976 1.6477

Age (>31) 0.109738 1.115985 0.202358 0.542 0.587615 0.75061 1.6592

Male 0.193617 1.213631 0.16135 1.2 0.230148 0.8846 1.6651

Female -0.14269 0.867021 0.133261 -1.071 0.284273 0.66772 1.1258

Single 0.194747 1.215004 0.207633 0.938 0.348275 0.8088 1.8252


11

Relationship -0.16667 0.846479 0.267441 -0.623 0.533152 0.50115 1.4298

Engaged -0.01465 0.985457 0.315843 -0.046 0.963005 0.53063 1.8301

Married 0.574132 1.775588 0.154453 3.717 0.000201 1.31181 2.4033

Its Complicated -0.37172 0.689545 0.290758 -1.278 0.201085 0.39 1.2191

Susceptibility (

Age (0-18) 0.12619 1.134497 0.096543 1.307 0.191186 0.93891 1.3708

Age (18-23) -0.22318 0.799971 0.111898 -1.995 0.046097 0.64243 0.9961

Age (23-31) -0.08167 0.921576 0.08891 -0.919 0.35832 0.77419 1.097

Age (>31) -0.16142 0.850936 0.089285 -1.808 0.070622 0.71433 1.0137

Male -0.16356 0.849112 0.071638 -2.283 0.022418 0.73788 0.9771

Female -0.31168 0.732218 0.072713 -4.286 1.82E-05 0.63496 0.8444

Single 0.295048 1.34319 0.106796 2.763 0.005732 1.08951 1.6559

Relationship 0.216238 1.241398 0.17696 1.222 0.221721 0.87757 1.7561

Engaged 0.721889 2.058319 0.223756 3.226 0.001254 1.32755 3.1913

Married 0.022139 1.022386 0.139041 0.159 0.873492 0.77851 1.3427

Its Complicated 0.181621 1.199159 0.513773 0.354 0.723711 0.43808 3.2825


Hometown (same) 0.017568 1.017723 0.226881 0.077 0.938279 0.65239 1.5876




College (same) 2.064974 7.885092 0.84599 2.441 0.014651 1.5021 41.3918



Num. common pages 0.003192 1.003197 0.002305 1.385 0.166127 0.99868 1.0077





proportional hazards model with network degree of user (i) and its interaction with number of notifications received added as an

additional control as a test of the robustness of our main findings. It estimates the impact of a user’s tie attributes (tie strength and

embeddedness) on his hazard to influence peers to adopt and on the hazard that his peers will spontaneously adopt, while control-

ling for individual influence and susceptibility associated with the individual attributes: age, gender or relationship status. Good-

ness of fit and model likelihood test statistics include: Concordance=0.839 (SE=0.009); Likelihood ratio test = 1882 on 69 de-

grees of freedom (p=0); Wald test statistic = 3672 on 69 degrees of freedom (p=0); Logrank statistic = 20700 on 69 degrees of

freedom (p=0) ; Robust Logrank statistic = 413.2 (p=0)

Table A7a: Estimates from the Cox Proportional Hazards Model of Influence with Profile Completeness Con-

trols

z Pr(>|z|)

CI

Lower .95

CI

Upper .95

Profile Controls (user i)

Number of Pages -0.00072 0.999283 0.000656 -1.093 0.274179 0.998 1.0006

Number of Groups 0.00198 1.001981 0.00112 1.767 0.07728 0.99978 1.0042


12

Number of Affiliations -0.269 0.764141 0.172157 -1.563 0.118158 0.5453 1.0708

Number of Photos -0.00041 0.999591 0.00019 -2.153 0.03132 0.99922 1

Profile Controls (peer j)

Number of Pages -0.00018 0.999819 0.000819 -0.221 0.824744 0.99822 1.0014

Number of Groups -0.00311 0.996896 0.00164 -1.896 0.057997 0.9937 1.0001

Number of Affiliations -0.6412 0.526658 0.118998 -5.388 7.11E-08 0.4171 0.665

Number of Photos 1.73E-05 1.000017 0.000171 0.101 0.919604 0.99968 1.0004

Treatment (

# Notifications 1.692051 5.430607 0.074733 22.641 < 2e-16 4.69068 6.2873


Age (0-18) 0.289388 1.33561 0.186627 1.551 0.120992 0.92645 1.9255

Age (18-23) -0.58752 0.555703 0.284544 -2.065 0.038944 0.31815 0.9706

Age (23-31) -0.22126 0.801507 0.243178 -0.91 0.362889 0.49764 1.2909

Age (>31) -0.08403 0.919401 0.176935 -0.475 0.634832 0.64998 1.3005

Male 0.039846 1.04065 0.189759 0.21 0.833683 0.71743 1.5095

Female 0.183395 1.201289 0.151699 1.209 0.226684 0.89232 1.6172

Single -0.12154 0.885555 0.175278 -0.693 0.488045 0.62809 1.2486

Relationship -0.06842 0.933867 0.249349 -0.274 0.783779 0.57285 1.5224

Engaged -0.22552 0.798102 0.454871 -0.496 0.620046 0.32724 1.9465

Married -0.23485 0.790686 0.1935 -1.214 0.224856 0.54112 1.1553

Its Complicated 0.066976 1.06927 0.451894 0.148 0.882176 0.441 2.5926


Age (0-18) -0.01851 0.981656 0.146374 -0.126 0.899348 0.73683 1.3078

Age (18-23) 0.009747 1.009795 0.155168 0.063 0.949911 0.745 1.3687

Age (23-31) -0.37716 0.685807 0.182537 -2.066 0.038809 0.47954 0.9808

Age (>31) 0.503104 1.653847 0.135722 3.707 0.00021 1.26756 2.1579

Male 0.468203 1.597122 0.132779 3.526 0.000422 1.23116 2.0719

Female 0.821661 2.274275 0.117041 7.02 2.21E-12 1.80808 2.8607

Single 0.425406 1.530211 0.144979 2.934 0.003343 1.15172 2.0331

Relationship 0.162355 1.176278 0.190556 0.852 0.394209 0.80967 1.7089

Engaged -0.12751 0.880281 0.373196 -0.342 0.732591 0.4236 1.8293

Married 0.576733 1.780213 0.172281 3.348 0.000815 1.27007 2.4953

Its Complicated -0.41846 0.658057 0.557426 -0.751 0.452828 0.22069 1.9622


Hometown (same) 0.360101 1.433474 0.257497 1.398 0.161972 0.86538 2.3745




College (same) -1.08115 0.339205 1.153665 -0.937 0.348684 0.03536 3.2543



13






Influence (

Age (0-18) -0.33167 0.717725 0.150319 -2.206 0.027354 0.53457 0.9636

Age (18-23) 0.200594 1.222129 0.180247 1.113 0.265757 0.8584 1.74

Age (23-31) -0.02416 0.976134 0.299419 -0.081 0.935702 0.5428 1.7554

Age (>31) 0.168744 1.183817 0.203419 0.83 0.406801 0.79457 1.7637

Male 0.146132 1.157349 0.16447 0.889 0.374271 0.83843 1.5976

Female -0.20511 0.814558 0.139725 -1.468 0.142117 0.61942 1.0712

Single 0.225345 1.252755 0.215854 1.044 0.2965 0.8206 1.9125

Relationship -0.15326 0.857909 0.265435 -0.577 0.563682 0.50992 1.4434

Engaged -0.03165 0.968847 0.314919 -0.1 0.91995 0.52263 1.796

Married 0.642045 1.900363 0.15706 4.088 4.35E-05 1.39684 2.5854

Its Complicated -0.30301 0.738589 0.322424 -0.94 0.347321 0.3926 1.3895

Susceptibility (

Age (0-18) 0.096512 1.101323 0.100044 0.965 0.334697 0.90523 1.3399

Age (18-23) -0.19252 0.824879 0.111073 -1.733 0.083047 0.66351 1.0255

Age (23-31) -0.08639 0.917238 0.085657 -1.009 0.313196 0.77548 1.0849

Age (>31) -0.18159 0.833943 0.087178 -2.083 0.037252 0.70296 0.9893

Male -0.22381 0.799464 0.067621 -3.31 0.000934 0.70023 0.9128

Female -0.36892 0.691482 0.070738 -5.215 1.84E-07 0.60196 0.7943

Single 0.333509 1.395858 0.109333 3.05 0.002285 1.12662 1.7294

Relationship 0.228135 1.256255 0.18112 1.26 0.207822 0.88086 1.7916

Engaged 0.729884 2.074841 0.243697 2.995 0.002744 1.28691 3.3452

Married -0.03235 0.968165 0.143522 -0.225 0.821653 0.73077 1.2827

Its Complicated 0.924919 2.521665 0.304237 3.04 0.002365 1.38906 4.5778


Hometown (same) 0.019518 1.019709 0.23593 0.083 0.934069 0.64217 1.6192




College (same) 2.47679 11.903 0.831548 2.979 0.002896 2.33261 60.7395



Num. common pages 0.00564 1.005656 0.002505 2.251 0.024366 1.00073 1.0106





14


proportional hazards model with profile completeness controls added for the number of photos, groups, pages, and affiliations as

a test of the robustness of our main findings. It estimates the impact of a user’s tie attributes (tie strength and embeddedness) on

his hazard to influence peers to adopt and on the hazard that his peers will spontaneously adopt, while controlling for individual

influence and susceptibility associated with the individual attributes: age, gender or relationship status. Goodness of fit and model

likelihood test statistics include: Concordance=0.833 (SE=0.009); Likelihood ratio test = 1864 on 75 degrees of freedom (p=0);

Wald test statistic = 3819 on 75 degrees of freedom (p=0); Logrank statistic = 20890 on 75 degrees of freedom (p=0) ; Robust

Logrank statistic = 425 (p=0)

Table A7b: Estimates from the Cox Proportional Hazards Model of Influence with Profile Completeness

Controls (Raw and Interacted)

z Pr(>|z|)

CI

Lower .95

CI

Upper .95

Raw Profile Controls (user i)

Number of Pages -2.86E-04 1.00E+00 7.34E-04 -0.389 0.697253 0.99828 1.0012

Number of Groups 1.32E-03 1.00E+00 1.42E-03 0.928 0.353573 0.99854 1.0041

Number of Affiliations -4.16E-01 6.59E-01 1.69E-01 -2.464 0.013731 0.47352 0.9183

Number of Photos -3.34E-04 1.00E+00 1.91E-04 -1.752 0.079828 0.99929 1

Interacted Profile Controls (user i)

Number of Pages -1.31E-03 9.99E-01 1.08E-03 -1.217 0.223643 0.99659 1.0008

Number of Groups 2.55E-03 1.00E+00 1.70E-03 1.495 0.134979 0.99921 1.0059

Number of Affiliations 5.37E-01 1.71E+00 2.06E-01 2.602 0.009273 1.14166 2.5642

Number of Photos -5.43E-04 1.00E+00 5.87E-04 -0.926 0.354382 0.99831 1.0006

Raw Profile Controls (peer j)

Number of Pages -3.17E-04 1.00E+00 7.66E-04 -0.414 0.6791 0.99818 1.0012

Number of Groups -2.00E-03 9.98E-01 1.42E-03 -1.407 0.159562 0.99523 1.0008

Number of Affiliations -6.41E-01 5.27E-01 1.18E-01 -5.422 5.89E-08 0.4177 0.664

Number of Photos 6.18E-05 1.00E+00 4.67E-05 1.321 0.186432 0.99997 1.0002

Interacted Profile Controls (peer j)

Number of Pages 3.71E-04 1.00E+00 7.31E-04 0.508 0.611648 0.99894 1.0018

Number of Groups -2.93E-03 9.97E-01 2.39E-03 -1.227 0.219669 0.99243 1.0017

Number of Affiliations -1.57E-02 9.84E-01 1.03E-01 -0.153 0.878463 0.8047 1.2042

Number of Photos 6.18E-05 1.00E+00 4.67E-05 1.321 0.186432 0.99997 1.0002

Treatment (



Age (0-18) 3.07E-01 1.36E+00 1.86E-01 1.649 0.099145 0.9437 1.9592

Age (18-23) -5.46E-01 5.80E-01 2.85E-01 -1.918 0.055141 0.33176 1.0121

Age (23-31) -1.85E-01 8.31E-01 2.47E-01 -0.749 0.453753 0.51235 1.3483

Age (>31) -4.68E-02 9.54E-01 1.80E-01 -0.261 0.79434 0.67113 1.3568

Male 2.65E-02 1.03E+00 1.90E-01 0.14 0.88886 0.70794 1.4895

Female 1.68E-01 1.18E+00 1.53E-01 1.096 0.273287 0.87622 1.5953

Single -1.01E-01 9.04E-01 1.75E-01 -0.575 0.565176 0.64151 1.2744



15

Engaged -2.14E-01 8.07E-01 4.60E-01 -0.465 0.642001 0.32757 1.9899

Married -2.20E-01 8.03E-01 1.93E-01 -1.14 0.254462 0.54991 1.1715



Age (0-18) -4.19E-02 9.59E-01 1.48E-01 -0.283 0.776863 0.71749 1.2816

Age (18-23) 9.02E-03 1.01E+00 1.55E-01 0.058 0.953489 0.74514 1.3665

Age (23-31) -3.86E-01 6.80E-01 1.83E-01 -2.107 0.03509 0.47478 0.9734

Age (>31) 5.01E-01 1.65E+00 1.36E-01 3.684 0.00023 1.26408 2.1537

Male 4.63E-01 1.59E+00 1.32E-01 3.508 0.000451 1.22671 2.0578

Female 7.96E-01 2.22E+00 1.16E-01 6.859 6.92E-12 1.76535 2.7817

Single 4.37E-01 1.55E+00 1.45E-01 3.005 0.002657 1.16402 2.0579


Engaged -1.25E-01 8.83E-01 3.76E-01 -0.332 0.739802 0.42265 1.8435

Married 5.81E-01 1.79E+00 1.73E-01 3.364 0.00077 1.27419 2.5069







College (same) -1.19E+00 3.04E-01 1.19E+00 -0.997 0.318629 0.02933 3.1547






Num. common friends 7.88E-03 1.01E+00 7.32E-04 10.763 < 2e-16 1.00647 1.0094

Influence (

Age (0-18) -3.34E-01 7.16E-01 1.54E-01 -2.173 0.029798 0.53015 0.9679

Age (18-23) 1.60E-01 1.17E+00 1.74E-01 0.92 0.357437 0.83471 1.6495

Age (23-31) -4.24E-02 9.59E-01 3.00E-01 -0.141 0.887683 0.53227 1.726

Age (>31) 1.21E-01 1.13E+00 2.01E-01 0.601 0.54779 0.76077 1.6742

Male 1.43E-01 1.15E+00 1.63E-01 0.875 0.381482 0.83756 1.5893

Female -1.89E-01 8.28E-01 1.31E-01 -1.443 0.14907 0.64001 1.0702

Single 2.02E-01 1.22E+00 2.13E-01 0.947 0.343737 0.8059 1.8573


Engaged -5.23E-02 9.49E-01 3.25E-01 -0.161 0.872273 0.50192 1.7946

Married 6.18E-01 1.86E+00 1.63E-01 3.784 0.000154 1.34678 2.5536


Susceptibility (


16

Age (0-18) 7.41E-02 1.08E+00 1.03E-01 0.72 0.471817 0.88009 1.3177

Age (18-23) -1.86E-01 8.30E-01 1.16E-01 -1.61 0.107506 0.6619 1.0413

Age (23-31) -3.86E-02 9.62E-01 9.74E-02 -0.396 0.692208 0.79491 1.1646

Age (>31) -1.64E-01 8.49E-01 9.17E-02 -1.788 0.073832 0.7091 1.0159

Male -2.20E-01 8.02E-01 6.97E-02 -3.162 0.001569 0.69986 0.9197

Female -3.44E-01 7.09E-01 7.15E-02 -4.821 1.43E-06 0.61602 0.8151

Single 3.96E-01 1.49E+00 1.22E-01 3.247 0.001164 1.16974 1.8854


Engaged 7.27E-01 2.07E+00 2.58E-01 2.814 0.004894 1.24684 3.4326

Married -1.66E-02 9.84E-01 1.45E-01 -0.114 0.909159 0.74005 1.3072

Its Complicated 1.05E+00 2.87E+00 3.52E-01 2.998 0.002716 1.44062 5.7173






College (same) 2.74E+00 1.55E+01 8.06E-01 3.402 0.000668 3.1984 75.3783






Num. common friends 5.78E-03 1.01E+00 1.60E-03 3.607 0.000309 1.00264 1.009


proportional hazards model with (raw and interacted) profile completeness controls added for the number of photos, groups, pag-

es, and affiliations as a test of the robustness of our main findings. It estimates the impact of a user’s tie attributes (tie strength

and embeddedness) on his hazard to influence peers to adopt and on the hazard that his peers will spontaneously adopt, while

controlling for individual influence and susceptibility associated with the individual attributes: age, gender or relationship status.

Goodness of fit and model likelihood test statistics include: Concordance=0.833 (SE=0.009); Likelihood ratio test = 1885 on 83

degrees of freedom (p=0); Wald test statistic = 4007 on 83 degrees of freedom (p=0); Logrank statistic = 22193 on 83 degrees of

freedom (p=0) ; Robust Logrank statistic = 432.1 (p=0)

Table A8: Estimates from the Cox Proportional Hazards Model of Influence with Control for # Notifications

Sent

z Pr(>|z|)

CI

Lower .95

CI

Upper .95

Added Controls

# Notifications Sent 0.014225 1.014327 0.002575 5.524 3.32E-08 1.00922 1.0195

Treatment (

# Notifications 1.464924 4.327216 0.08536 17.162 < 2e-16 3.66058 5.1153


Age (0-18) 0.25013 1.284193 0.18403 1.359 0.174089 0.89533 1.8419

Age (18-23) -0.56626 0.567645 0.282914 -2.002 0.045336 0.32603 0.9883

Age (23-31) -0.16296 0.849622 0.260839 -0.625 0.532124 0.50956 1.4166


17

Age (>31) -0.03422 0.966359 0.164866 -0.208 0.835573 0.69953 1.335

Male 0.105067 1.110785 0.19283 0.545 0.585843 0.76119 1.6209

Female 0.220813 1.24709 0.14962 1.476 0.139991 0.93012 1.6721

Single -0.29237 0.746493 0.167433 -1.746 0.080779 0.53766 1.0364

Relationship -0.21704 0.804901 0.257668 -0.842 0.399615 0.48575 1.3337

Engaged -0.38872 0.677927 0.446989 -0.87 0.384501 0.2823 1.628

Married -0.37914 0.684447 0.185708 -2.042 0.04119 0.47563 0.985

Its Complicated -0.4553 0.634256 0.599669 -0.759 0.4477 0.19581 2.0545


Age (0-18) -0.02845 0.971951 0.143796 -0.198 0.843161 0.73324 1.2884

Age (18-23) 0.029066 1.029493 0.15337 0.19 0.849687 0.76221 1.3905

Age (23-31) -0.37312 0.688585 0.181459 -2.056 0.039763 0.4825 0.9827

Age (>31) 0.498642 1.646484 0.133423 3.737 0.000186 1.26762 2.1386

Male 0.380701 1.46331 0.125275 3.039 0.002374 1.14473 1.8706

Female 0.745689 2.107892 0.110121 6.772 1.27E-11 1.69869 2.6157

Single 0.219145 1.245012 0.140678 1.558 0.119287 0.94499 1.6403

Relationship -0.07616 0.926671 0.189891 -0.401 0.688379 0.63869 1.3445

Engaged -0.34296 0.709666 0.365057 -0.939 0.347487 0.34699 1.4514

Married 0.343022 1.4092 0.169084 2.029 0.042488 1.01169 1.9629

Its Complicated -0.5652 0.568245 0.554911 -1.019 0.308418 0.19151 1.6861


Hometown (same) 0.452303 1.571928 0.251585 1.798 0.072206 0.96003 2.5738




College (same) -0.99948 0.36807 1.1478 -0.871 0.383873 0.03881 3.4909







Influence (

Age (0-18) -0.2913 0.74729 0.147188 -1.979 0.047802 0.56002 0.9972

Age (18-23) 0.224406 1.251579 0.172874 1.298 0.194257 0.89188 1.7563

Age (23-31) -0.15299 0.858135 0.307504 -0.498 0.618812 0.46969 1.5678

Age (>31) 0.163793 1.17797 0.197333 0.83 0.40652 0.80014 1.7342

Male 0.205508 1.228149 0.162625 1.264 0.20634 0.89294 1.6892

Female -0.17836 0.836643 0.131916 -1.352 0.176358 0.64603 1.0835

Single 0.307474 1.359985 0.213123 1.443 0.149103 0.89562 2.0651


18

Relationship -0.26835 0.764638 0.307221 -0.873 0.3824 0.41874 1.3962

Engaged -0.0647 0.937348 0.334543 -0.193 0.846646 0.48656 1.8058

Married 0.529111 1.697423 0.155509 3.402 0.000668 1.25147 2.3023

Its Complicated -0.22013 0.802416 0.326045 -0.675 0.499584 0.42352 1.5203

Susceptibility (

Age (0-18) 0.115897 1.12288 0.094643 1.225 0.220738 0.93277 1.3517

Age (18-23) -0.18928 0.827559 0.103982 -1.82 0.068719 0.67498 1.0146

Age (23-31) -0.08478 0.918718 0.093488 -0.907 0.364505 0.7649 1.1035

Age (>31) -0.17606 0.838564 0.088312 -1.994 0.046188 0.70529 0.997

Male -0.21592 0.8058 0.074436 -2.901 0.003723 0.69641 0.9324

Female -0.33029 0.718715 0.074355 -4.442 8.91E-06 0.62125 0.8315

Single 0.271787 1.312308 0.107161 2.536 0.011204 1.0637 1.619

Relationship 0.248355 1.281915 0.159944 1.553 0.12048 0.93695 1.7539

Engaged 0.676197 1.966386 0.218658 3.092 0.001985 1.28099 3.0185

Married 0.042997 1.043935 0.136339 0.315 0.752479 0.79914 1.3637

Its Complicated 0.731664 2.078537 0.299525 2.443 0.014576 1.15558 3.7386


Hometown (same) 0.002236 1.002238 0.21644 0.01 0.991758 0.65575 1.5318




College (same) 2.018962 7.5305 0.853658 2.365 0.018027 1.41315 40.1291



Num. common pages 0.003698 1.003705 0.002204 1.678 0.093376 0.99938 1.0081





proportional hazards model with the number of notifications sent by user (i) added as an additional control as a test of the robust-

ness of our main findings. It estimates the impact of a user’s tie attributes (tie strength and embeddedness) on his hazard to influ-

ence peers to adopt and on the hazard that his peers will spontaneously adopt, while controlling for individual influence and sus-

ceptibility associated with the individual attributes: age, gender or relationship status. Goodness of fit and model likelihood test

statistics include: Concordance=0.855 (SE=0.009); Likelihood ratio test = 1949 on 68 degrees of freedom (p=0); Wald test statis-

tic = 3444 on 68 degrees of freedom (p=0); Logrank statistic = 20755 on 68 degrees of freedom (p=0) ; Robust Logrank statistic

= 421 (p=0)

Table A9a: Estimates from the Cox Proportional Hazards Model of Influence with Controls for #Notifica-

tions Sent, Stratified by nns_greater_than_average

z Pr(>|z|)

CI

Lower .95

CI

Upper .95

Added Controls

# Notifications Sent 1.18E-03 1.00E+00 1.87E-03 0.632 0.527428 0.99752 1.0049

Treatment (


19



Age (0-18) 1.86E-01 1.20E+00 1.95E-01 0.957 0.338424 0.82258 1.7651

Age (18-23) -4.74E-01 6.22E-01 2.96E-01 -1.604 0.108794 0.3486 1.1111

Age (23-31) -2.03E-01 8.17E-01 2.51E-01 -0.806 0.420482 0.49888 1.3368

Age (>31) -7.46E-02 9.28E-01 1.76E-01 -0.425 0.67107 0.65786 1.3095

Male 2.04E-01 1.23E+00 2.04E-01 0.998 0.318499 0.82151 1.8298

Female 2.94E-01 1.34E+00 1.48E-01 1.983 0.047375 1.00342 1.7958

Single -3.81E-01 6.83E-01 1.73E-01 -2.2 0.027822 0.48668 0.9593


Engaged -4.82E-01 6.18E-01 4.79E-01 -1.005 0.315035 0.24152 1.5806

Married -4.34E-01 6.48E-01 1.95E-01 -2.225 0.026073 0.44194 0.9496



Age (0-18) -9.41E-02 9.10E-01 1.47E-01 -0.64 0.522292 0.68228 1.2143

Age (18-23) 3.36E-02 1.03E+00 1.55E-01 0.217 0.82809 0.76361 1.4006

Age (23-31) -3.54E-01 7.02E-01 1.84E-01 -1.919 0.054929 0.48913 1.0075

Age (>31) 4.95E-01 1.64E+00 1.36E-01 3.646 0.000266 1.25734 2.1413

Male 3.68E-01 1.44E+00 1.27E-01 2.897 0.003766 1.12629 1.8522

Female 7.46E-01 2.11E+00 1.11E-01 6.72 1.82E-11 1.69657 2.6221

Single 2.94E-01 1.34E+00 1.45E-01 2.023 0.043056 1.00924 1.7849


Engaged -3.59E-01 6.98E-01 3.75E-01 -0.956 0.338983 0.33471 1.4575

Married 4.52E-01 1.57E+00 1.73E-01 2.618 0.008846 1.12032 2.2044







College (same) -9.75E-01 3.77E-01 1.23E+00 -0.795 0.426806 0.03407 4.1768


Num. common affiliations -1.66E-01 8.47E-01 3.42E-01 -0.485 0.627334 0.43292 1.6566




Num. common friends 7.87E-03 1.01E+00 7.56E-04 10.409 < 2e-16 1.00641 1.0094

Influence (

Age (0-18) -2.21E-01 8.02E-01 1.53E-01 -1.441 0.149624 0.59352 1.0829

Age (18-23) 1.62E-01 1.18E+00 1.78E-01 0.908 0.364034 0.82922 1.6659


20

Age (23-31) -1.76E-01 8.39E-01 2.99E-01 -0.588 0.55681 0.46663 1.5077

Age (>31) 7.07E-02 1.07E+00 1.95E-01 0.362 0.717003 0.73224 1.5731

Male 1.53E-01 1.17E+00 1.65E-01 0.929 0.352971 0.84334 1.6118

Female -2.09E-01 8.11E-01 1.34E-01 -1.553 0.120364 0.62343 1.0562

Single 2.78E-01 1.32E+00 2.00E-01 1.387 0.165433 0.89149 1.9562


Engaged 4.77E-03 1.00E+00 3.50E-01 0.014 0.989117 0.50626 1.9942

Married 5.30E-01 1.70E+00 1.72E-01 3.087 0.002022 1.21344 2.3781


Susceptibility (

Age (0-18) 1.09E-01 1.12E+00 1.04E-01 1.048 0.294489 0.90929 1.3686

Age (18-23) -1.66E-01 8.47E-01 1.13E-01 -1.47 0.141555 0.67956 1.0567

Age (23-31) -9.76E-02 9.07E-01 1.05E-01 -0.934 0.350436 0.73892 1.1133

Age (>31) -2.19E-01 8.03E-01 9.67E-02 -2.266 0.023442 0.66453 0.9708

Male -2.14E-01 8.07E-01 7.71E-02 -2.779 0.005453 0.694 0.9388

Female -3.27E-01 7.21E-01 7.41E-02 -4.414 1.01E-05 0.62341 0.8336

Single 2.41E-01 1.27E+00 1.15E-01 2.093 0.036379 1.01539 1.5941


Engaged 6.89E-01 1.99E+00 2.36E-01 2.918 0.003522 1.25403 3.166

Married 3.52E-02 1.04E+00 1.43E-01 0.246 0.80558 0.78275 1.3707



Hometown (same) -3.70E-02 9.64E-01 2.48E-01 -0.149 0.881353 0.59282 1.5665




College (same) 1.94E+00 6.97E+00 8.87E-01 2.189 0.028612 1.22509 39.6747






Num. common friends 3.86E-03 1.00E+00 1.60E-03 2.406 0.016148 1.00072 1.007


proportional hazards model with controls for number of notifications sent and stratified over nns_greater_than_average. It esti-

mates the impact of a user’s tie attributes (tie strength and embeddedness) on his hazard to influence peers to adopt and on the

hazard that his peers will spontaneously adopt, while controlling for individual influence and susceptibility associated with the

individual attributes: age, gender or relationship status. Goodness of fit and model likelihood test statistics include: Concord-

ance=0.772 (SE=0.015); Likelihood ratio test = 1310 on 68 degrees of freedom (p=0); Wald test statistic = 1984 on 68 degrees of

freedom (p=0); Logrank statistic = 6644 on 68 degrees of freedom (p=0) ; Robust Logrank statistic = 388.3 (p=0)

Table A9b: Estimates from the Cox Proportional Hazards Model of Influence Stratified by #Notifications

Sent


21

z Pr(>|z|)

CI

Lower .95

CI

Upper .95

Treatment (

# Notifications 1.424819 4.157104 0.110755 12.865 < 2e-16 3.34592 5.1649


Age (0-18) 0.173673 1.189666 0.205157 0.847 0.397254 0.79578 1.7785

Age (18-23) -0.24188 0.785147 0.259985 -0.93 0.352175 0.47168 1.3069

Age (23-31) -0.24608 0.781859 0.238555 -1.032 0.302284 0.48986 1.2479

Age (>31) -0.10081 0.904105 0.194162 -0.519 0.603618 0.61794 1.3228

Male 0.179032 1.196059 0.21283 0.841 0.400236 0.78812 1.8152

Female 0.259843 1.296726 0.144898 1.793 0.072927 0.97614 1.7226

Single -0.3944 0.674087 0.188145 -2.096 0.036062 0.46619 0.9747

Relationship -0.3364 0.714336 0.237894 -1.414 0.157337 0.44813 1.1387

Engaged -0.5486 0.577756 0.564333 -0.972 0.330987 0.19115 1.7462

Married -0.40187 0.66907 0.199429 -2.015 0.043895 0.4526 0.9891

Its Complicated -0.30187 0.739433 0.380628 -0.793 0.427725 0.35068 1.5592


Age (0-18) -0.07947 0.923608 0.15038 -0.528 0.597188 0.68783 1.2402

Age (18-23) 0.036373 1.037043 0.160949 0.226 0.821208 0.75648 1.4217

Age (23-31) -0.35518 0.701046 0.18751 -1.894 0.058198 0.48544 1.0124

Age (>31) 0.467114 1.595383 0.139408 3.351 0.000806 1.21395 2.0967

Male 0.364286 1.439486 0.130098 2.8 0.005109 1.1155 1.8576

Female 0.748858 2.114583 0.113326 6.608 3.90E-11 1.69341 2.6405

Single 0.265419 1.303977 0.147853 1.795 0.072629 0.97593 1.7423

Relationship -0.06455 0.937492 0.20077 -0.321 0.747834 0.63252 1.3895

Engaged -0.48628 0.614907 0.386483 -1.258 0.208309 0.28829 1.3115

Married 0.406377 1.501368 0.175845 2.311 0.020833 1.06367 2.1192

Its Complicated -0.58726 0.555849 0.579123 -1.014 0.31056 0.17865 1.7294


Hometown (same) 0.502592 1.653 0.256785 1.957 0.050318 0.9993 2.7343




College (same) -0.94015 0.39057 1.277937 -0.736 0.461927 0.03191 4.7806







Influence (


22

Age (0-18) -0.6331 0.530942 0.206391 -3.067 0.002159 0.3543 0.7957

Age (18-23) -0.09671 0.907816 0.245433 -0.394 0.693541 0.56116 1.4686

Age (23-31) -0.07893 0.924106 0.348486 -0.226 0.82082 0.46676 1.8296

Age (>31) 0.021281 1.021509 0.236417 0.09 0.928275 0.64269 1.6236

Male 0.317019 1.373029 0.213507 1.485 0.137592 0.90353 2.0865

Female -0.12015 0.886791 0.192091 -0.625 0.531668 0.60857 1.2922

Single 0.36136 1.43528 0.222302 1.626 0.104049 0.92835 2.219

Relationship -0.42512 0.653689 0.338001 -1.258 0.208478 0.33703 1.2679

Engaged -0.09755 0.907059 0.410011 -0.238 0.811948 0.4061 2.026

Married 0.468724 1.597953 0.209936 2.233 0.025569 1.05893 2.4114

Its Complicated 0.057211 1.05888 0.430793 0.133 0.894348 0.45515 2.4634

Susceptibility (

Age (0-18) 0.135851 1.145511 0.114341 1.188 0.234786 0.91553 1.4333

Age (18-23) -0.13985 0.869486 0.137164 -1.02 0.307916 0.66452 1.1377

Age (23-31) -0.085 0.918514 0.126557 -0.672 0.501825 0.71674 1.1771

Age (>31) -0.22436 0.799025 0.119054 -1.885 0.05949 0.63274 1.009

Male -0.19417 0.823518 0.093215 -2.083 0.037247 0.68601 0.9886

Female -0.31408 0.730459 0.088448 -3.551 0.000384 0.6142 0.8687

Single 0.20194 1.223775 0.129473 1.56 0.11883 0.9495 1.5773

Relationship 0.14631 1.157555 0.199364 0.734 0.46302 0.78315 1.711

Engaged 0.7091 2.032161 0.29731 2.385 0.017077 1.13472 3.6394

Married 0.046915 1.048032 0.159703 0.294 0.768941 0.76636 1.4332

Its Complicated 0.847257 2.333237 0.354146 2.392 0.016739 1.16549 4.671


Hometown (same) 0.169906 1.185193 0.293983 0.578 0.563301 0.66612 2.1088




College (same) 1.769994 5.870818 0.921268 1.921 0.054699 0.96497 35.7177



Num. common pages 0.002424 1.002427 0.002562 0.946 0.344145 0.99741 1.0075





proportional hazards model stratified over number of notifications sent. It estimates the impact of a user’s tie attributes (tie

strength and embeddedness) on his hazard to influence peers to adopt and on the hazard that his peers will spontaneously adopt,

while controlling for individual influence and susceptibility associated with the individual attributes: age, gender or relationship

status. Goodness of fit and model likelihood test statistics include: Concordance=0.715 (SE=0.022); Likelihood ratio test = 1175

on 67 degrees of freedom (p=0); Wald test statistic = 1429 on 67 degrees of freedom (p=0); Logrank statistic = 3897 on 67 de-

grees of freedom (p=0) ; Robust Logrank statistic = 375.3 (p=0)


23

Figure A3: Martingale Residuals to Assess Nonlinearity of Number of Notifications Received

Plot of the martingale residuals versus the number of notifications received (nnr). Black circles signify the martingale residuals.

Solid blue triangles signify the mean of martingale residuals for the specified number of notifications received. A slight nonline-

arity is present for nnr ≥ 4. These events are relatively infrequent in the data (less than 300 peers out of 1.3M received 4 or more

notifications).

Table A10: Estimates from the Cox Proportional Hazards Model of Influence – Assessment of nonlinearity in

# notifications received

z Pr(>|z|)

CI

Lower .95

CI

Upper .95

Treatment (

# Notifications 4.422243 83.28285 0.213289 20.734 < 2e-16 54.82812 126.505

(# Notifications)^2 -1.05348 0.348722 0.120201 -8.764 < 2e-16 0.27553 0.4414


Age (0-18) 0.290913 1.337649 0.204535 1.422 0.154935 0.89586 1.9973

Age (18-23) -0.67785 0.507706 0.328586 -2.063 0.039118 0.26664 0.9667

Age (23-31) 0.033284 1.033844 0.288496 0.115 0.908151 0.58734 1.8198

Age (>31) 0.197772 1.218685 0.194136 1.019 0.308331 0.833 1.783

Male -0.19418 0.823512 0.214323 -0.906 0.364935 0.54105 1.2534

Female 0.005604 1.00562 0.167177 0.034 0.973257 0.72466 1.3955

Single -0.0251 0.975213 0.190537 -0.132 0.8952 0.6713 0.190537

Relationship 0.029041 1.029467 0.277843 0.105 0.916753 0.59719 0.277843

Engaged -0.29963 0.741092 0.546899 -0.548 0.58378 0.25372 0.546899

Married -0.26398 0.76799 0.22107 -1.194 0.23244 0.49794 0.22107

Its Complicated 0.037573 1.038288 0.454824 0.083 0.934161 0.42577 0.454824


Age (0-18) -0.08661 0.917036 0.174806 -0.495 0.620279 0.65102 1.2918

Age (18-23) 0.045933 1.047004 0.178889 0.257 0.797358 0.73736 1.4867


24

Age (23-31) -0.38283 0.681928 0.222986 -1.717 0.086008 0.44049 1.0557

Age (>31) 0.565725 1.760724 0.158469 3.57 0.000357 1.29063 2.402

Male 0.285853 1.330896 0.151374 1.888 0.058974 0.98922 1.7906

Female 0.600479 1.822992 0.135605 4.428 9.50E-06 1.39752 2.378

Single 0.297484 1.346467 0.159414 1.866 0.062026 0.98515 1.8403

Relationship 0.015718 1.015842 0.2221 0.071 0.943582 0.65732 1.5699

Engaged -0.50279 0.604839 0.445555 -1.128 0.259124 0.25257 1.4484

Married 0.407824 1.503543 0.194722 2.094 0.036225 1.02652 2.2022

Its Complicated -0.68278 0.505213 0.658469 -1.037 0.299776 0.13899 1.8364


Hometown (same) 0.351529 1.421239 0.285497 1.231 0.218215 0.81218 0.285497




College (same) -0.99349 0.370281 1.314807 -0.756 0.449877 0.02814 4.8719







Influence (

Age (0-18) -0.1976 0.820699 0.226283 -0.873 0.382534 0.52671 0.226283

Age (18-23) 0.582443 1.790407 0.263113 2.214 0.026852 1.06903 0.263113

Age (23-31) -0.46553 0.627802 0.351517 -1.324 0.185388 0.31522 0.351517

Age (>31) -0.27382 0.760466 0.227858 -1.202 0.229467 0.48655 0.227858

Male 0.590312 1.804552 0.223827 2.637 0.008355 1.16372 0.223827

Female 0.183569 1.201498 0.190512 0.964 0.335269 0.8271 0.190512

Single -0.32343 0.723664 0.245936 -1.315 0.188479 0.44688 0.245936

Relationship -1.08009 0.339563 0.420513 -2.569 0.010214 0.14893 0.420513

Engaged -0.3278 0.720509 0.553683 -0.592 0.55383 0.24341 0.553683

Married 0.041835 1.042723 0.268351 0.156 0.876113 0.61624 0.268351

Its Complicated -0.55144 0.576118 0.370124 -1.49 0.136253 0.27891 0.370124

Susceptibility (

Age (0-18) 0.127324 1.135785 0.188442 0.676 0.499254 0.78504 1.6432

Age (18-23) -0.06946 0.932898 0.202551 -0.343 0.731657 0.62722 1.3875

Age (23-31) -0.02309 0.977173 0.259055 -0.089 0.928971 0.58812 1.6236

Age (>31) -0.37622 0.686453 0.169289 -2.222 0.026261 0.49262 0.9566

Male -0.13872 0.870472 0.160185 -0.866 0.386494 0.63592 1.1915

Female -0.1458 0.864334 0.143695 -1.015 0.310284 0.65218 1.1455

Single 0.196067 1.216609 0.173093 1.133 0.257327 0.86659 1.708


25

Relationship 0.02437 1.02467 0.280941 0.087 0.930874 0.59081 1.7771

Engaged 0.89752 2.45351 0.393223 2.282 0.022462 1.13521 5.3027

Married 0.119894 1.127377 0.224199 0.535 0.592812 0.72649 1.7495

Its Complicated 0.869676 2.386139 0.463453 1.877 0.060585 0.96206 5.9182


Hometown (same) -0.02759 0.972789 0.374364 -0.074 0.941255 0.46705 2.0262




College (same) 1.53463 4.639608 0.929746 1.651 0.098822 0.75003 28.7



Num. common pages 0.002149 1.002152 0.002115 1.016 0.309527 0.99801 1.0063



Num. common friends -0.00244 0.99756 0.001922 -1.271 0.203706 0.99381 1.0013


proportional hazards model with an addition term that is quadratic in the number of notifications received as a test of nonlinearity

in response to receiving multiple notifications. It estimates the impact of a user’s tie attributes (tie strength and embeddedness) on

his hazard to influence peers to adopt and on the hazard that his peers will spontaneously adopt, while controlling for individual

influence and susceptibility associated with the individual attributes: age, gender or relationship status. Goodness of fit and model

likelihood test statistics include: Concordance=0.833 (SE=0.009); Likelihood ratio test = 2381 on 68 degrees of freedom (p=0);

Wald test statistic = 3790 on 68 degrees of freedom (p=0); Logrank statistic = 20798 on 68 degrees of freedom (p=0) ; Robust

Logrank statistic = 426 (p=0)

tie strength, embeddedness & social influence: a large ...web.mit.edu/sinana/www/msta14.pdf ·...

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