基于逆序的城市数目与累积规模关系探讨

doi:10.11821/dlyj201508005

摘要/Abstract

摘要：

在解读区域城市体系规模结构特征的基础上,建立了用于分析逆向排序的城市累积规模与城市数目之间关系的模型。采用全国第六次人口普查数据,利用位序—规模法则与提出的逆序累积规模模型测度了2010年中国城市体系规模结构的省际差异及其空间分布特征,并对影响区域城市体系的地理因素进行了分析。研究发现：位序—规模法则在刻画区域城市体系规模特征方面存在一定的缺陷。对于明显存在首位分布、双中心城市、或者城市数量较少的城市体系描述不够准确,导致使用位序—规模法则得到的Q值和选取的地理变量之间没有必然的联系,在进行不同区域间城市体系结构比较研究中存在一定的局限性。整体来看,逆序累积规模模型的拟合效果要优于位序—规模法则。在使用位序—规模法则拟合效果不理想的情况下,逆序累积规模模型的普适性更强。β值与区域的经济总量、城市化率、人口密度以及复种指数存在较高的统计关系,在城市化进程中,应该根据各个区域的特征及其发展态势,探索与区域发展相适应的城市体系化道路。空间自回归模型与一般回归模型的统计结果表明：中国各省区城市体系的形成与演化在空间上联系很弱,基本上处于孤立发展的封闭状态,其原因可能与中国严格的户籍管理政策及地方保护主义有关。

关键词: 城市体系, 规模结构, 逆序累积规模, 位序—规模法则

Abstract:

Based on investigating and interpreting the characteristics of the size structure of regional urban system, this paper firstly aims to build a model on analyzing the relationships between reverse urban cumulative size and number of cities. Secondly, based on the sixth national population census data of 2010, traditional rank-size rule and the model of reverse cumulative size proposed in this paper are used to measure the inter-provincial differences and their spatial distribution characteristics of urban size structure in China. Thirdly, the geographic factors which have influence on regional urban system are discussed. The results show that the rank-size rule has few shortcomings in interpreting the characteristics of the size structure of regional urban system, especially for the urban system in which there is the distribution of primary city, two-centre city, or small number of cities. The shortcoming leads to the fact that there is no necessary linkage between the value of Q derived from the rank-size rule and the selected geographic variables. As a result, there are certain limitations in the comparative study between different regional urban system structures. Overall, the fitting provided by the model of reverse cumulative size given in this paper is better than that provided by the rank-size rule. Particularly, when the fitting provided by the rank-size rule is not ideal, the model of reverse cumulative size can overcome this shortcoming, and provides accurate fitting to more realistically and objectively reflect the characteristics of the size and structure of regional urban system. Moreover, the results also show that there is a close statistical relationship between the selected regional variables, such as regional economy, urbanization, population density and the composite index, and the value of β given by the model of reverse cumulative size. In the process of urbanization, path of the urban system coordinated with regional development should be explored in term of the tendency of development and characteristics of different regions. According to the statistics derived from the general regression model and spatial auto regression model, there is a weak spatial linkage between the formation and evolution of the regional urban systems of each province in China. That is to say, the formation and evolution of the regional urban systems of each province is in a close state of isolated development. The reason should be related to the strict administration and policies of household registration and the prevalence of local protectionism in China.

Key words: urban system, size structure, reverse cumulative size, rank-size rule

叶浩, 庄大昌, 陈少沛, 杨蕾. 基于逆序的城市数目与累积规模关系探讨[J]. 地理研究, 2015, 34(8): 1461-1470.

Hao YE, Dachang ZHUANG, Shaopei CHEN, Lei YANG. Derivation of relations between city reverse cumulative size and city number[J]. GEOGRAPHICAL RESEARCH, 2015, 34(8): 1461-1470.

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省区	位序—规模法则			逆序累积规模模型			省区	位序—规模法则				逆序累积规模模型
省区	Q值		R²	AIC		β值	R²	AIC	Q值	R²	AIC	β值	R²	AIC
河北	1.110	0.973	-0.749	1.426	0.988	-3.822	湖北	0.913	0.922	-0.020		1.339	0.985	-4.010
山西	1.067	0.978	-1.062	1.420	0.993	-4.410	湖南	1.108	0.799	1.437		1.502	0.992	-3.975
内蒙古	1.183	0.866	1.039	1.635	0.997	-4.541	广东	1.152	0.971	-0.575		1.334	0.982	-3.747
辽宁	1.174	0.941	0.160	1.450	0.970	-2.840	广西	1.153	0.974	-0.767		1.479	0.990	-3.936
吉林	0.966	0.940	-0.215	1.419	0.993	-4.403	海南	1.149	0.906	0.508		1.677	0.968	-2.244
黑龙江	1.202	0.971	-0.535	1.463	0.989	-3.857	四川	0.996	0.896	0.462		1.465	0.971	-2.825
江苏	1.003	0.991	-2.018	1.300	0.993	-4.959	贵州	0.997	0.902	0.302		1.529	0.995	-4.564
浙江	0.859	0.931	-0.290	1.340	0.983	-3.888	云南	0.899	0.791	1.023		1.506	0.952	-2.205
安徽	0.884	0.940	-0.419	1.367	0.997	-5.725	陕西	1.269	0.913	0.651		1.419	0.982	-3.555
福建	1.041	0.987	-1.687	1.392	0.987	-3.968	甘肃	1.119	0.871	0.869		1.613	0.991	-3.614
江西	0.980	0.663	1.866	1.573	0.964	-2.295	宁夏	1.623	0.985	-0.745		1.751	0.986	-2.747
山东	0.838	0.960	-0.883	1.297	0.996	-5.573	新疆	1.324	0.814	0.559		1.670	0.987	-3.058
河南	0.926	0.910	0.174	1.414	0.971	-3.002	平均值	1.077	0.912	-0.037		1.471	0.984	-3.750

Q	1.000
β	0.661	1.000
X₁	0.053	0.176	1.000
X₂	-0.533	-0.851	0.070	1.000
X₃	-0.658	-0.815	0.161	0.901	1.000
X₄	0.000	-0.430	-0.136	0.609	0.205	1.000
X₅	0.099	-0.341	-0.246	0.438	0.055	0.888	1.000
X₆	-0.501	-0.713	-0.729	0.567	0.559	0.257	0.245	1.000
X₇	-0.551	-0.707	-0.683	0.537	0.573	0.165	0.137	0.971	1.000
X₈	0.378	0.542	0.474	-0.567	-0.514	-0.339	-0.270	-0.755	-0.698	1.000
X₉	-0.342	-0.367	-0.208	0.500	0.553	0.116	0.037	0.559	0.563	-0.692	1.000
X₁₀	-0.202	0.137	0.263	-0.130	-0.041	-0.218	-0.073	-0.249	-0.255	-0.124	0.148	1.000
变量	Q	β	X₁	X₂	X₃	X₄	X₅	X₆	X₇	X₈	X₉	X₁₀

Q值回归	系数	标准差	t值	P	β值回归	系数	标准差	t值	P
常量	2.473	0.334	7.402	0.000	常量	2.727	0.313	8.703	0.000
X₃	-0.167	0.040	-4.191	0.000	X₃	-0.134	0.020	-6.638	0.000
-	-	-	-	-	X₅	-0.133	0.057	-2.344	0.030
-	-	-	-	-	X₆	-0.058	0.015	-3.732	0.001
-	-	-	-	-	X₉	0.139	0.055	2.514	0.020
统计检验	R²	lg L	AIC	SC	统计检验	R²	lg L	AIC	SC
统计值	0.433	16.009	-28.018	-25.580	统计值	0.856	41.475	-72.950	-66.856

Q值回归	系数	标准差	Z值	P	β值回归	系数	标准差	Z值	P
ρ	0.225	0.101	2.181	0.029	ρ	-0.031	0.039	-0.787	0.431
常量	2.384	0.297	8.024	0.000	常量	2.752	0.278	9.889	0.000
X₃	-0.184	0.037	-5.031	0.000	X₃	-0.124	0.022	-5.643	0.000
-	-	-	-	-	X₅	-0.135	0.050	-2.690	0.007
-	-	-	-	-	X₆	-0.062	0.015	-4.212	0.000
-	-	-	-	-	X₉	0.132	0.050	2.662	0.001
统计检验	R²	lg L	AIC	SC	统计检验	R²	lg L	AIC	SC
统计值	0.517	17.935	-29.871	-26.214	统计值	0.859	41.777	-71.555	-64.241