*2.3. Analysis*

#### 2.3.1. GIS Spatial Analysis Method

We used ArcGIS software for basic data processing, topological analysis, summary statistics, spatial display, thematic map production, etc. [40], and the GIS spatial overlay tool to carry out overlay analysis on land types in two different periods. The final land use transition matrix was formed through statistical analysis. The land use transfer matrix can quantitatively describe the quantity and direction of mutual conversion between land types in a specific area in a certain period of time. By analyzing the transfer matrix of urban–rural construction land area, the total change between land types in two phases can be obtained. In this study, the land use transfer matrix [41] was used to describe the structural transformation trend between urban–rural construction land and other land types, and its mathematical expression is as follows:

$$S\_{ij} = \begin{bmatrix} S\_{11} & S\_{12} & \cdots & S\_{1m} \\ S\_{21} & S\_{22} & \cdots & S\_{2m} \\ \vdots & \vdots & \vdots & \vdots \\ S\_{m1} & S\_{m2} & \cdots & S\_{mm} \end{bmatrix} \tag{1}$$

where *S* is the area of land use, *m* is the type of land use, and *i* and *j* are the land use types used in the initial and final stages, respectively. The land use transfer matrix is mainly used to study the transfer of land use types between two adjacent periods to clarify variations in each type at the beginning of the study and the source and composition of each type at the end of the study [42].

#### 2.3.2. Selection of Influencing Factors

Combined with the actual social economy and natural environment conditions in Qixingguan District, and based on the principle of data accessibility, the following 3 categories and 12 detection factors were selected as explanatory variables to explore the driving factors of urban–rural construction land transformation (Table 1). The influencing factors mainly include the economic development level [43,44], social living conditions, and basic natural conditions. The geomorphology of the present study area is of the mid-size mountain type, and it is located in the sloping zone of the transition from the eastern Yunnan Plateau to the original hills of the central Guizhou Mountains. The altitudinal variation is 1754 m. Altitude, terrain slope, and road network density are the natural constraints of urban spatial layout. Urban–rural construction land is the main spatial carrier in the process of regional economic and social development. The improvement of the overall economic development level (total social investment in fixed assets, total fiscal revenue, per capita GDP, per land GDP, and total industrial output value) continuously promotes the speed of urban–rural construction land expansion. In addition, the urbanization rate, population density, year-end resident population, and year-end salary of employees were used to represent the effects of regional social living conditions on the expansion of urban–rural construction land.

On the basis of index construction, SPSS 19.0 software was used to conduct the Kai-ser-Meyer-Olkin (KMO) test to check correlations and partial correlations between variables. The resulting values are between 0 and 1; the closer the KMO statistic is to 1, the stronger the correlation between variables, and the weaker the partial correlation, the better the effect of factor analysis. Bartlett's sphericity test judges whether the correlation matrix is a unit matrix, and if the independent factor analysis method of each variable is invalid. When the test results of the 12 indicators in 4 monitoring periods by SPSS showed a *p*-value < 0.05, this meant that the standard was met, the data were spherically distributed, and the variables had a spherical distribution independent of each other to a certain extent. The calculated KMO values were 0.665, 0.713, 0.785, and 0.692, which were all greater than the threshold of 0.5. Bartlett's test results were all significant at the 0.01 level, indicating a correlation between the variables of each index, and factor analysis could be carried out.


**Table 1.** Detection indicators of influencing factors of urban–rural construction land changes.

### 2.3.3. Geographical Detector

The spatial distribution patterns of the geography or phenomena in a region are driven by both natural and human factors. By analyzing the relationship between the dependent and independent variables, the geographic detector can better describe the spatial heterogeneity of the dependent variable, and it is an effective spatial analysis method for revealing mechanisms [45]. It has been widely used [46–48]. If the independent variable has a significant effect on the dependent variable, then the spatial distributions of the two variables are similar. The formula is as follows:

$$PD = 1 - \frac{1}{n\sigma^2} \sum\_{h=1}^{L} n\_h \sigma\_h^2 = 1 - \frac{SSW}{SST} \tag{2}$$

$$SSW = \sum\_{h=1}^{L} N\_h a\_{h\prime}^2 \text{ } SST = Na^2 \tag{3}$$

In this formula, *PD* is the explanatory power, with a value ranging from 0 to 1; *n* and *nh* are the numbers of samples in the entire area and in layer *h*, respectively; *σ<sup>2</sup>* and *σ<sup>h</sup>* 2 are the dispersion variance of the entire area and layer *h*, respectively; *L* is the number of subareas; and *SST* and *SSW* are the total variance of the study area and the sum of the variance of the subregions, respectively. The larger the PD value, the stronger the driving effect of the detection factor on the evolution of urban–rural construction land.

The steps of the geographical detection operation are as follows:

(1) Extract information. In ArcGIS 10.5, villages and towns or streets are taken as the basic research units, and then the data of urban–rural construction land and influencing factors of each town or street are correlated according to the spatial location to generate an attribute table and obtain the quantitative relationship between the corresponding urban–rural construction land and each selected indicator.

(2) Classify impact factors. Using the Reclassify tool in ArcGIS, each impact factor is classified according to the natural breakpoint method [49], and the classification value of each variable is extracted. Then, the per capita GDP, land average GDP, urbanization rate, total industrial output value, completion of fixed asset investment in the whole society, and total salary of employees at the end of the year are divided into 5 grades, and the average slope, average elevation, year-end total population, and population density are divided into 6 grades. In addition, total fiscal revenue and road network density are divided into 7 and 9 categories, respectively.

(3) Input the dependent variable Y (statistical value of urban–rural construction land area) and the independent variable X (gradual value of each influencing factor) into Excel Geodetector software (http://www.geodetector.cn) to detect the influence of factors and their interactions.
