Spatial Heterogeneity in the Local Clustering of Traditional Villages in Southern Zhejiang, China: Insights from Random Forest–SHAP and Multiscale Spatial Regression Models

Abstract

This study develops a scale-aware and reproducible framework for examining the local clustering intensity of 612 recognized traditional villages in southern Zhejiang, China. Equal-weight Gaussian leave-one-out kernel density estimation (LOO-KDE; h = 21.01 km) excluded each focal village’s direct self-contribution, while explicitly acknowledging shared-neighbour dependence among the derived outcomes. Village-scale models used the same X1–X12 predictor set after correlation and variance-inflation screening; county socioeconomic indicators were analyzed separately for the 27 represented county-level units. A Random Forest selected from 144 prespecified candidates achieved an out-of-bag R2 of 0.353 and a county-grouped pooled R2 of 0.115. Repeated spatial holdouts yielded weak transferability: mean R2 was −0.081 for coordinate K-means and 0.082 for shifted 50 km grids without buffers, and became negative for both designs with one- or two-bandwidth buffers. SHAP ranked elevation, topographic relief, and village household count as the leading village-scale predictive contributors. OLS explained 30.5% of outcome variance, whereas SLM and SEM results depended strongly on whether structural/filtered fits or covariate-only predictions were evaluated. GWR and MGWR reached R2 = 0.9743 and 0.9984, and residual Moran’s I remained significant for all models except MGWR (I = 0.002, p = 0.429). At the county scale, rural disposable income and tertiary-industry output were negatively correlated with mean LOO-KDE, but multivariable HC3 estimates were imprecise and ecologically interpreted. The results identify associations with the clustering of recognized villages, not causes of individual-village heritage persistence.

1. Introduction

1.1. The Research Topic: Spatial Clustering of Traditional Villages

Traditional villages are part of a wider international concern with vernacular heritage, rural cultural landscapes, and historically layered settlement systems. International conservation discourse has moved beyond the protection of isolated monuments toward landscape-scale and relational approaches that consider settlements, productive land, ecological settings, infrastructure, and everyday cultural practices as integrated heritage systems [1,2,3,4]. Within this broader perspective, the spatial clustering of traditional settlements is not merely a cartographic pattern; it is a record of long-term human-environment adaptation, changing accessibility, uneven modernization pressure, and the institutional processes through which certain landscapes become recognized as heritage. Therefore, methods that can distinguish local clustering intensity, regional context, spatial dependence, and spatial heterogeneity are relevant not only to Chinese traditional villages but also to comparative studies of rural heritage landscapes in other regions.

In China, rapid urbanization has profoundly reshaped rural settlement systems [5]. The National Traditional Village Protection Project, launched in 2012, has produced an official heritage inventory of 8155 villages across six batches, and these recognized villages form pronounced regional clusters rather than an even spatial distribution. Existing Chinese studies have documented large-scale distribution patterns and associated factors using GIS, Geodetector, GWR, spatial econometrics, and machine-learning methods [6,7,8,9,10,11,12,13,14,15,16]. These studies provide an important empirical basis, but they often rely on administrative counts or conventional KDE surfaces and therefore have difficulty separating the clustering intensity surrounding a focal village from the focal village’s own presence. They also tend to apply machine-learning interpretation, spatial dependence modelling, and local spatial heterogeneity analysis as separate procedures, sometimes with different variable sets. This makes it difficult to compare predictive relevance, spatial dependence, and local non-stationarity within a unified framework.

Southern Zhejiang provides a useful case for demonstrating such a framework because it combines dense rural heritage resources, mountainous terrain, river-valley settlement systems, and big internal differences in development context. The region differs markedly from the water-town lowlands of northern Zhejiang and the more urbanized central basins. Previous research on southwest Zhejiang has shown that village boundaries are frequently clustered or banded and that morphology is closely related to terrain, rivers, roads, and long-term settlement adaptation [17]. However, the question addressed here is not simply how individual village forms evolved, but how recognized traditional villages are locally clustered and how that clustering can be interpreted through a consistent cross-scale modelling workflow.

The present distribution of recognized traditional villages is treated as a conditional heritage-inventory pattern rather than as direct evidence of why individual settlements were established or preserved. Local terrain, hydrology, and accessibility describe the environmental settings in which settlement systems developed, whereas village size and county-level socio-economic indicators describe contemporary contexts surrounding the recognized clusters. These variables may be associated with clustering intensity, but the cross-sectional design cannot determine whether development contexts altered heritage persistence, whether heritage recognition influenced local development, or whether both reflect unobserved historical and institutional processes.

1.2. Existing Research on Traditional Villages

Although studies in architecture and planning have explored traditional villages from the perspectives of spatial form [18], construction techniques [19], morphology [20], and human–environment interaction [21], comprehensive analyses of their spatial distribution patterns and associated factors remain limited. Recent regional studies have increasingly emphasized that traditional village distribution is not random, but is shaped by the interaction of natural geographical constraints, historical processes, and socio-economic development. For instance, Yuan et al. studied 777 traditional villages in Yunnan Province using GWR and Geodetector, revealing an evidently clustered pattern described as “three high-density areas and multiple medium-density belts,” and showing the influence of elevation, slope, climate, hydrology, transportation, population density, and GDP on village distribution [22]. Similarly, Cao and Kim analyzed traditional villages in the Liaoxi Corridor and found that they form high-density settlement areas in Chaoyang County and Beizhen City, with most villages located in hilly and mountainous areas and river valleys under the combined influence of topography, water sources, immigration, settlement history, border defence, and ethnic integration [23]. These studies confirm the importance of integrating natural and human factors when explaining the spatial formation of traditional villages.

In addition to spatial distribution and influencing factors, recent studies have begun to examine the transformation, connectivity, and development potential of traditional villages. Jia et al. investigated the tourism transformation levels of traditional villages in Shaanxi Province using Geodetector and grounded theory. Their results show that most traditional villages had not yet developed tourism, with only 11.98% reaching a relatively mature tourism stage, suggesting that tourism and service-sector development do not automatically translate into heritage revitalization [24]. Fan et al. further examined traditional village clusters in Qiandongnan Prefecture, a major traditional village agglomeration area with 415 nationally designated villages. Their study found a “dense core, sparse periphery, and localized jumps” spatial pattern, a clustered but internally fragile connectivity network, and medium-to-low overall development potential [25]. These findings suggest that traditional village research should move beyond isolated village description toward regional coordination, spatial network analysis, and differentiated development strategies.

1.3. Quantitative Methodological Tools

Geographic tools such as GIS were initially used to evaluate risks to traditional built heritage [26]; subsequent spatial differentiation studies in areas such as Southwest China demonstrated the relevance of spatial pattern analysis for rural revitalization [27]. Among spatial models, Geographically Weighted Regression (GWR) has gained popularity for capturing spatial non-stationarity in regression relationships [28,29,30,31]. GWR typically outperforms traditional regression models in accuracy and flexibility [32,33,34], and has inspired further developments [35,36,37,38]. However, standard GWR models use a single distance-based kernel for all variables, which may be inadequate when different factors operate at different spatial scales.

To address this, Fotheringham et al. (2017) introduced the Multiscale Geographically Weighted Regression (MGWR) model [36], which enables different explanatory variables to operate at variable spatial scales. MGWR has since been applied in heritage-related contexts, including risk assessment for cultural heritage [39] and rural spatial analysis [40,41,42,43,44,45]. Compared to conventional GWR, MGWR better captures spatial heterogeneity and reduces estimation bias by adjusting bandwidths per variable. The methodological relevance of multi-scale analysis is also supported by recent traditional-village studies [16,22], indicating that traditional village distribution should be understood through both spatial heterogeneity and factor interaction.

Despite these advancements, many studies neglect variables such as cultivated land area, forest cover, transportation networks, and broader socio-economic conditions. Recently, machine learning models like Random Forest (RF) have been introduced to address these limitations [46,47]. RF offers high predictive accuracy and robustness but lacks interpretability due to its black-box nature. To overcome this, model-agnostic tools such as SHAP (SHapley Additive exPlanations) have been employed. Proposed by Lundberg and Lee (2017), SHAP uses cooperative game theory to quantify each variable’s contribution [48], enhancing interpretability for complex models like RF. The TreeSHAP extension allows for efficient, theoretically sound computation in tree-based models [49], along with effective visualization techniques [50].

In parallel with local regression approaches, spatial econometric models such as the spatial lag model (SLM) and the spatial error model (SEM) provide an explicit treatment of spatial dependence, either in the outcome variable itself or in the error structure [51]. Because the residuals of regressions fitted to spatial data frequently remain autocorrelated, residual Moran’s I statistics and local indicators of spatial association (LISA) are standard diagnostics for judging whether spatial dependence has been adequately absorbed. These tools play different roles: machine-learning interpretation (RF-SHAP) identifies predictive relevance rather than causal importance; spatial econometric models diagnose and absorb spatial dependence; and GWR/MGWR explore spatial non-stationarity and the operating scales of individual variables. When the three perspectives share one pre-screened variable set, their results can be compared without confounding differences in model inputs.

The innovation of this study does not rest on introducing RF, SHAP, spatial econometric models, or MGWR individually. It lies in a scale-aware workflow for point-referenced heritage inventories that separates outcome construction, village-scale predictive interpretation, county-level ecological association, spatial dependence, and spatial non-stationarity. The LOO-KDE outcome removes direct self-contribution while retaining the shared-neighbour dependence inherent in a density surface derived from one point pattern. Village-varying predictors and county-level contextual indicators are therefore analyzed separately, and validation is designed to expose rather than conceal spatial leakage and limited geographic transferability. The framework is intended to show which claims can be supported at each analytical scale, while the empirical description of a Lishui-centred multi-core pattern remains specific to southern Zhejiang. For traditional villages and other forms of architectural and regional cultural heritage, identifying spatial concentration and contiguity may also help reveal relationships among building ensembles, settlement morphology, productive landscapes, routes, waterways, ritual spaces, craftsmanship, and collective memory that extend beyond individual village boundaries.

1.4. Research Questions and Objectives

Zhejiang Province, ranking fourth in China for the number of designated traditional villages, is a vital region for such research. Within it, southern Zhejiang is a core cluster area (Figure 1), sharing geographical, climatic, and cultural features. However, modernization has led to growing disparities between its cities, affecting village distribution and preservation. Existing national and provincial studies provide important references, but they often fail to fully capture the distinctive conditions of southern Zhejiang: rugged mountainous terrain, dense river systems, historically clan-based settlements, improved transportation accessibility, and rapid socio-economic restructuring.

Conceptually, path dependence, rural resilience, and cultural-landscape continuity provide reasons to expect spatially structured associations between inherited settlement systems and their environmental and regional contexts [52,53,54,55,56]. These perspectives do not establish tertiary-industry output, income, or city distance as direct measures of modernization pressure. Accordingly, village-scale variables describe local settlement environments, whereas county-level indicators of per capita GDP, rural per capita disposable income, and primary-, secondary-, and tertiary-industry output describe repeated development contexts. These contextual indicators are interpreted only at the county ecological scale after their formal codes are defined in

Table 1. Dependent variable and explanatory variables for traditional villages in southern Zhejiang, with units, spatial scales, and data sources: (N) natural geographic factors; (S) socio-economic factors.

Code	Variable	Definition/Calculation	Unit	Spatial Scale	Data Source	Reference Year
Y	LOO-KDE local clustering intensity	Gaussian leave-one-out KDE calculated from all other recognized villages; focal village excluded	villages km−2	village point	Recognized-village inventory; authors’ Python/GIS calculation	Inventory to 2023
X1	Elevation	DEM elevation extracted at the village centroid	m	village point	ASTER GDEM 30 m, RESDC	Terrain invariant
X2	Slope	Slope derived from DEM at village centroid	degree	village point	ASTER GDEM 30 m; authors’ GIS calculation	Terrain invariant
X3	Slope aspect	Aspect azimuth derived from DEM	degree (0–360)	village point	ASTER GDEM 30 m; authors’ GIS calculation	Terrain invariant
X4	Topographic relief	Maximum–minimum elevation difference within local terrain window	m	local terrain window	ASTER GDEM 30 m; authors’ GIS calculation	Terrain invariant
X5	River level	Order/grade of the nearest mapped river	ordinal grade	nearest river feature	RESDC water-body/river data; authors’ extraction	2023-aligned
X6	Distance to rivers	Euclidean distance from village centroid to nearest mapped river	m	village point	RESDC water data; authors’ GIS calculation	2023-aligned
X7	Cultivated land area	Registered cultivated land area associated with the village	mu (1 mu = 1/15 ha = 666.7 m2)	village unit	Field investigation and local government statistics	2023
X8	Forest land area	Registered forest land area associated with the village	mu	village unit	Field investigation and local government statistics	2023
X9	Geological hazards	Recorded geological-hazard events within 3 km of the village	count	3 km village buffer	RESDC geological-hazard records; authors’ GIS calculation	records to 2023
X10	Distance to the central city	Euclidean distance from village to nearest designated central-city coordinate	m	village point	Compiled city coordinates; authors’ GIS calculation	2023-aligned
X11	Distance to roads	Euclidean distance to the nearest road in the analysis network	m	village point	National 1:250,000 road network; authors’ GIS calculation	2023
X12	Number of households	Registered households in the village	households	village unit	Authors’ field survey and village records	2024 records; surveyed 2025
X13	GDP	Total GDP of the county-level administrative unit	10,000 CNY	county/district context	Taizhou, Wenzhou, and Lishui statistical yearbooks	2023
X14	Per capita GDP	County/district GDP per resident	CNY/person	county/district context	Municipal statistical yearbooks	2023
X15	Rural per capita disposable income	County/district rural disposable income per resident	CNY/person	county/district context	Municipal statistical yearbooks	2023
X16	Primary industry output	Gross output value of the primary industry	10,000 CNY	county/district context	Municipal statistical yearbooks	2023
X17	Secondary industry output	Gross output value of the secondary industry	10,000 CNY	county/district context	Municipal statistical yearbooks	2023
X18	Tertiary industry output	Gross output value of the tertiary industry	10,000 CNY	county/district context	Municipal statistical yearbooks	2023

, with reverse causality and unobserved institutional processes remaining possible.

Accordingly, this study distinguishes two components throughout the paper: the development of a generalizable analytical workflow and its application to the case of southern Zhejiang. The research asks three questions. (1) How can the local clustering intensity of recognized traditional villages be measured without self-contribution bias? (2) Where are the recognized traditional villages in southern Zhejiang locally clustered more strongly? (3) Which village-scale and county-level contextual variables are associated with this clustering intensity, and at which spatial operating scales are these associations expressed?

To answer these questions, this study pursues three objectives: (1) to construct and test a LOO-KDE indicator as a transferable outcome measure for local clustering intensity; (2) to integrate RF-SHAP, OLS, SLM, SEM, GWR, MGWR, residual diagnostics, and sensitivity analysis under one pre-screened variable set so that different modelling assumptions can be compared transparently; and (3) to demonstrate how the workflow can support cautious, spatially differentiated interpretation of heritage settlement clusters while acknowledging the limits of cross-sectional and cross-scale data. The overall workflow is summarized in Figure 2.

2. Materials and Methods

2.1. Case Study Area and Rationale

The southern Zhejiang region refers to the three southernmost municipalities in Zhejiang Province, China, geographically delineated by the Tiantai Mountains, Kuocang Mountains, and Xianxia Mountains. These mountains separate the region from the major basins and plains to the north. Administratively, the study area includes Taizhou, Wenzhou, and Lishui, comprising a total of 30 counties (county-level cities or districts), with a combined land area of 39,428.43 km². Of these 30 units, three contain no nationally, provincially, or municipally designated traditional village and therefore contribute no sampled village records; the remaining 27 units, each represented by at least one sampled village, supply the effective county-level context data used in the ecological analysis. The formal variable codes are introduced only in Table 1.

The study focuses on the traditional villages currently listed as national-level, provincial-level (Zhejiang), and municipal-level traditional villages within the southern Zhejiang region. As of 2025, six batches of traditional villages have been officially designated. Based on the publicized lists of the 1st to 6th batches of national traditional villages, as well as provincial and municipal designations, a total of 612 traditional villages are located in southern Zhejiang, accounting for 45.67% of the 1340 traditional villages in the entire province. This makes the region one of the most densely concentrated areas of traditional villages in southeastern China (Figure 1).

Within this provincial context, southern Zhejiang is appropriate as a case study for testing a cross-scale clustering workflow. It is neither a purely remote mountain region nor a uniformly urbanized coastal belt. Instead, it contains mountainous cores, river-valley corridors, coastal and inland development gradients, and uneven county-level economic restructuring. This combination makes it possible to examine whether recognized traditional-village clusters are associated with both local settlement-environment conditions and broader county-level development contexts.

The case also has methodological value. First, its 612 recognized traditional villages are numerous enough for point-referenced modelling but unevenly distributed enough to expose the problem of spatial dependence and spatial leakage. Second, the sample combines village-scale environmental variables with county-level socio-economic context, allowing the study to test how far a cross-scale framework can be interpreted without falling into village-level causal claims or pseudo-replication. These features make southern Zhejiang a suitable demonstration case, while the workflow itself is intended to be transferable to other rural heritage landscapes where detailed village-level socio-economic data are limited.

2.2. Data Sources

The data used in this study were collected from the following sources:

Traditional village lists: The 1st to 6th batches of national-level traditional villages (a total of 8155 villages) were published on the official website of the Ministry of Housing and Urban–Rural Development of China; the most recent (sixth) batch of the national list was published in 2023. Additional provincial- and municipal-level traditional villages were obtained from the Zhejiang Provincial Department of Housing and Urban–Rural Development. The geographic centroid coordinates of each village were extracted and converted into a vector database in ArcGIS, including fields such as village name, province, city, county (or district), address, and geographic coordinates.

Elevation data: Digital Elevation Model (DEM) data (ASTER GDEM) with a spatial resolution of 30 m for all counties and districts in southern Zhejiang were obtained from the Resource and Environment Science and Data Center (RESDC), Chinese Academy of Sciences (http://www.resdc.cn/; accessed on 19 July 2026).

Land use data: Land use remote sensing data were also obtained from the RESDC, using the 2023 raster dataset at 1 km resolution (https://www.resdc.cn/DOI/DOI.aspx?DOIID=54; accessed on 19 July 2026). From these data, the distribution of water bodies was extracted.

Road network data: National-scale 1:250,000 road network data were sourced from the National Geospatial Information Resources Catalog Service System (2023 edition). These data include national highways, provincial roads, county roads, township roads, other public roads, urban streets, and rural roads.

Socioeconomic data: County- and district-level data on Gross Domestic Product (GDP), per capita GDP, rural per capita disposable income, and the output of the primary, secondary, and tertiary industries were collected from the 2023 statistical yearbooks of the three municipalities (Taizhou, Wenzhou, and Lishui).

Demographic data: Village-scale demographic conditions were measured as the number of households in each village, with the Seventh National Population Census of China (2020) used as background reference data. The household counts themselves were collected through field investigation: each of the 612 sample villages was surveyed by the authors in 2025, and the reported counts reflect the household statistics registered within each village for 2024. The household, rather than the total population, was adopted as the indicator of village scale because it is a basic unit of rural production and daily life in Chinese traditional villages; the corresponding code is defined later in Table 1.

Urban location data: The geographic coordinates of major cities in the study area were compiled for proximity analysis.

Cultivated and forest land area: Data on the area of cultivated and forest land for each village were obtained through on-site surveys and field investigations, supplemented by 2023 statistics provided with the assistance of local government departments.

Geological hazard data: Data on geological hazards were sourced from the RESDC online data platform (https://www.resdc.cn/DataSearch.aspx; accessed on 19 July 2026), using records up to 2023.

All spatial and attribute data were processed in ArcGIS Desktop 10.8 (Esri, Redlands, CA, USA), and the statistical workflow was implemented in Python 3.12.13 (Python Software Foundation). The reproducible environment used NumPy 2.4.6, pandas 3.0.3, GeoPandas 1.1.3, SciPy 1.17.1, scikit-learn 1.9.0, SHAP 0.52.0, libpysal 4.14.1, esda 2.9.0, spreg 1.9.0, mgwr 2.2.1, Matplotlib 3.10.9, and openpyxl 3.1.5. GeoPandas handled spatial data, scikit-learn implemented the Random Forest, SHAP provided TreeSHAP values, spreg implemented the spatial econometric models, mgwr implemented GWR and MGWR, and esda/libpysal supported spatial weights and Moran/LISA diagnostics.

Because multi-source spatial data are updated on different cycles, all variables were aligned as closely as possible to a common reference period centred on 2023: the land use, road network, socio-economic, and geological hazard data all refer to 2023, while household counts reflect 2024 village statistics collected through field surveys in 2025. The remaining temporal differences are small relative to the slow-changing nature of the corresponding variables (terrain, hydrology, and settlement scale), and are acknowledged as a limitation in Section 4.5.

The explanatory variables used in this study were derived from different spatial scales. Village-scale environmental, accessibility, land use, hazard, centrality, and household variables were extracted or recorded for each traditional village and represent local settlement conditions. In contrast, per capita GDP, rural per capita disposable income, and industrial output were obtained at the county level and assigned according to administrative membership. Consistent village-level socio-economic measures corresponding to these county indicators were not publicly available or obtainable through field investigation. All variable codes are introduced only after the indicator system is formally defined in Table 1.

This distinction requires scale-separated analysis rather than a label alone. The village-scale primary specification uses only predictors that genuinely vary among villages in RF-SHAP, OLS, SLM, SEM, GWR, and MGWR. County-level socio-economic indicators are constant for every village within a county and therefore provide far fewer independent realizations than the village sample size; assigning them repeatedly to village rows creates pseudo-replication for village-level inference. They are consequently reserved for a separate county ecological analysis based on represented counties, using the county mean and median LOO-KDE and village count. A mixed-scale model that combines the village-scale predictors with the county-level indicators is reported only as a secondary descriptive sensitivity analysis and is not interpreted as 612 independent village-level effects. The formal codes for both predictor groups are introduced in Table 1 immediately below.

2.3. Indicator System

The spatial distribution of traditional villages is influenced by the interaction of natural geographic conditions and socio-economic processes. Previous studies have commonly considered variables related to topography, hydrology, climate, population, transportation, economic development, and urbanization. While these factors provide a useful basis for understanding traditional village distribution, they may not fully capture the ecological constraints and socio-spatial characteristics of mountainous regions such as southern Zhejiang.

Therefore, rather than directly adopting an existing indicator system, this study constructs a context-sensitive explanatory framework based on the geographical characteristics of southern Zhejiang and the availability of multi-source spatial data. The region is characterized by complex mountainous terrain, dense river networks, extensive forest resources, uneven transport accessibility, and significant differences in village scale and economic development. Accordingly, this study expands the range of explanatory variables by incorporating ecological and settlement-related indicators, such as cultivated land area, forest coverage, geological hazards, distance to major roads, and number of households.

The final indicator system consists of two broad groups: natural geographic factors and socio-economic factors. Natural geographic factors are subdivided into topographic, hydrological, ecological resources, and safety-related factors. Socio-economic factors are subdivided into urbanization-related, transportation, demographic, and economic factors. Altogether, the study includes eight categories of explanatory factors and 18 specific indicator variables, as shown in Table 1. The dependent variable is the leave-one-out kernel density (LOO-KDE) value at each village location, which measures the local clustering intensity of the surrounding recognized traditional villages (Section 2.4.1).

2.4. Methods

The implemented workflow comprised seven reproducible stages: (1) audit 612 point records, identifiers, EPSG:4549 metre-based coordinates, administrative membership, missingness, and coincident points; (2) reconstruct equal-weight Gaussian LOO-KDE with the focal row excluded; (3) screen X1–X12 and use the identical retained set in RF-SHAP, OLS, SLM, SEM, GWR, and MGWR; (4) aggregate mean and median LOO-KDE and village counts to 27 represented county-level units for ecological analysis of county context; (5) tune RF with county-grouped folds and evaluate county- and municipality-held-out transfer; (6) repeat 30 coordinate K-means partitions and 30 independently shifted 50 km grids under 0, h, and 2 h buffers; and (7) compare bandwidth sensitivity, GWR/MGWR operating scales, and residual Moran/LISA diagnostics. Invalid spatial folds were retained in the audit log rather than forced into performance summaries.

2.4.1. Kernel Density Estimation and the LOO-KDE Dependent Variable

Kernel density estimation (KDE) is a spatial analysis method used to measure the concentration of point features in space by applying a kernel function to assign distance-decaying weights within a search radius. It has been widely applied in analyzing spatial distribution patterns of geographic phenomena [57]. The standard KDE is defined as

$$f\left(x\right)={\displaystyle \frac{1}{nh}}{\displaystyle {{\displaystyle \sum }}_{i=1}^n}K\left[{\displaystyle \frac{1}{h}}\left(x-x_i\right)\right]$$

(1)

where f(x) is the estimated kernel density at location x; h is the bandwidth (search radius); n is the number of points within the search window; and K(·) is the kernel function that converts distance into weight.

Figure 1 was generated using the default Kernel Density workflow in ArcGIS Desktop 10.8. Each point was treated as an equally weighted event. The national, Zhejiang Province, and southern Zhejiang panels used search radii of 1.252596958, 0.257038784, and 0.216042493 decimal degrees, respectively, with corresponding cell sizes of 0.020000000, 0.016061372, and 0.016544490 degrees. The displayed value ranges were 0–207.039, 0–724.257, and 0–754.802, respectively. All calculations were performed in the EPSG:4326 coordinate reference system. The three kernel-density surfaces were not compared numerically, used as inputs in any model, or treated as the LOO-KDE outcome variable in this study; they were included solely as cartographic illustrations of the relative degree of spatial clustering.

A direct use of the KDE value at each village location as a dependent variable would be problematic because the focal village itself contributes to its own density estimate, creating a mechanical circularity between the outcome and the observation. To avoid this self-contribution bias, this study constructs a leave-one-out KDE (LOO-KDE) indicator: for each focal village i, the kernel density is calculated from all other recognized villages, with the focal village excluded by setting the diagonal of the pairwise distance matrix to infinity. A Gaussian kernel was used:

$${\widehat{\lambda }}_{-i}\left(s_i\right)={\displaystyle \frac{{10}^6}{2\pi h^2}}{\displaystyle \sum }_{j\ne i}\exp \left[-{\displaystyle \frac{\Vert s_i-s_j{\Vert }^2}{2h^2}}\right]$$

(2)

where s_i is the focal location, j indexes every other village, h is the fixed bandwidth in metres, and the factor 10⁶ converts square metres to square kilometres. The expression is a point-intensity sum and is therefore not divided by n − 1; dividing by n − 1 would estimate an average probability density rather than the reported clustering intensity in villages per square kilometre. The diagonal pairwise distance was set to infinity so that j never equals i.

The main bandwidth was determined by the two-dimensional Scott–Silverman rule of thumb, h = mean(SD_x, SD_y)·n^−1/6, yielding h = 21,006.62 m. Two alternative bandwidths, 0.75 h = 15,754.96 m and 1.25 h = 26,258.27 m, were used for sensitivity analysis (Section 2.4.6). Each village point entered the KDE as an equally weighted event; in particular, the household variable X12 was not used as a KDE weight and was retained only as an explanatory variable, so that the dependent variable reflects the clustering of village entities rather than household intensity.

LOO-KDE is used as a point-referenced measure of the local clustering intensity surrounding each focal village. Excluding the focal village removes its direct contribution to its own density estimate, but it does not make the 612 derived outcomes mutually independent. All values are constructed from the same village point pattern, and nearby focal villages share many kernel-weighted neighbours. The resulting shared-neighbour construction induces structural and spatial dependence before any explanatory model is fitted. This dependence can make ordinary random cross-validation optimistic, complicate conventional regression inference, and contribute to residual spatial autocorrelation. Residual Moran’s I is therefore interpreted as a diagnostic of remaining spatial structure, not as a test that the LOO-KDE outcomes have become independent.

Retaining LOO-KDE as the dependent variable is nevertheless a deliberate and defensible choice. First, the shared-neighbour dependence is not specific to LOO-KDE: any local clustering measure computed from a single realized point pattern, including quadrat counts, nearest-neighbour indices, and local K-functions, reuses the same point locations and therefore carries an analogous dependence structure, so the practical choice is between differently smoothed dependent measures rather than between dependent and independent alternatives. Second, leave-one-out exclusion removes the only dependence component that can be eliminated by construction, the mechanical self-contribution, while preserving the quantity of substantive interest, namely the intensity of other recognized villages surrounding each focal site. Third, the remaining dependence is managed by design rather than ignored: it motivates the county-grouped and buffered validation in Section 2.4.3 and Section 2.4.6, the model-native residual diagnostics in Section 2.4.6, and the restriction of all interpretation to associations with local clustering intensity. Explicit point-process models, such as inhomogeneous Poisson or log-Gaussian Cox process regression, treat the villages themselves as random events and model the intensity surface and its stochastic dependence jointly; they are identified in Section 4.3 and Section 4.5 as a complementary direction. They were not adopted as the primary design because this study requires a fixed village-level outcome that can be passed to heterogeneous interpretive tools, RF-SHAP, global spatial regression, and MGWR, under one common predictor set.

2.4.2. Variable Screening: Correlation and VIF Diagnostics

Variable screening was conducted separately by analytical scale. For the village-scale primary models, Pearson and Spearman correlations and VIF diagnostics were calculated only for X1–X12. All 12 predictors were retained because VIF values ranged from 1.029 to 1.963, and the maximum absolute Pearson correlation was 0.558. The same X1–X12 set was then used in RF-SHAP, OLS, SLM, SEM, GWR, and MGWR. County-level indicators were not screened as 612 independent village observations; they were analyzed with the 27 represented county-level units as ecological observations. A mixed-scale model combining X1–X12 with X14, X15, X16, and X18 was reported only as a secondary prediction sensitivity check.

2.4.3. Random Forest and SHAP

Random Forest (RF) is an ensemble learning algorithm proposed by Breiman, which enhances model performance by integrating predictions from multiple decision trees [46]. Compared with traditional regression models, RF offers high accuracy, robustness against overfitting, effective handling of high-dimensional data, and the ability to output feature importance scores [58]. The ensemble prediction is

$$\hat{\mathrm{y}}\left(x\right)={\displaystyle \frac{1}{N}}{\displaystyle {{\displaystyle \sum }}_{i=1}^N}{T}_i\left(x\right)$$

(3)

where $\hat{y}\left(x\right)$ is the predicted output for input x; N is the number of decision trees; and T_i(x) is the prediction of the i-th tree.

RF tuning evaluated all 144 combinations of n_estimators in {300, 600, 1000}, maximum depth in {unrestricted, 6, 9, 12}, minimum leaf size in {2, 4, 6, 10}, and max_features in {sqrt, 0.50, 0.75}. Each candidate was evaluated with a five-fold GroupKFold using the 27 represented county-level units as groups. The primary criterion was the mean fold RMSE; pooled R2 and MAE were secondary metrics, and held-out test outcomes and OOB scores were not used to select the candidate. Ties were resolved in favour of the less complex candidate. With seed 20260711, the selected configuration contained 300 trees, maximum depth 6, minimum leaf size 4, sqrt feature sampling, and bootstrap sampling. The final full-sample model additionally retained OOB predictions for diagnosis. Candidate-level and fold-level results, the final configuration, and software versions are supplied with the reproducible code.

Although Random Forest models can produce accurate predictions, their black-box nature makes it difficult to interpret which features contribute to predictions of the dependent variable. Therefore, this study adopts SHAP (SHapley Additive exPlanations) to interpret the model outputs. Grounded in cooperative game theory, SHAP quantifies the marginal contribution of each feature to model predictions, offering both local and global interpretability while addressing the limitations of methods like permutation importance and LIME [48]. The TreeSHAP algorithm enables efficient and theoretically consistent computation for tree-based models [49], with effective visualization techniques [50]. SHAP values were computed with the TreeExplainer. RF-SHAP identifies predictive relevance, not causal importance. Throughout this paper, SHAP results are therefore described as predictive contributions or associations rather than as driving mechanisms or determinants.

2.4.4. Global Spatial Regression Models: OLS, SLM, and SEM

The OLS model is a global non-spatial regression method [59,60,61]. The X1–X12 predictors were standardized to z scores, while LOO-KDE remained in villages per square kilometre. Therefore, coefficients represent the response change associated with a one-standard-deviation predictor difference. OLS provides a non-spatial benchmark; its uncertainty is interpreted cautiously when residual spatial autocorrelation remains.

$$y_i={\beta }_0+{\displaystyle {{\displaystyle \sum }}_{j=1}^k}{\beta }_j{x}_{ij}+{\epsilon }_i$$

(4)

where y_i is the dependent variable, β₀ is the intercept, β_j is the regression coefficient of the j-th explanatory variable x_ij, k is the number of explanatory variables, and ε_i is a random error term.

OLS, SLM, and SEM were estimated with z-score-standardized X1–X12 predictors and the original LOO-KDE outcome scale. SLM and SEM used a row-standardized eight-nearest-neighbour (KNN-8) weights matrix. For auditability, the SLM structural fitted value rho Wy + X beta was separated from its covariate-only reduced-form prediction (I − rho W)⁻¹ X beta. For SEM, the systematic prediction X beta and raw residual y-X beta were separated from the filtered innovation and the diagnostic fitted value y minus the filtered innovation. Consequently, response-scale RMSE and R2 were reported under explicitly named definitions; package pseudo-R2 statistics were retained only with their native definitions and were not assumed to be comparable across model classes. Model-native SLM disturbances and SEM filtered innovations were used for residual Moran/LISA diagnostics. Because the estimated spatial parameters are close to one in this application, the structural and filtered quantities are dominated by observed neighbouring outcomes and chiefly measure within-sample reconstruction; the covariate-only definitions measure prediction from the predictors alone and are therefore the appropriate basis for comparing explanatory content across model classes.

$$y=\rho Wy+X\beta +\epsilon$$

(5)

and the spatial error model (SEM) models spatial dependence in the error structure:

$$y=X\beta +u, u=\lambda Wu+\epsilon$$

(6)

where W is the spatial weights matrix, ρ is the spatial autoregressive parameter, λ is the spatial error parameter, and u is the spatially structured error term. Lagrange multiplier (LM) and robust LM diagnostics on the OLS residuals were used to assess the form of spatial dependence.

2.4.5. GWR and Multiscale Geographically Weighted Regression (MGWR)

GWR is a local regression model that embeds the spatial location of the study object into regression parameters based on OLS to explore the spatial relationship between variables at a fixed scale [28,62]:

$$y_i={\beta }_0\left(u_i, v_i\right)+{\displaystyle {{\displaystyle \sum }}_{j=1}^k}{\beta }_j\left(u_i, v_i\right)x_{ij}+{\epsilon }_i$$

(7)

where y_i is the observed value of the dependent variable (the LOO-KDE local clustering intensity); x_ij is the j-th explanatory variable of village i; (u_i, v_i) are the coordinates of village i; β₀(u_i, v_i) and β_j(u_i, v_i) are the local intercept and coefficients; and ε_i is the random error term.

MGWR improves upon GWR by assigning an adaptive bandwidth to each explanatory variable, accounting for differences in spatial scale and variability [36]. MGWR is an improvement of the classical GWR model [63,64], allowing different variables to have their own bandwidth values [65,66]. For variables with strong local variation, MGWR uses narrower bandwidths, while more spatially stable variables are assigned broader bandwidths:

$$y_i={\beta }_{bw0}\left(u_i, v_i\right)+{\displaystyle {{\displaystyle \sum }}_{j=1}^k}{\beta }_{bwj}\left(u_i, v_i\right)x_{ij}+{\epsilon }_i$$

(8)

where bwj indicates the variable-specific bandwidth used for calibrating the j-th coefficient surface, and the remaining notation follows Equation (7).

GWR and MGWR were fitted to the same standardized X1–X12 predictors using adaptive bisquare kernels. GWR bandwidth was selected by AICc golden-section search over 60–612 neighbours (tolerance 1 × 10⁻⁵), selecting 67 neighbours; all 11 evaluated bandwidth-AICc pairs were retained. The initial MGWR search over 60–612 neighbours, started at a common bandwidth of 300, converged, but placed nine terms one neighbour above the lower bound. We therefore extended the audit to lower bounds of 2, 5, 10, 15, 20, 30, 40, 50, 60, and 80 and used initial common bandwidths of 67, 300, and 500 where numerically feasible. New low-domain runs allowed up to 300 backfitting iterations. A start at 11 neighbours failed because of a singular local design matrix, and a start at 20 neighbours was terminated after approximately 44 min without completion. Among converged solutions with no active lower-bound term, the lowest observed AICc was obtained with lower bound 5 and initial bandwidth 500. This revised primary candidate converged after 123 recorded iterations (final score 9.99 × 10⁻⁶) and selected 9 (intercept), 21 (X1), 114 (X2), 611 (X3), 609 (X4), 31 (X5), 22 (X6), 611 (X7), 608 (X8), 37 (X9), 15 (X10), 25 (X11), and 26 (X12) neighbours. Its minimum bandwidth of 9 exceeded the smallest permitted candidate of 6, so the lower bound was inactive. X3 and X7 selected 611 neighbours, the natural near-global limit for a 612-village sample; the result is therefore not fully interior in the mathematical sense. A lower-bound-10 run attained a slightly lower AICc (−6188.301) but retained a boundary intercept and was not eligible under the lower-bound-inactive rule. Because completed starts reached different bandwidth vectors and AICc values, the selected model is described as the best observed converged lower-bound-inactive candidate, not as a proven unique global optimum. The former lower-60 specification is retained as a conservative support sensitivity. Small local bandwidths, near-global upper-bound terms, high effective complexity, multi-start sensitivity, and elevated GWR local condition numbers require exploratory interpretation of coefficient surfaces.

2.4.6. Residual Diagnostics and Sensitivity Analysis

To verify whether spatial autocorrelation remains after estimation, global Moran’s I was computed for the residuals of OLS, SLM, SEM, GWR, and MGWR under the common spatial-weight specification reported separately in Section 2.4.8, with significance assessed by 999 random permutations (alpha = 0.05):

$$I={\displaystyle \frac{n}{S_0}}\cdot {\displaystyle \frac{{{\displaystyle \sum }}_i{{\displaystyle \sum }}_j{w}_{ij}{z}_i{z}_j}{{{\displaystyle \sum }}_i{z}_i^2}}$$

(9)

where z_i is the residual of observation i expressed as a deviation from the mean, w_ij is the spatial weight between observations i and j, and S₀ is the sum of all spatial weights. Local Moran’s I (LISA) was used to identify the locations and types of significant residual clusters (High–High, Low–Low, High–Low, Low–High).

LOO-KDE robustness was evaluated at 0.75 h and 1.25 h, where h denotes the main fixed bandwidth, using Pearson and Spearman correlations and quintile agreement. The two coincident coordinate pairs were retained as distinct inventory records in the main analysis; an additional unique-coordinate event sensitivity quantified their influence. Residual Moran’s I was recomputed under the alternative spatial-weight settings specified separately in Section 2.4.8. These checks distinguish the robustness of the descriptive clustering indicator from the robustness of model transfer.

Predictive robustness was examined through county-grouped tuning, leave-one-county-out prediction, leave-one-municipality-out prediction, 30 coordinate K-means initializations, and 30 independently shifted 50 km grids. For each spatial partition, training villages were retained without a buffer or excluded within one bandwidth (h) or two bandwidths (2 h) of any test village. Training, test, excluded, and valid-fold counts were saved. R², RMSE, and MAE were summarized by mean, median, standard deviation, quartiles, and range. These procedures are described as repeated spatially grouped and buffered holdout validation, not as proof of universally robust geographic transfer.

2.4.7. Consolidated Kernel and Bandwidth Specifications

Table A1. Kernel functions, bandwidth types, numerical values, units, and selection criteria for conventional KDE, LOO-KDE, GWR, and all MGWR terms.

Analysis/Term	Kernel/Weights	Bandwidth Type	Value	Unit	Selection Criterion	Notes
Conventional KDE: China (Figure 1a)	ArcGIS quartic; equal events	fixed distance, data-driven	1.252596958	decimal degrees	approximate ArcGIS default reconstruction	EPSG:4326; PLANAR; SQUARE_MAP_UNITS; cell 0.020000000 deg; display 0–207.039; approximate cartographic reconstruction; descriptive only
Conventional KDE: Zhejiang (Figure 1b)	ArcGIS quartic; equal events	fixed distance, data-driven	0.257038784	decimal degrees	approximate ArcGIS default reconstruction	EPSG:4326; PLANAR; SQUARE_MAP_UNITS; cell 0.016061372 deg; display 0–724.257; approximate cartographic reconstruction; descriptive only
Conventional KDE: southern Zhejiang (Figure 1c)	ArcGIS quartic; equal events	fixed distance, data-driven	0.216042493	decimal degrees	approximate ArcGIS default reconstruction	EPSG:4326; PLANAR; SQUARE_MAP_UNITS; cell 0.016544490 deg; display 0–754.802; approximate cartographic reconstruction; descriptive only
LOO-KDE 0.75 h	Gaussian; equal event weights	fixed distance	15,754.964	m	0.75× main h	Sensitivity outcome; focal village excluded; X12 not a weight
LOO-KDE main	Gaussian; equal event weights	fixed distance	21,006.619	m	isotropic 2D Scott rule	EPSG:4549; h = mean(SDx, SDy)n(−1/6); focal village excluded; X12 not a weight
LOO-KDE 1.25 h	Gaussian; equal event weights	fixed distance	26,258.273	m	1.25× main h	Sensitivity outcome; focal village excluded; X12 not a weight
GWR: all coefficients	bisquare	adaptive nearest-neighbour count	67	neighbours	AICc golden-section search	search 60–612; tolerance 1 × 10−5; all 11 evaluations saved
MGWR: Intercept	bisquare	term-specific adaptive	9	neighbours	AICc golden-section backfitting	selected lower-inactive audit: lower 5; upper 612; init 500; tol 1 × 10−5
MGWR: X1	bisquare	term-specific adaptive	21	neighbours	AICc golden-section backfitting	selected lower-inactive audit: lower 5; upper 612; init 500; tol 1 × 10−5
MGWR: X2	bisquare	term-specific adaptive	114	neighbours	AICc golden-section backfitting	selected lower-inactive audit: lower 5; upper 612; init 500; tol 1 × 10−5
MGWR: X3	bisquare	term-specific adaptive	611	neighbours	AICc golden-section backfitting	selected lower-inactive audit: lower 5; upper 612; init 500; tol 1 × 10−5
MGWR: X4	bisquare	term-specific adaptive	609	neighbours	AICc golden-section backfitting	selected lower-inactive audit: lower 5; upper 612; init 500; tol 1 × 10−5
MGWR: X5	bisquare	term-specific adaptive	31	neighbours	AICc golden-section backfitting	selected lower-inactive audit: lower 5; upper 612; init 500; tol 1 × 10−5
MGWR: X6	bisquare	term-specific adaptive	22	neighbours	AICc golden-section backfitting	selected lower-inactive audit: lower 5; upper 612; init 500; tol 1 × 10−5
MGWR: X7	bisquare	term-specific adaptive	611	neighbours	AICc golden-section backfitting	selected lower-inactive audit: lower 5; upper 612; init 500; tol 1 × 10−5
MGWR: X8	bisquare	term-specific adaptive	608	neighbours	AICc golden-section backfitting	selected lower-inactive audit: lower 5; upper 612; init 500; tol 1 × 10−5
MGWR: X9	bisquare	term-specific adaptive	37	neighbours	AICc golden-section backfitting	selected lower-inactive audit: lower 5; upper 612; init 500; tol 1 × 10−5
MGWR: X10	bisquare	term-specific adaptive	15	neighbours	AICc golden-section backfitting	selected lower-inactive audit: lower 5; upper 612; init 500; tol 1 × 10−5
MGWR: X11	bisquare	term-specific adaptive	25	neighbours	AICc golden-section backfitting	selected lower-inactive audit: lower 5; upper 612; init 500; tol 1 × 10−5
MGWR: X12	bisquare	term-specific adaptive	26	neighbours	AICc golden-section backfitting	selected lower-inactive audit: lower 5; upper 612; init 500; tol 1 × 10−5

reports the kernel function, fixed or adaptive bandwidth type, numerical value, unit, selection criterion, and analytical role for the three reconstructed conventional KDE panels, the main and sensitivity LOO-KDE outcomes, GWR, and every term in the revised primary MGWR.

Table A2. MGWR lower-bound sensitivity. A boundary term selected a bandwidth no more than one neighbour above the imposed lower bound.

Lower Bound	Initial bw	Status	Lower Inactive	Selected Range	R2	Adjusted R2	AICc
2	11	Failed: singular	No	-	-	-	-
2	20	Terminated	No	13–611	-	-	-
2	67	Converged; lower inactive	Yes	12–140	0.998775	0.994764	−4153.255
2	300	Converged; lower inactive; upper active	Yes	9–611	0.998559	0.996168	−6053.290
2	500	Converged; lower inactive; upper active	Yes	9–611	0.998739	0.996147	−5645.049
5	67	Converged; lower inactive	Yes	12–141	0.998777	0.994810	−4193.840
5	300	Converged; lower inactive; upper active	Yes	9–611	0.998598	0.996194	−6001.522
5	500	Converged; lower inactive; upper active	Yes	9–611	0.998401	0.995963	−6155.204
10	300	Converged; boundary	No	11–611	0.997962	0.995153	−6188.301
15	300	Converged; boundary	No	16–611	0.997446	0.993212	−5704.966
20	300	Not converged	No	21–500	0.995828	0.989560	−5596.283
30	300	Converged; boundary	No	31–448	0.992320	0.982939	−5569.445
40	300	Converged; boundary	No	41–526	0.986217	0.974466	−5666.191
50	300	Converged; boundary	No	51–531	0.980482	0.967011	−5653.116
60	300	Converged; boundary	No	61–524	0.974384	0.959467	−5619.522
80	300	Converged; boundary	No	81–611	0.959387	0.943165	−5562.369

and Figure A1 report the lower-bound and multi-start audit, including failed, non-converged, lower-bound-active, lower-bound-inactive, and near-global upper-bound solutions. Conventional KDE, LOO-KDE, GWR, and MGWR are kept distinct because they use different kernels, coordinate units, and inferential roles. The numerical audits underlying the GWR/MGWR bandwidth specifications and residual spatial diagnostics are provided in Supplementary Files S1–S3.

2.4.8. Spatial-Weight Specification

SLM/SEM estimation and the Moran/LISA residual diagnostics do not use smoothing kernels or kernel bandwidths. They use a row-standardized eight-nearest-neighbour (KNN-8) spatial weights matrix, with K = 4, 12, and 16 examined as residual-weight sensitivities. These settings are reported separately in

Table A3. Spatial-weight specifications reported separately from kernel methods.

Analysis	Spatial-Weight Function	K	Standardization	Selection/Role	Notes
SLM and SEM estimation	K-nearest neighbours	8	row-standardized	pre-specified common W	not a smoothing kernel or kernel bandwidth
Residual Global Moran’s I and LISA	K-nearest neighbours	8	row-standardized	same W as spatial regression	999 random permutations
Residual spatial-weight sensitivity	K-nearest neighbours	4, 12, 16	row-standardized	sensitivity around K = 8	reported separately from kernel methods

to avoid conflating neighbourhood weights with KDE or geographically weighted regression kernels.

3. Results

3.1. Overall Distribution Pattern and Local Clustering Intensity

An examination of the spatial distribution of traditional villages in southern Zhejiang reveals that they are primarily concentrated in several specific areas. These include Songyang, Jingning, Longquan, and Jinyun counties in Lishui; Xianju, Tiantai, Linhai, and Sanmen in Taizhou; and Yongjia and Taishun in Wenzhou. Among them, Songyang County in Lishui City exhibits the highest concentration, forming the core of a distinct multi-nucleus concentration pattern. Overall, the spatial structure can be characterized as comprising “two cores and two clusters” (Figure 3). The two cores refer to (1) the high-density concentration of traditional villages within the administrative boundaries of Songyang County, and (2) a second prominent concentration zone formed jointly by Jingning and Longquan. The two clusters refer to (1) a moderately dense distribution at the intersection of Lishui, Taizhou, and Wenzhou, including Jinyun, Xianju, and Yongjia, and (2) another medium-density cluster in northern Taizhou, covering Tiantai, Linhai, and Sanmen.

The LOO-KDE indicator quantified this pattern at individual village locations. At the main bandwidth, the mean was 0.01825 villages km⁻², the median was 0.01684, and the maximum was 0.03381. The 0.75 h and 1.25 h alternatives changed the degree of local smoothing but preserved the broad ordering. Treating coincident coordinate pairs as one spatial event changed LOO-KDE by only 0.000050 on average and produced a Spearman correlation of 0.9999 with the main indicator. The two coincident pairs were therefore retained as distinct recognized-village records, with the unique-coordinate result reported as a sensitivity rather than as an unrecorded deletion.

Geographically, the distribution of traditional villages in southern Zhejiang is closely associated with the combined structure of mountains and river valleys. As shown in Figure 4, most villages are concentrated in hilly and mountainous areas rather than in lowland plains or highly urbanized coastal zones. They are especially dense in the western and southwestern mountainous parts of southern Zhejiang, where high-relief terrain, valley systems, and relatively enclosed settlement environments provide favourable conditions for the long-term continuity of traditional settlements. The village points also show an evident corridor-like pattern along major mountain ranges such as Baishanzu, Kuocang, and Tiantai, forming several mountainous settlement belts. In addition, the river-network layer indicates that many traditional villages are located along main streams and tributary valleys, suggesting that river corridors not only provided water resources and transportation routes, but also shaped the linear spatial organization of settlement clusters. Overall, Figure 4 demonstrates that the local clustering of traditional villages in southern Zhejiang is not randomly distributed, but is strongly related to terrain constraints, valley accessibility, and mountain–water spatial structures.

3.2. Variable Screening Results

The village-scale correlation structure did not require variable deletion. VIF values ranged from 1.029 for X9 to 1.963 for X4, and all tolerances exceeded 0.509. The largest pairwise Pearson correlations were X1–X4 (r = 0.558), X2–X4 (r = 0.513), and X7–X12 (r = 0.426). Accordingly, X1–X12 formed the common primary set for every village-level model. The county context was analyzed separately rather than being allowed to determine village-scale VIF screening (

Table 2. Correlation-screening decision and VIF results for the final X1–X12 village-scale predictor set.

Variable	VIF	Tolerance	Decision
X1	1.727	0.579	Retained
X2	1.407	0.711	Retained
X3	1.032	0.969	Retained
X4	1.963	0.509	Retained
X5	1.169	0.855	Retained
X6	1.067	0.937	Retained
X7	1.528	0.654	Retained
X8	1.378	0.726	Retained
X9	1.029	0.972	Retained
X10	1.134	0.882	Retained
X11	1.189	0.841	Retained
X12	1.543	0.648	Retained

).

3.3. Random Forest Performance and SHAP Interpretation

The selected RF showed substantially different performance across evaluation designs. Apparent training R2 was 0.576 (RMSE = 0.005553), OOB R2 was 0.353 (RMSE = 0.006861), and five-fold county-grouped pooled R2 was 0.115 (RMSE = 0.008026). Leave-one-county-out prediction yielded R2 = 0.066, whereas pooled leave-one-municipality-out prediction was negative (R2 = −0.862). Across 30 repetitions, unbuffered coordinate K-means produced a mean R2 = −0.081, while shifted 50 km grids produced a mean R2 = 0.082. At a one-bandwidth buffer, mean R2 fell to −0.143 and −0.239, respectively; at two bandwidths, it fell to −0.475 and −0.650. These results indicate modest within-region predictive structure but weak spatial transfer once geographic separation is imposed (Figure 5).

TreeSHAP for the final X1–X12 RF ranked elevation (X1; mean |SHAP| = 0.001645), topographic relief (X4; 0.001027), household count (X12; 0.000965), distance to the central city (X10; 0.000685), and forest land area (X8; 0.000551) as the five largest global predictive contributions. Higher elevation and relief generally shifted predictions upward, while larger household count and greater city distance tended to shift predictions downward over substantial parts of their observed ranges. These directions describe the fitted model and do not establish causes of heritage persistence (Figure 6).

Feature stability was stronger for the leading full-sample ranking than for geographically held-out permutation importance. Across 50 bootstrap refits, X1 ranked first in every run; X4 and X12 appeared in the top three in 94% and 82% of runs. However, in five county-grouped test folds, permutation ranks varied, and several mean importance changes approached or crossed zero. The dependence and interaction plots are therefore used to describe nonlinear predictive patterns within the study region, while the spatial holdout results define their limited transferability.

County socioeconomic indicators were excluded from the primary SHAP analysis. In the separate 27-unit ecological analysis, mean county LOO-KDE was negatively correlated with rural per capita disposable income (X15; Spearman rho = −0.632, p = 0.0004) and tertiary-industry output (X18; rho = −0.665, p = 0.0002). Correlations for per capita GDP (X14; rho = −0.308) and primary-industry output (X16; rho = −0.366) were not significant at 0.05. The four-predictor standardized HC3 model had R2 = 0.532 and adjusted R2 = 0.447, but no coefficient was conventionally significant; X15 was borderline (beta = −0.977, p = 0.0502). Because X15 and X18 were collinear at the county scale and n = 27, these findings are ecological associations with substantial uncertainty.

The X1–X12 dependence plots show marked nonlinearity and interactions rather than constant marginal slopes. The interaction summary concentrates the largest joint contributions among the leading terrain, settlement-size, and accessibility variables. Because SHAP interactions inherit the RF’s weak buffered spatial transfer, they are treated as exploratory descriptions of the fitted regional pattern and not as evidence of stable mechanisms (Figure 7 and Figure 8).

3.4. Global Spatial Regression: OLS, SLM, and SEM

OLS explained 30.5% of the in-sample variance (RMSE = 0.007113). Under conventional OLS inference, X1, X4, and X5 were positively associated with LOO-KDE, while X6, X10, and X12 were negative; however, the OLS residual Moran’s I of 0.794 shows that independent-error inference is untenable. The SLM spatial parameter was rho = 0.9846, and the SEM parameter was lambda = 0.9887. In the SLM, X1 was positive, and X10–X11 were negative at p < 0.05; in the SEM, X6, X10, and X11 were negative at p < 0.05. These coefficients describe conditional spatial-model associations and remain sensitive to the shared-neighbour construction of the outcome (

Table 3. OLS, SLM, and SEM coefficients for standardized X1–X12 predictors on the original LOO-KDE scale. SLM/SEM spatial parameters are reported as rho and lambda; KNN-8 weights are row-standardized.

Term	OLS Beta	OLS p	SLM Beta	SLM p	SEM Beta	SEM p
Intercept	0.018250	1.07 × 10−265	−1.93 × 10−4	3.49 × 10−4	−0.022640	3.46 × 10−7
X1	0.003146	1.11 × 10−15	1.56 × 10−4	0.0191	1.78 × 10−4	0.0642
X2	1.14 × 10−4	0.7419	1.12 × 10−5	0.8498	1.53 × 10−5	0.7832
X3	4.21 × 10−4	0.1540	3.45 × 10−5	0.4935	1.12 × 10−6	0.9820
X4	0.001707	3.19 × 10−5	1.08 × 10−4	0.1216	6.10 × 10−5	0.3995
X5	0.001652	2.06 × 10−7	5.00 × 10−5	0.3531	3.13 × 10−5	0.5904
X6	−9.11 × 10−4	0.0025	−9.80 × 10−5	0.0562	−1.17 × 10−4	0.0429
X7	−6.36 × 10−5	0.8595	−7.81 × 10−6	0.8989	2.47 × 10−5	0.7064
X8	5.38 × 10−5	0.8747	−2.21 × 10−5	0.7048	5.65 × 10−5	0.3600
X9	1.97 × 10−4	0.5038	3.71 × 10−5	0.4625	4.79 × 10−5	0.3883
X10	−0.002135	1.34 × 10−11	−1.82 × 10−4	7.45 × 10−4	−2.65 × 10−4	0.0241
X11	−2.47 × 10−4	0.4355	−1.67 × 10−4	0.0021	−1.25 × 10−4	0.0325
X12	−0.001062	0.0034	4.83 × 10−6	0.9378	−1.10 × 10−5	0.8703
rho	-	-	0.984637	0.0000	-	-
lambda	-	-	-	-	0.988723	0.0000

).

The prediction audit resolved the previous apparent contradiction. The SLM package pseudo-R2 was 0.9803; its structural fitted values, which include the observed spatial lag Wy, gave RMSE = 0.001229 and R2 = 0.9792. Its covariate-only reduced form instead gave RMSE = 0.028057 and R2 = −9.8195. The SEM package pseudo-R2 was 0.1615; its systematic X beta prediction gave RMSE = 0.041743, whereas subtracting the spatially filtered innovation from y gave a diagnostic RMSE of 0.001233. Thus, the similar 0.00123 values refer to model-native structural/filtered diagnostics, not to directly comparable covariate-only predictions. All arrays are supplied at the observation level (

Table 4. Definition-audited model fit. SLM structural and SEM filtered rows are in-sample model-native diagnostics; SLM reduced-form and SEM systematic rows are covariate-based predictions. Package pseudo-R2 values are not directly comparable across definitions.

Model/Metric	Definition	R2	RMSE	MAE	Package R2/Pseudo-R2	AIC or AICc
OLS	response-scale fitted value X beta	0.3047	0.007113	0.005871	-	−4290.97
SLM structural fit	rho W y + X beta	0.9792	0.001229	8.93 × 10−4	0.9803	−6266.48
SLM reduced form	(I − rho W)−1 X beta	−9.8195	0.028057	0.026555	0.9803	−6266.48
SEM systematic	X beta	−22.9488	0.041743	0.040889	0.1615	−6256.19
SEM filtered fit	y minus filtered innovation	0.9791	0.001233	8.88 × 10−4	0.1615	−6256.19
GWR	response fitted value	0.9743	0.001368	9.59 × 10−4	0.9743	−5463.77
MGWR	response fitted value	0.9984	0.000341	2.22 × 10−4	0.9984	−6155.20

).

Read plainly, the two similar RMSE values and the two dissimilar pseudo-R2 values answer different questions, and their combination is expected rather than contradictory. With rho = 0.9846 and lambda = 0.9887, both models attribute almost all systematic variation to spatial structure rather than to the covariates, so any fitted quantity that conditions on observed neighbouring outcomes reproduces the observed values almost exactly; this common conditioning, not equivalent covariate content, is why both model-native diagnostics approach RMSE = 0.00123. The package pseudo-R2 values differ sharply only because the SLM statistic is computed from the lag-inclusive structural fit, whereas the SEM statistic is computed from the covariate-only systematic component. Near-unit spatial parameters are themselves consistent with the outcome construction described in Section 2.4.1: a shared-neighbour outcome behaves locally like a spatial average of nearby outcomes, which a spatial-lag or spatial-error specification absorbs into rho or lambda. Under the comparable covariate-only definitions, both models predict weakly, in line with the modest grouped spatial validation of the Random Forest; the prediction audit, the dependence statement, and the validation results therefore corroborate one another.

3.5. GWR and MGWR: Model Comparison and Operating Scales

GWR selected 67 neighbours and achieved R2 = 0.974286, adjusted R2 = 0.956107, AICc = −5463.77, RMSE = 0.001368, and ENP = 253.05. The revised primary MGWR, selected as the best observed converged lower-bound-inactive candidate in the multi-start audit, achieved R2 = 0.998401, adjusted R2 = 0.995963, AICc = −6155.20, RMSE = 0.000341, and ENP = 369.05. Thus, MGWR produced a substantial in-sample reduction in residual error and a lower AICc, but at markedly greater effective complexity, with sensitivity to the search start and near-global upper-bound terms. These are calibration results, not geographically held-out validation, so they do not override the weak RF transfer results or establish universal out-of-region performance.

The revised MGWR bandwidths ranged from nine to 611 neighbours. X3 and X7 selected 611 neighbours, while X4 and X8 selected 609 and 608, indicating nearly global surfaces. In contrast, the intercepts, X10, X1, X6, X11, and X12, used 9–26 neighbours, indicating strongly localized calibration. None selected the lower-bound candidate of six, but the large contrast between local and near-global terms and the strong multi-start dependence show that the objective surface is complex. The GWR local condition number had a median of 95.9, a 95th percentile of 201.8, and a maximum of 2190.4. The mapped MGWR surfaces are therefore presented as exploratory evidence of scale heterogeneity rather than stable pointwise effects (Figure 9).

3.6. Spatial Heterogeneity of MGWR Coefficients

Figure 10 maps the six X1–X12 variables with the largest local coefficient standard deviations in the revised primary MGWR: distance to the central city (X10), elevation (X1), distance to rivers (X6), distance to roads (X11), geological hazards (X9), and river level (X5). Sign changes and localized extremes are visible, but the surfaces should be read together with the multi-start audit, bandwidth scale, effective complexity, and local conditioning diagnostics rather than as independently stable local effects.

County-level coefficient surfaces are not included in the primary MGWR result because repeated county values do not support village-level local-effect inference. Therefore, Figure 10 reports only the X1–X12 surfaces, together with external province, city, and county boundaries for geographic context.

3.7. Residual Spatial Autocorrelation Diagnostics

Under row-standardized KNN-8 weights and 999 permutations, residual spatial autocorrelation remained significant for OLS (Moran’s I = 0.794, p = 0.001), the SLM structural disturbance (I = 0.288, p = 0.001), the SEM filtered innovation (I = 0.298, p = 0.001), and GWR (I = 0.223, p = 0.001). In contrast, the revised primary MGWR residual Moran’s I was 0.002 (p = 0.429). It also remained small and non-significant under K = 4, 12, and 16 (I = 0.008, 0.011, and 0.018; p = 0.349, 0.200, and 0.079). This indicates that the revised MGWR absorbed the residual spatial autocorrelation detectable under the tested KNN definitions. It does not make the shared-neighbour LOO-KDE outcomes mathematically independent, and the very strong in-sample fit, small local bandwidths, and multi-start sensitivity remain important qualifications (

Table 5. Residual global Moran’s I and significant LISA cluster counts for the final X1–X12 models (row-standardized KNN-8 weights; 999 permutations).

Model	Residual Moran’s I	z (Permutation)	p (Permutation)	Significant LISA n	HH/LL/HL/LH
OLS	0.7943	42.62	0.001	328	188/133/4/3
SLM	0.2882	15.59	0.001	156	96/44/9/7
SEM	0.2980	15.96	0.001	172	111/48/8/5
GWR	0.2231	11.53	0.001	124	53/39/20/12
MGWR	0.0021	0.19	0.429	38	2/12/14/10

; Figure 11, Figure 12 and Figure 13).

3.8. Sensitivity Analysis of the LOO-KDE Dependent Variable

The LOO-KDE ordering was robust to bandwidth choice. Relative to the main bandwidth, 0.75 h produced Pearson r = 0.9834 and Spearman rho = 0.9861, while 1.25 h produced Pearson r = 0.9904 and Spearman rho = 0.9886. Exact quintile agreement was 77.8% and 88.6%, respectively, and every village remained within one quintile under both alternatives. The unique-coordinate event sensitivity had Pearson r = 0.99995, Spearman rho = 0.99990, and 99.35% exact quintile agreement. Thus, bandwidth and coincident-point handling did not materially alter the broad spatial ranking (Figure 14).

3.9. Repeated Spatial Validation, County Ecology, and Geographic Transfer

Repeated spatial validation materially narrowed the predictive claim. For coordinate K-means, mean R² across 30 repetitions was −0.081 without a buffer, −0.143 with a one-bandwidth buffer (h), and −0.475 with a two-bandwidth buffer (2 h). For 30 shifted 50 km grids, mean R² was 0.082 without a buffer, −0.239 with a one-bandwidth buffer (h), and −0.650 with a two-bandwidth buffer (2 h). All 30 repetitions remained numerically valid at each buffer, and detailed fold counts identify the training observations removed around test regions. These are repeated, buffered, spatially grouped holdouts; they demonstrate limited geographic transfer rather than universal robustness (

Table 6. RF tuning, administrative transfer, and repeated spatially grouped holdout results for X1–X12. Spatial rows report means across 30 repetitions.

Validation Design	Predictors	R2	RMSE	MAE	Interpretation
apparent_training	X1–X12	0.5762	0.005553	0.004564	diagnostic/grouped estimate
out_of_bag	X1–X12	0.3531	0.006861	0.005656	diagnostic/grouped estimate
county_GroupKFold_pooled	X1–X12	0.1147	0.008026	0.006663	diagnostic/grouped estimate
leave_one_county_out	X1–X12	0.0664	0.008224	0.006804	administrative transfer
municipality_held_out	X1–X12	−0.8620	0.011639	0.009719	administrative transfer
coordinate_kmeans; buffer 0	X1–X12	−0.0807	0.008867	0.007483	mean of 30 repetitions
coordinate_kmeans; buffer h	X1–X12	−0.1426	0.009118	0.007681	mean of 30 repetitions
coordinate_kmeans; buffer 2 h	X1–X12	−0.4753	0.010360	0.008631	mean of 30 repetitions
shifted_50 km_grid; buffer 0	X1–X12	0.0818	0.008162	0.006770	mean of 30 repetitions
shifted_50 km_grid; buffer h	X1–X12	−0.2388	0.009463	0.007768	mean of 30 repetitions
shifted_50 km_grid; buffer 2 h	X1–X12	−0.6503	0.010914	0.008997	mean of 30 repetitions

; Figure 15).

The county ecological analysis used 27 represented units and did not treat village rows as independent replications of the county context. Spearman results were similar for the county mean and median LOO-KDE. The multivariable HC3 model explained 53.2% of standardized mean-LOO-KDE variance, but its coefficient uncertainty and leave-one-county sensitivity preclude strong claims. The negative bivariate associations of X15 and X18 are best understood as contextual contrasts among represented counties, not explanations of why individual villages remained traditional.

Municipality-held-out performance was poor for each city: R2 = −2.200 when Lishui was held out, −0.942 for Taizhou, and −6.078 for Wenzhou; pooled R2 was −0.862. Therefore, the imbalance in sample size (Lishui 390, Taizhou 134, Wenzhou 88) and outcome distribution limits geographic generalization. The main SHAP ranking describes a within-region predictive structure dominated by the Lishui-rich sample and should not be extrapolated to an unobserved municipality (Figure 16).

The final X1–X12 MGWR removed repeated county indicators and was selected from an archived lower-bound and multi-start audit. The revised primary candidate used a 5–612-neighbour search domain, started at 500 neighbours, converged after 123 iterations, and selected term-specific bandwidths of 9–611 neighbours. Its lower bound was inactive, while X3 and X7 reached the natural near-global upper limit. All bandwidths, convergence scores, local coefficients, fitted values, residuals, and competing starts are supplied. The lower-60 model remains a conservative sensitivity, while the revised primary is described as the best observed converged lower-bound-inactive candidate rather than a unique or fully interior global optimum (

Table 7. AICc-selected GWR/MGWR adaptive bandwidths and MGWR local coefficient variability for the X1–X12 specification.

Term	GWR Bandwidth	MGWR Bandwidth	MGWR Mean Beta	Local Beta SD	Local Beta Range
Intercept	67	9	0.019326	0.007057	0.00403 to 0.03148
X1	67	21	5.85 × 10−4	0.001360	−0.00259 to 0.00505
X2	67	114	2.14 × 10−5	6.98 × 10−5	−2.01 × 10−4 to 1.87 × 10−4
X3	67	611	−5.60 × 10−5	5.71 × 10−6	−6.85 × 10−5 to −4.94 × 10−5
X4	67	609	−1.70 × 10−5	6.81 × 10−6	−2.99 × 10−5 to −6.61 × 10−6
X5	67	31	5.54 × 10−5	3.68 × 10−4	−7.50 × 10−4 to 0.00172
X6	67	22	−1.89 × 10−4	7.27 × 10−4	−0.00252 to 0.00205
X7	67	611	−5.14 × 10−5	3.52 × 10−6	−5.64 × 10−5 to −4.57 × 10−5
X8	67	608	1.03 × 10−5	1.50 × 10−5	−5.18 × 10−6 to 3.89 × 10−5
X9	67	37	2.21 × 10−4	3.86 × 10−4	−4.28 × 10−4 to 0.00184
X10	67	15	−6.95 × 10−4	0.001653	−0.00433 to 0.00332
X11	67	25	−3.24 × 10−5	4.79 × 10−4	−0.00116 to 0.00273
X12	67	26	1.30 × 10−4	3.64 × 10−4	−6.49 × 10−4 to 0.00246

).

4. Discussion

4.1. Methodological Contribution and Applicability to Other Cases

The methodological contribution is a scale-aware workflow for measuring and interpreting the local clustering of recognized rural heritage settlements. LOO-KDE excludes the focal village from its own density estimate, thereby removing direct self-contribution, but it does not make the derived outcomes independent because nearby focal villages share many contributors. Therefore, the framework couples scale-separated predictors with dependence-aware validation and residual diagnostics.

A second contribution is the separation of modelling tasks and inferential scales. RF-SHAP identifies nonlinear predictive associations among village-varying predictors; SLM and SEM diagnose spatial dependence; GWR/MGWR explore spatially varying village-scale associations and operating scales; and county socio-economic indicators are examined separately as ecological/contextual associations. Comparisons are meaningful only when the village models use one common confirmed predictor set.

The framework is nevertheless not a substitute for causal historical explanation. Cross-sectional models cannot establish whether modernization indicators weaken clustering, whether heritage clusters shape local development, or whether both are jointly produced by unobserved historical and institutional processes. The workflow is best understood as a diagnostic and comparative tool that can guide more detailed archival, field, and longitudinal research.

4.2. Empirical Insights from the Southern Zhejiang Case

The southern Zhejiang application shows that recognized traditional villages form a multi-core pattern rather than a random distribution. The strongest clustering occurs in the Songyang and Jingning–Longquan areas, with additional clusters around the tri-city junction and northern Taizhou. This pattern is consistent with mountainous and river-valley settlement systems in which historical settlement suitability, relative enclosure, and continuity of rural land use functions have shaped the persistence and recognition of traditional villages.

The results distinguish three kinds of evidence. First, village-scale RF-SHAP consistently placed X1, X4, and X12 near the top within the observed region, but grouped and buffered validation showed weak geographic transfer. Second, OLS, SLM, SEM, and GWR retained significant residual spatial structure, whereas the revised primary MGWR reduced KNN-8 residual Moran’s I to a non-significant value near zero; this improvement is in-sample and accompanies greater effective complexity and multi-start sensitivity. Third, the county mean and median LOO-KDE were negatively correlated with X15 and X18, but the 27-unit multivariable analysis was imprecise. Together, the findings support bounded associations with local clustering intensity, not causal explanations of heritage persistence.

The uneven sample distribution is central to the interpretation. Because Lishui contains most of the sample villages and both major clustering cores, the results primarily reveal the structure of southern Zhejiang as a heritage-dense mountainous region with a strong Lishui core. They should not be overgeneralized as balanced evidence for Taizhou and Wenzhou without the additional municipality-based robustness checks noted in Section 2.4.

4.3. Spatial Dependence, Cross-Scale Data, and Model Boundaries

Residual diagnostics remain important, but they cannot by themselves separate omitted substantive spatial processes from dependence inherited through the shared-neighbour construction of LOO-KDE. Significant residual Moran’s I indicates remaining spatial structure; a value near zero would indicate little residual autocorrelation under the chosen weights, not mathematical independence of the derived outcomes. Planning interpretation must therefore remain diagnostic and associational.

Repeated county-level socio-economic values impose a central inferential boundary. Treating village rows as independent would understate uncertainty and inflate the apparent evidential weight of county indicators. Therefore, this study treats X1–X12 as the village-scale primary model and analyzes per capita GDP, rural disposable income, and industrial output separately, at the county ecological scale. Any 16-variable mixed-scale output is secondary and cannot support village-level SHAP importance, coefficient significance, or local-effect claims.

The revised primary MGWR materially improved in-sample fit relative to GWR and removed detectable residual autocorrelation under KNN-4, 8, 12, and 16. However, this result was obtained with ENP = 369.05, several very local bandwidths, two near-global upper-bound terms, and a path-dependent multiscale search. Different initial bandwidths reached materially different AICc values and coefficient scales; a lower-bound-active solution even attained a lower AICc than the selected lower-bound-inactive candidate. MGWR is therefore retained as an exploratory scale and residual-structure diagnostic, not as proof of a unique optimum, universally superior prediction, or stable causal local effects.

These boundaries also define the intended scope of application of the workflow. It is designed for reasonably dense point-referenced heritage inventories and for diagnostic, within-region questions: measuring local clustering intensity, screening candidate correlates, comparing operating scales, and locating residual spatial structure. For such purposes, generated-outcome dependence is acceptable because it is disclosed, diagnosed, and reflected in deliberately associational language. The workflow is not recommended when confirmatory inference on individual coefficients is the objective, when the inventory is so sparse relative to the bandwidth that a few shared neighbours dominate many outcomes, or when out-of-region prediction is required. In those settings, explicit point-process formulations such as log-Gaussian Cox process regression, or simulation-based propagation of the uncertainty inherited from the generated outcome, provide more defensible uncertainty statements, at the cost of a less direct interface with village-level machine-learning interpretation.

4.4. Implications for Cautious Cluster-Oriented Planning

The results support cautious cluster-oriented thinking rather than direct prescription. In high-clustering mountainous cores, conservation planning may need to consider groups of neighbouring recognized villages, shared valleys, access routes, and landscape settings rather than individual villages alone. In transitional areas, the analysis suggests that road projects, land conversion, and tourism development should be evaluated for their potential effects on the continuity of village clusters. This cluster-oriented view is also consistent with scholarship emphasizing the integrated diversity and living inheritance value of traditional villages [67].

These implications are not direct policy prescriptions derived mechanically from model coefficients. They are planning hypotheses that should be combined with field survey, historical evidence, community consultation, and heritage-quality assessment. The LOO-KDE surface and residual diagnostics can help identify where such qualitative and planning investigations should be prioritized, but they cannot replace local conservation judgment.

4.5. Limitations and Future Work

Several limitations remain. The cross-sectional, policy-conditioned inventory cannot identify causal direction or represent all historically traditional settlements. LOO-KDE removes direct self-contribution but retains shared-neighbour dependence, affecting inference, validation, and residual diagnostics. County analysis is limited to 27 represented units and remains vulnerable to ecological fallacy, multicollinearity, MAUP, and influential counties. Poor municipality and buffered spatial transfer show that fitted RF relationships are not geographically universal. Finally, elevated local condition numbers, small MGWR bandwidths, high effective complexity, and multi-start path dependence mean that the non-significant revised MGWR residual Moran’s I should not be equated with independent outcomes or stable local mechanisms. Future work should combine temporal inventories, archival evidence, field-based heritage-quality measures, community data, external regional validation, simulation-based assessment of generated-outcome uncertainty, and explicit point-process modelling such as log-Gaussian Cox process regression, which treats settlements as random events and models intensity and dependence jointly.

5. Conclusions

This study establishes a reproducible, scale-aware workflow for analyzing local clustering intensity in point-referenced traditional-village inventories. Its contribution is the explicit separation of self-excluding outcome construction, village-scale predictive interpretation, county-level ecological association, spatial dependence, and spatial non-stationarity, together with validation that exposes shared-neighbour dependence and geographic leakage.

In southern Zhejiang, the 612 recognized villages form a multi-core mountain-valley pattern with a pronounced Lishui concentration. The LOO-KDE ranking was stable to bandwidth and coincident-point sensitivity. Within the common X1–X12 specification, elevation, topographic relief, and household count had the largest RF-SHAP contributions, but county-grouped and buffered spatial validation showed only modest or negative transfer performance.

Model comparisons depended on the quantity evaluated. SLM structural and SEM filtered diagnostic fits had nearly identical RMSE around 0.00123 despite different package pseudo-R2 definitions, whereas covariate-only predictions were much weaker. The revised primary MGWR improved in-sample R2 and AICc relative to GWR and reduced residual Moran’s I to 0.002 (p = 0.429), but it also used substantially more effective parameters and was sensitive to the starting bandwidth. Therefore, the result supports multiscale residual reduction within the observed sample, not a claim of a unique global optimum or external predictive superiority.

Overall, the study offers a transferable diagnostic framework and a deliberately bounded case interpretation. County socioeconomic findings are ecological contextual associations, and village-scale findings concern predictive contributions to local clustering intensity. Neither set explains why an individual village retained traditional status. Cluster-oriented conservation may nevertheless be useful for protecting connected building ensembles, settlement morphology, productive landscapes, routes, waterways, ritual spaces, craftsmanship, and collective memory, provided model outputs are combined with field survey, historical evidence, community consultation, heritage-quality assessment, and local planning review.

Use of Artificial Intelligence

During the preparation of this manuscript, the authors made limited use of ChatGPT (OpenAI) to assist with translating parts of the initial draft into English and with language polishing.