A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991–2014
Table 5
A comparison between the allometric scaling exponents based on MLE and those based on OLS.
Year
MLE-based results
OLS-based results
D
d
1991
3.3627
2.1953
2.3627
1.1953
1.9767
0.5277
0.3680
1992
3.1902
2.2092
2.1902
1.2092
1.8113
0.5115
0.3904
1993
3.2499
2.6439
2.2499
1.6439
1.3686
0.5065
0.3711
1994
3.3373
2.2475
2.3373
1.2475
1.8736
0.5132
0.4158
1995
3.5408
2.9049
2.5408
1.9049
1.3338
0.5324
0.4402
1996
3.3537
2.1760
2.3537
1.1760
2.0014
0.5631
0.5043
1997
3.2685
2.1876
2.2685
1.1876
1.9102
0.5679
0.5193
1998
3.3128
2.5258
2.3128
1.5258
1.5158
0.5873
0.5502
1999
2.1752
3.4990
1.1752
2.4990
0.4703
0.5908
0.5571
2000
3.1175
2.1752
2.1175
1.1752
1.8018
0.5990
0.5692
2001
2.7759
2.5755
1.7759
1.5755
1.1272
0.6834
0.7054
2002
2.9099
2.5192
1.9099
1.5192
1.2572
0.7328
0.7922
2003
1.9351
2.4149
0.9351
1.4149
0.6609
0.7837
0.8339
2004
1.9716
2.4939
0.9716
1.4939
0.6504
0.8036
0.8373
2005
1.9901
2.4060
0.9901
1.4060
0.7042
0.8160
0.8415
2006
2.0938
2.1734
1.0938
1.1734
0.9322
0.8616
0.8771
2007
2.3322
2.3922
1.3322
1.3922
0.9569
0.8798
0.8763
2008
2.1116
2.3188
1.1116
1.3188
0.8429
0.9029
0.8883
2009
2.3777
2.2339
1.3777
1.2339
1.1165
0.8977
0.8862
2010
2.3387
2.2373
1.3387
1.2373
1.0820
0.8985
0.8764
2011
2.1632
2.3573
1.1632
1.3573
0.8570
0.8954
0.8770
2012
2.1875
2.3560
1.1875
1.3560
0.8757
0.8923
0.8775
2013
2.1670
2.3210
1.1670
1.3210
0.8834
0.8644
0.8709
2014
2.1237
2.3043
1.1237
1.3043
0.8615
0.8741
0.8761
Note. The MLE-based allometric scaling exponent and the OLS-based allometric scaling exponent values are both based on Zipf’s distributions, and are estimated by the rank-size allometric scaling relation. values are different from the results shown in Table 2, which is based on hierarchical allometric scaling.
