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Frontiers of Earth Science

ISSN 2095-0195

ISSN 2095-0209(Online)

CN 11-5982/P

邮发代号 80-963

2019 Impact Factor: 1.62

Frontiers of Earth Science  2014, Vol. 8 Issue (4): 512-523   https://doi.org/10.1007/s11707-014-0426-y
  本期目录
Comparison of multinomial logistic regression and logistic regression: which is more efficient in allocating land use?
Yingzhi LIN1,*(),Xiangzheng DENG2,3,Xing LI1,Enjun MA1
1. School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
2. Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China
3. Center for Chinese Agricultural Policy, Chinese Academy of Sciences, Beijing 100101, China
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Abstract

Spatially explicit simulation of land use change is the basis for estimating the effects of land use and cover change on energy fluxes, ecology and the environment. At the pixel level, logistic regression is one of the most common approaches used in spatially explicit land use allocation models to determine the relationship between land use and its causal factors in driving land use change, and thereby to evaluate land use suitability. However, these models have a drawback in that they do not determine/allocate land use based on the direct relationship between land use change and its driving factors. Consequently, a multinomial logistic regression method was introduced to address this flaw, and thereby, judge the suitability of a type of land use in any given pixel in a case study area of the Jiangxi Province, China. A comparison of the two regression methods indicated that the proportion of correctly allocated pixels using multinomial logistic regression was 92.98%, which was 8.47% higher than that obtained using logistic regression. Paired t-test results also showed that pixels were more clearly distinguished by multinomial logistic regression than by logistic regression. In conclusion, multinomial logistic regression is a more efficient and accurate method for the spatial allocation of land use changes. The application of this method in future land use change studies may improve the accuracy of predicting the effects of land use and cover change on energy fluxes, ecology, and environment.

Key wordsmultinomial logistic regression    land use change    logistic regression    land use suitability    land use allocation
收稿日期: 2013-04-03      出版日期: 2015-01-13
Corresponding Author(s): Yingzhi LIN   
 引用本文:   
. [J]. Frontiers of Earth Science, 2014, 8(4): 512-523.
Yingzhi LIN,Xiangzheng DENG,Xing LI,Enjun MA. Comparison of multinomial logistic regression and logistic regression: which is more efficient in allocating land use?. Front. Earth Sci., 2014, 8(4): 512-523.
 链接本文:  
https://academic.hep.com.cn/fesci/CN/10.1007/s11707-014-0426-y
https://academic.hep.com.cn/fesci/CN/Y2014/V8/I4/512
Fig.1  
Variable Logistic regression* Multinomial logistic regression**
Median Mean Std. Dev. Median Mean Std. Dev.
Dependent variables
?DCLand1995–2000 1?? 1.32 0.79
?Land2000,1 0??? 0.27 0.44
?Land2000,2 1??? 0.62 0.48
?Land2000,3 0??? 0.04 0.20
?Land2000,4 0??? 0.04 0.20
?Land2000,5 0??? 0.02 0.13
?Land2000,6 0??? 0.01 0.07
Independent variables
?Elevation/m 200.00?? 251.64?? 229.43?? 88.00? 129.67?? 133.71??
?Slope/(°) 1.67 2.73 2.99 0.54 1.31 1.90
?Aspect/(°) 93.51? 93.75? 52.95? 103.76?? 100.43?? 53.42?
?Precipitation/mm 1846.70??? 1841.41??? 152.62?? 1922.39??? 1878.90??? 146.77??
?Temperature/°C 18.18? 17.94? 1.23 18.12? 17.81? 1.24
?Dtoroad/km 1.00 0.68 0.82 0.00 0.50 0.66
?Dtocity/km 159.00?? 173.27?? 82.05? 130.00?? 146.68?? 81.44?
?Dtowater/km 0.00 0.34 18.31? 0.00 0.02 4.68
?pH 4.60 4.69 0.76 4.60 4.71 0.67
?Loam/% 24.00? 26.00? 4.68 24.00? 26.44? 5.02
?Organics/% 3.14 3.08 0.90 3.14 3.01 0.67
?Nitrogen/% 0.16 0.15 0.03 0.16 0.15 0.03
?Phosphorous/% 0.04 0.04 0.01 0.04 0.04 0.01
?Potassium/% 1.79 1.78 0.28 1.79 1.77 0.21
?Bufferfarmland/% 16.53? 27.26? 28.88? 62.81? 60.38? 25.46?
?Bufferbuiltup/% 0.00 1.66 5.66 0.00 3.31 5.81
?Bufferforest/% 73.55? 62.23? 34.92? 23.97? 30.46? 28.05?
Tab.1  
Variable Median Mean Std. Dev. Obs.
Elevation/m 84.00 125.85 127.92
Slope/degree 0.54 1.29 1.88
Aspect/degree 105.86 101.65 53.19
Precipitation/mm 1,609.04 1,610.64 57.57
Temperature/ oC 18.38 18.05 1.15
Dtoroad/km 0.00 0.49 0.64
Dtocity/km 129.00 146.11 81.11
Dtowater/km 0.00 0.02 4.71
pH 4.60 4.71 0.67
Loam/% 24.00 26.43 5.02
Organics/% 3.14 3.01 0.66
Nitrogen/% 0.16 0.15 0.03
Phosphorus/% 0.04 0.04 0.01
Potassium/% 1.79 1.77 0.21
Bufferfarmland/% 62.81 60.51 25.27
Bufferbuiltup/% 0.00 3.36 5.85
Bufferforest/% 23.97 30.07 27.79
Tab.2  
Variable Variance Inflation Factor (VIF)
Originally prepared variables Finally selected variables
Organics 15.42?
Nitrogen 15.20? 5.45
pH 10.17? 8.75
Potassium 7.31 6.06
Phosphorous 6.11 6.02
Bufferforest 4.23 4.20
Bufferfarmland 3.69 3.67
Dtocity 3.16 3.15
Elevation 2.80 2.75
Precipitation 2.41 2.40
Slope 2.17 2.17
Loam 1.81 1.62
Temperature 1.80 1.76
Dtoroad 1.25 1.25
Bufferbuiltup 1.21 1.21
Aspect 1.08 1.08
Stowater 1.00
Mean VIF 4.75 3.44
Tab.3  
Dependent variable
Land2000,1 Land2000,2 Land2000,3 Land2000,4 Land2000,5 Land2000,6
Elevation -5.79×10-4(7.37)*** -3.09×10-4(4.88)*** -1.29×10-3(13.81)*** -8.32×10-3(21.14)*** -7.06×10-4(2.13)** -4.68×10-4(0.43)
Slope 0.02(5.48)*** 0.01(3.42)*** 0.08(11.10)*** -0.06(3.58)*** 0.02(1.29) -0.53(3.64)***
Aspect 1.02×10-3(6.58)*** 3.84×10-4(2.37)** -4.56×10-3(15.79)** 1.17×10-3(5.45)*** 6.65×10-4(1.51) 2.32×10-3(3.34)***
Precipitation -0.81×10-4(1.01) -3.51×10-4(2.07)** -4.69×10-3(14.08)*** -2.94×10-3(6.62)*** -1.99×10-4(0.38) 5.50×10-3(3.17)**
Temperature 0.02(1.87)* 0.04(3.79)*** 0.04(2.00)** 0.10(4.50)*** 0.03(0.94) -0.28(3.76)***
Dtoroad -0.16(12.72)*** -0.03(2.31)** -0.54(27.15)*** -0.14(9.01)*** -0.14(3.64)*** 0.14(6.40)***
Dtocity 1.17×10-3(6.89)*** 2.37×10-4(1.49) 7.86×10-3(26.08)*** -1.36×10-3(3.68)*** 1.99×10-4(0.45) -0.02×10-4(9.10)***
pH 3.58×10-3(0.09) 0.06(1.55) 0.68(18.35)*** 0.29(6.10)*** 0.06(0.45) 0.35(3.61)***
Loam -0.01(4.84)*** -3.29×10-3(1.39) -0.07(18.41)*** -0.01(2.87)*** -1.75×10-4(0.03) 0.02(1.94)*
Nitrogen 0.58(0.78) 0.84(1.07) 7.16(12.10)*** 1.19(1.27) 1.57(0.67) 3.76(1.11)
Phosphorous 8.19(2.19)** -7.18(2.03)** 23.76(5.84)*** -36.68(5.85)*** -3.82(0.28) 59.47(3.71)***
Potassium -0.11(1.32) 0.06(0.70) -1.52(14.90)*** -0.51(2.56)*** 0.19(0.66) -1.63(3.07)***
Bufferfarmland 0.07(116.70)*** 2.29×10-3(3.68)*** -0.06(78.94)*** -0.06(76.36)*** 0.02(11.93)*** -0.06(23.70)***
Bufferbuiltup -0.01(6.36)*** 3.89×10-3(1.92)* -0.10(21.74)* -0.04(20.71)*** 0.14(52.71)*** -0.06(5.38)***
Bufferforest 3.89×10-3(7.31)*** 0.08×10-3(134.45)*** 0.08(118.57)*** -0.06(70.97)*** -0.01(5.58)*** -0.07(13.84)***
Intercept -4.00(16.49)*** -3.16(10.96)*** -7.53(14.67)*** 6.15(10.99)*** -6.30(7.92)*** -6.15(3.22)***
Pseudo R2 0.44 0.54 0.38 0.52 0.39 0.59
Tab.4  
Dependent variable: DCLand1995-2000 (=1 is the comparison group)
(=2) (=3) (=4) (=5) (=6)
Elevation -6.42×10-5(0.40) 1.85×10-3(3.83)*** -6.06×10-3(5.67)*** 2.54×10-4(0.42) 4.55×10-3(0.61)
Slope -0.03(3.69)*** -0.03(0.94) -0.07(1.48)*** 4.47(0.14) -0.71(1.09)
Aspect -2.17×10-3(7.24)*** -2.88×10-3(3.36)** 2.22×10-3(3.20)** 1.24×10-3(1.86)* 2.33×10-3(0.57)
Precipitation -1.15×10-4(0.74) 9.59×10-5(0.18) -7.95×10-4(1.66)* -9.95×10-4(2.47)** 1.83×10-3(0.47)
Temperature -0.08(5.03)*** 0.21(3.94)*** 0.12(3.32)*** 0.02(0.73) -0.56(3.37)***
Dtoroad -0.01(0.58) -0.10(1.34) 0.36(8.25)*** -0.03(0.51) 0.16(0.63)
Dtocity 4.87×10-3(1.49) 2.61×10-4(0.25) 4.53×10-3(4.95)*** -1.77×10-3(2.27)** -8.24×10-3(1.15)
pH -0.04(0.40) 0.45(2.15)** -0.03(0.15) 0.09(0.39) -0.97(1.57)
Loam -6.50×10-3(1.45) -0.05(4.24)*** 0.01(1.34) 4.04×10-4(0.05) 0.01(0.28)
Nitrogen -1.20(0.64) 10.69(3.08)*** 1.07(0.30) 1.88(0.45) -16.67(1.13)
Phosphorous 1.52(0.18) 6.15(0.28) 13.96(0.61) 0.90(0.04) -22.95(0.29)
Potassium 0.16(0.81) -1.29(2.64)*** -0.44(0.77) -0.31(0.61) 4.60(1.51)
Bufferfarmland -6.21×10-3(2.96)*** -0.09(35.06)*** -0.06(28.80)*** -2.26×10-3(0.64) -0.09(8.55)***
Bufferbuiltup -0.03(4.88)*** -0.11(8.96)*** -0.05(7.32)*** 0.10(22.40)*** -0.17(2.20)**
Bufferforest 0.04(22.26)*** -0.08(33.81)*** -0.05(19.99)*** -0.01(2.52)** -0.14(3.68)***
Intercept -1.14(2.18)** -0.75(0.48) 1.29(1.12) -2.70(2.36)** 6.43(0.85)***
Pseudo R2 0.23
Tab.5  
Fig.2  
Land use type Remote sensing Pixels being allocated correctly
Logistic regression Multinomial logistic regression
Number Proportion/% Number Proportion/%
Cultivated land 28,227 24,169 85.62 27,531 97.53
Forest 12,151 11,835 97.40 11,704 96.32
Grassland 1,117 501 44.85 421 37.69
Water area 1,171 602 51.41 651 55.59
Built-up area 1,862 1,092 58.65 1,126 60.47
Unused land 33 0 0.00 0 0.00
Total 38,199 85.72 41,433 92.98
Tab.6  
(1) (2) (3) (4) (5) (6) MNL
(1) 413.89 865.64 898.11 924.46 993.63 (1)
(2) 129.09 151.89 135.92 132.59 170.00 (2)
(3) 404.25 161.02 -40.27 -35.04 56.92 (3)
(4) 418.51 160.14 0.10 -3.62 115.49 (4)
(5) 429.33 150.24 -14.93 -17.68 111.64 (5)
(6) 444.60 186.11 84.43 120.29 97.17 (6)
LR (1) (2) (3) (4) (5) (6)
Tab.7  
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