Table A1:

Heterogeneity . | Network Size . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . |
---|---|---|---|---|---|---|---|

$k$ | $R2$ | 0.0293 | 0.0140 | 0.0347 | 0.0534 | 0.0725 | 0.0974 |

$p$-value for F-statistic versus Constant | $3.9\xd710-42$ | $1.8\xd710-20$ | $7.1\xd710-50$ | $4.9\xd710-77$ | $2.2\xd710-105$ | $3.9\xd710-143$ | |

$h$ | $R2$ | 0.0103 | 0.01794 | 0.0606 | 0.0382 | 0.0530 | 0.0888 |

$p$-value for F-statistic versus Constant | $3.6\xd710-15$ | $6.7\xd710-26$ | $1.4\xd710-87$ | $6.7\xd710-55$ | $2.3\xd710-76$ | $5.2\xd710-130$ | |

$b$ | $R2$ | 0.0141 | 0.0164 | 0.0357 | 0.0577 | 0.0620 | 0.0918 |

$p$-value for F-statistic versus Constant | $1.6\xd710-20$ | $9.1\xd710-24$ | $3.3\xd710-51$ | $2.1\xd710-83$ | $1.2\xd710-89$ | $1.3\xd710-134$ | |

Heterogeneity | Network Size | 2 | 3 | 4 | 5 | 6 | 7 |

$k$ | $R2$ | 0.0068 | 0.0019 | 0.0060 | 0.0191 | 0.0315 | 0.0401 |

$p$-value for F-statistic versus Constant | $3.6\xd710-10$ | 0.0022 | $4.5\xd710-9$ | $1.5\xd710-27$ | $3.0\xd710-45$ | $1.6\xd710-57$ | |

$h$ | $R2$ | 0.0014 | 0.0020 | 0.0101 | 0.0171 | 0.0181 | 0.0356 |

$p$-value for F-statistic versus Constant | 0.0032 | $3.8\xd710-4$ | $7.2\xd710-15$ | $1.2\xd710-24$ | $4.3\xd710-26$ | $4.5\xd710-51$ | |

$b$ | $R2$ | 0.0029 | 0.0047 | 0.0062 | 0.0222 | 0.0290 | 0.0329 |

$p$-value for F-statistic versus Constant | $8.3\xd710-5$ | $2.5\xd710-7$ | $2.4\xd710-9$ | $6.5\xd710-32$ | $1.4\xd710-41$ | $3.2\xd710-47$ |

Heterogeneity . | Network Size . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . |
---|---|---|---|---|---|---|---|

$k$ | $R2$ | 0.0293 | 0.0140 | 0.0347 | 0.0534 | 0.0725 | 0.0974 |

$p$-value for F-statistic versus Constant | $3.9\xd710-42$ | $1.8\xd710-20$ | $7.1\xd710-50$ | $4.9\xd710-77$ | $2.2\xd710-105$ | $3.9\xd710-143$ | |

$h$ | $R2$ | 0.0103 | 0.01794 | 0.0606 | 0.0382 | 0.0530 | 0.0888 |

$p$-value for F-statistic versus Constant | $3.6\xd710-15$ | $6.7\xd710-26$ | $1.4\xd710-87$ | $6.7\xd710-55$ | $2.3\xd710-76$ | $5.2\xd710-130$ | |

$b$ | $R2$ | 0.0141 | 0.0164 | 0.0357 | 0.0577 | 0.0620 | 0.0918 |

$p$-value for F-statistic versus Constant | $1.6\xd710-20$ | $9.1\xd710-24$ | $3.3\xd710-51$ | $2.1\xd710-83$ | $1.2\xd710-89$ | $1.3\xd710-134$ | |

Heterogeneity | Network Size | 2 | 3 | 4 | 5 | 6 | 7 |

$k$ | $R2$ | 0.0068 | 0.0019 | 0.0060 | 0.0191 | 0.0315 | 0.0401 |

$p$-value for F-statistic versus Constant | $3.6\xd710-10$ | 0.0022 | $4.5\xd710-9$ | $1.5\xd710-27$ | $3.0\xd710-45$ | $1.6\xd710-57$ | |

$h$ | $R2$ | 0.0014 | 0.0020 | 0.0101 | 0.0171 | 0.0181 | 0.0356 |

$p$-value for F-statistic versus Constant | 0.0032 | $3.8\xd710-4$ | $7.2\xd710-15$ | $1.2\xd710-24$ | $4.3\xd710-26$ | $4.5\xd710-51$ | |

$b$ | $R2$ | 0.0029 | 0.0047 | 0.0062 | 0.0222 | 0.0290 | 0.0329 |

$p$-value for F-statistic versus Constant | $8.3\xd710-5$ | $2.5\xd710-7$ | $2.4\xd710-9$ | $6.5\xd710-32$ | $1.4\xd710-41$ | $3.2\xd710-47$ |

Note: The numbers in bold correspond to quadratic fits where the optimal level of heterogeneity is not in the interior.

Table A2:

Heterogeneity . | Network Size . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . |
---|---|---|---|---|---|---|---|

$k$ | $R2$ | 0.0018 | 0.0123 | 0.0076 | 0.0149 | 0.0212 | 0.0357 |

$p$-value for F-statistic versus Constant | 0.003 | $6.0\xd710-18$ | $2.2\xd710-11$ | $1.4\xd710-21$ | $1.6\xd710-30$ | $2.9\xd710-51$ | |

$h$ | $R2$ | 0.0199 | 0.0159 | 0.0166 | 0.0156 | 0.0232 | 0.0356 |

$p$-value for F-statistic versus Constant | $1.1\xd710-28$ | $4.6\xd710-23$ | $5.3\xd710-24$ | $1.4\xd710-22$ | $2.4\xd710-33$ | $4.4\xd710-51$ | |

$b$ | $R2$ | 0.0008 | 0.0027 | 0.0032 | 0.0048 | 0.0160 | 0.0251 |

$p$-value for F-statistic versus Constant | 0.0237 | $1.8\xd710-4$ | $3.9\xd710-5$ | $1.9\xd710-7$ | $4.3\xd710-23$ | $4.0\xd710-36$ |

Heterogeneity . | Network Size . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . |
---|---|---|---|---|---|---|---|

$k$ | $R2$ | 0.0018 | 0.0123 | 0.0076 | 0.0149 | 0.0212 | 0.0357 |

$p$-value for F-statistic versus Constant | 0.003 | $6.0\xd710-18$ | $2.2\xd710-11$ | $1.4\xd710-21$ | $1.6\xd710-30$ | $2.9\xd710-51$ | |

$h$ | $R2$ | 0.0199 | 0.0159 | 0.0166 | 0.0156 | 0.0232 | 0.0356 |

$p$-value for F-statistic versus Constant | $1.1\xd710-28$ | $4.6\xd710-23$ | $5.3\xd710-24$ | $1.4\xd710-22$ | $2.4\xd710-33$ | $4.4\xd710-51$ | |

$b$ | $R2$ | 0.0008 | 0.0027 | 0.0032 | 0.0048 | 0.0160 | 0.0251 |

$p$-value for F-statistic versus Constant | 0.0237 | $1.8\xd710-4$ | $3.9\xd710-5$ | $1.9\xd710-7$ | $4.3\xd710-23$ | $4.0\xd710-36$ |

Note: The numbers in bold correspond to quadratic fits where the optimal level of heterogeneity is not in the interior.

Figure A1:

Figure A2:

Figure A3:

Figure A4:

Figure A5:

Figure A6:

Figure A7:

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