Capturing Spatial Non-Stationarity in Agricultural Land Sustainability: A Geographically Weighted Logistic Regression Approach

Abstract

Paddy field sustainability is essential for food security in paddy-dependent countries but is shaped by complex and spatially heterogeneous interactions among environmental, social, and economic factors. Conventional land-use models often assume spatial stationarity, limiting their ability to capture localized dynamics. This study proposes a spatially explicit analytical framework by integrating Geographically Weighted Logistic Regression (GWLR) with multi-layer probabilistic surface analysis to model and classify paddy field sustainability. The framework is applied in Indramayu and Majalengka Regencies, Indonesia, using 400 stratified samples (53% paddy, 47% non-paddy) and 10,000 prediction points. Results show that GWLR outperforms global models, explaining 25.5% of deviance compared to 7.4% for logistic regression. More importantly, it reveals spatially non-stationary relationships: environmental variables exhibit relatively continuous effects, while social and economic variables show strong local heterogeneity. By transforming local coefficients into integrated probability surfaces, this study introduces a novel typology distinguishing stable paddy fields, vulnerable areas, and spatially differentiated sustainability conditions. This approach moves beyond aggregate accuracy metrics and highlights the importance of spatial context in land-use analysis. The proposed framework offers a transferable method to support place-based agricultural protection strategies in complex geographical systems.

1. Introduction

Food security remains a critical challenge for many countries that rely heavily on a single staple crop, particularly in regions experiencing rapid land-use change. This issue has become more urgent as agricultural landscapes face increasing competition from urbanization, industrial development, and demographic pressure [1]. In paddy-dependent countries such as Indonesia, the sustainability of paddy fields plays a decisive role in maintaining food availability, socio-economic stability, and regional development trajectories, consistent with broader evidence linking agricultural land protection to national food security [2]. However, the spatial distribution of paddy fields and their long-term persistence are increasingly shaped by uneven development pressures, especially in densely populated regions where agricultural land competes with urban expansion and infrastructure development.

Previous studies on paddy field sustainability have largely focused on biophysical suitability, emphasizing environmental factors such as soil characteristics, water availability, and topography [3]. These approaches have provided important insights into land capability but often overlook the socio-economic forces that drive land conversion even in physically suitable areas. Empirical evidence suggests that paddy fields with favorable environmental conditions are frequently converted due to population pressure, accessibility to infrastructure, and increasing land values near urban and industrial centers [4]. This indicates that paddy field sustainability emerges from the interaction between environmental suitability and socio-economic dynamics rather than from biophysical conditions alone.

Despite growing recognition of these interactions, most existing studies still rely on global modeling approaches that assume spatially stationary relationships between explanatory factors and land-use outcomes. Such assumptions are problematic in heterogeneous geographic systems, where the influence of environmental, social, and economic factors varies significantly across space [5,6]. Global models tend to obscure local variations, limiting their usefulness for spatially targeted land protection policies. The limitations of global logistic regression in representing spatial complexity have been widely noted in land-use and ecological modeling literature [7,8].

Recent advances in spatial analysis provide opportunities to address this limitation through local modeling approaches that explicitly account for spatial non-stationarity. Geographically Weighted Regression (GWR) and its extension, Geographically Weighted Logistic Regression (GWLR), enable location-specific parameter estimation, allowing researchers to explore how the strength and direction of relationships vary across space [9,10]. GWLR is particularly suitable for modeling binary land-use outcomes, such as the presence or absence of paddy fields, while capturing local variations in driving factors. Recent methodological developments—including multiscale GWR and enhanced kernel optimization—further strengthen the capability of local modeling frameworks to capture complex land-use processes [6]. Despite these advances, several limitations remain in the existing literature on paddy field sustainability and spatial land-use modelling. First, many studies continue to rely on global models that assume spatial stationarity, potentially obscuring localized relationships between land-use drivers and paddy field persistence. Second, previous studies often examine environmental, social, and economic factors separately rather than within an integrated spatial framework. Third, local spatial modelling outputs are rarely translated into operational sustainability typologies or spatial decision-support frameworks that can directly support geographically differentiated agricultural protection strategies.

Accordingly, the novelty of this study lies not merely in the application of Geographically Weighted Logistic Regression (GWLR), but in the integration of multidimensional environmental, social, and economic variables within a unified local spatial modelling framework, combined with GWLR-derived probability surface analysis and spatial typology classification. Unlike many previous GWLR-based land-use studies that focus primarily on coefficient interpretation or prediction accuracy, this study extends local spatial modelling toward spatially explicit sustainability classification and place-based policy interpretation for paddy field protection and development planning.

In this study, we apply GWLR to model the spatial sustainability of paddy fields by integrating environmental, social, and economic variables within a unified spatial framework. The analysis focuses on Indramayu and Majalengka Regencies in West Java, Indonesia—two strategically important paddy-producing regions that exhibit contrasting physical characteristics and development trajectories, consistent with recent spatial analyses of agricultural transformation in Java [11]. By generating spatially explicit probability surfaces and local coefficient estimates, this study proposes how multidimensional factors interact locally to shape paddy field sustainability. The results provide both methodological insights for spatial land-use modeling and empirical evidence to support geographically differentiated strategies for agricultural land protection, aligning with current policy frameworks emphasizing place-based approaches to food security [12,13].

Therefore, this study aims to:

(1)

evaluate spatial non-stationarity in the relationships between environmental, social, and economic factors and paddy field sustainability;

(2)

compare the interpretative capability of global and local spatial models; and

(3)

develop an integrated spatial typology framework based on GWLR-derived probability surfaces to support geographically differentiated paddy field protection and development strategies.

To address these objectives, the study is guided by the following research questions:

(1)

How do environmental, social, and economic variables spatially influence paddy field sustainability?

(2)

To what extent does GWLR improve the interpretation of spatially heterogeneous land-use processes compared to global models?

(3)

How can local probability structures derived from GWLR be translated into spatially explicit sustainability typologies for agricultural land-use planning?

2. Materials and Methods

2.1. Study Area

The study was conducted in Indramayu Regency and Majalengka Regency, West Java Province, Indonesia. The spatial extent and geographic context of the study area are presented in Figure 1. These two regions play a strategic role in national paddy production while exhibiting contrasting geographical and development characteristics. Indramayu represents a lowland agricultural landscape dominated by irrigated paddy fields with high production intensity, whereas Majalengka is characterized by more heterogeneous topography and increasing land-use pressure driven by infrastructure development and urban expansion. The total study area covers approximately 338,508 hectares, encompassing geographically heterogeneous landscapes ranging from lowland irrigated paddy fields and coastal aquaculture zones to upland agricultural and peri-urban areas.

The study area exhibits heterogeneous landscape characteristics, including lowland irrigated rice fields in Indramayu, upland agricultural and forested areas in Majalengka, coastal aquaculture zones, and expanding built-up areas. These contrasting land-cover conditions provide an important spatial context for understanding the variability of paddy field sustainability across the region.

Such spatial contrasts are typical of paddy-producing landscapes undergoing differential development trajectories in Southeast Asia [14,15], making them suitable for examining spatial non-stationarity in the determinants of paddy field sustainability. An overview of the analytical workflow applied in this study, from data preparation through model evaluation and spatial interpretation, is presented in Figure 2.

Based on land use/land cover analysis of the study area, paddy fields constitute approximately 53% of the total landscape, while non-paddy areas (including built-up land, forests, dryland agriculture, and water bodies) comprise the remaining 47%. This composition reflects the agricultural dominance of both regencies while acknowledging ongoing land-use transformation pressures, particularly in peri-urban zones.

2.2. Data Sources and Variables

This study integrates environmental, social, and economic variables to capture the multidimensional drivers of paddy field sustainability. All spatial datasets were obtained from authoritative government sources and processed within a unified spatial framework, following standard GIS data integration practices [16]. A detailed list of all variables, data types, sources, and spatial resolutions is provided in

Table 1. Spatial datasets and variables used in the analysis, grouped into environmental, social, and economic factors. The table summarizes variable types, data sources, and spatial resolutions incorporated into the modeling framework.

No	Category	Variable	Data Type	Source	Spatial Resolution/Unit
1	Environmental	Soil texture	Vector (Original) Raster (processed)	West Java Provincial Government	25 m
2		Soil permeability		West Java Provincial Government	25 m
3		Soil pH		West Java Provincial Government	25 m
4		Rock Formation		West Java Provincial Government	25 m
5		Soil Type		West Java Provincial Government	25 m
6		Rainfall	Vector (Original) Raster (processed)	Geospatial Information Agency	1 km
7		Distance to rivers	Raster (derived)	Geospatial Information Agency	Euclidean distance (m)
8		Wetness index	Raster (derived)	NASA/USGS SRTM (via USGS EarthExplorer)	25 m
9		Slope	Raster (derived)	Geospatial Information Agency	8 m
10		Elevation	Raster	Geospatial Information Agency	8 m
11	Social	Population density	Tabular → raster	Statistics Indonesia	People/km2
12		Pre-prosperous households	Tabular → raster	Indonesian Ministry of Home Affairs	Population
13		Population without formal education	Tabular → raster	Indonesian Ministry of Home Affairs	Population
14	Economic	Distance to roads	Raster (derived)	Geospatial Information Agency	Euclidean distance (m)
15		Distance to built-up areas	Raster (derived)	Geospatial Information Agency	Euclidean distance (m)
16		Distance to paddy mills	Raster (derived)	Field Survey	Euclidean distance (m)
17	Response	Paddy field presence	Vector	Ministry of Agrarian Affairs and Spatial Planning/National Land Agency	Binary (0/1)

to ensure full transparency of the dataset used in this study.

The datasets used in this study were obtained from multiple reference years, including land cover (2018), roads (2018), built-up areas (2018), paddy fields (2019), rainfall (2021), and population data (2023). The primary temporal reference of the study was 2019, particularly for the paddy field dataset used as the main analytical reference.

The selected variables were determined based on their theoretical and empirical relationships with paddy field sustainability, land suitability, agricultural productivity, land conversion pressure, and long-term agricultural persistence. The variables were grouped into environmental, social, and economic dimensions to represent the multidimensional characteristics influencing the sustainability of paddy fields within heterogeneous geographical contexts.

The variables were not assigned subjective weights and were not assumed to have equal influence prior to modelling. Instead, all variables were simultaneously incorporated into the modelling framework, while their relative influence was evaluated statistically through Random Forest variable importance analysis and through the magnitude and spatial variation of coefficients in the Logistic Regression and GWLR models.

2.2.1. Environmental Variables

Environmental variables describe the biophysical suitability of land for paddy cultivation, typically grouped into soil, hydrological, and topographic factors. Soil characteristics such as soil type, texture, depth or permeability, drainage, and pH determine the land’s capacity to support paddy growth and the long-term stability of paddy systems [17]. Hydrological conditions, including rainfall patterns, surface water availability, and proximity to rivers or other water sources, regulate water supply, which is critical for sustaining paddy productivity. Topographic attributes, particularly slope and elevation, influence surface runoff, water accumulation, and erosion risk, thereby shaping the ecological suitability of land for wet paddy cultivation [15].

Taken together, these variables are widely employed in biophysical land suitability and agro-ecological evaluation models for paddy, as they capture both land capability and key ecological constraints that affect the productivity and persistence of paddy fields [18].The inclusion of hydrological and topographic indicators follows established approaches for characterizing environmental suitability in paddy ecosystems [19].

Environmental variables were primarily associated with biophysical suitability and ecological constraints affecting paddy cultivation. Variables such as rainfall, river proximity, Topographic Wetness Index (TWI), soil characteristics, elevation, slope, permeability, and geological formation were included because they influence water availability, soil fertility, infiltration capacity, drainage conditions, erosion potential, and land suitability for rice cultivation.

2.2.2. Social Variables

Social variables capture demographic pressure and socio-economic vulnerability that can accelerate the conversion of paddy fields, even where biophysical conditions remain suitable for paddy cultivation. Indicators such as high population density, a large share of poor or vulnerable households, and low levels of formal education often coincide with stronger incentives to shift land from agriculture to non-agricultural uses [20].

Empirical studies on agricultural land conversion in Java and other Asian paddy-growing regions show that rapid population growth, urban expansion, and limited livelihood options in rural areas increase land values and create pressure on farmers to sell or repurpose their paddy fields. In contexts where many households face economic insecurity and lack access to education or stable off-farm employment, paddy fields become highly vulnerable to conversion for housing, industry, and infrastructure, despite their environmental suitability for continued paddy production [21].

Social variables were selected to represent human capital, demographic pressure, and socio-economic resilience affecting agricultural sustainability and land conversion dynamics. Education level, population density, and welfare conditions were considered important because they influence environmental awareness, land-use pressure, community adaptation capacity, and the long-term persistence of agricultural activities.

2.2.3. Economic Variables

Economic variables describe accessibility and development pressure through distance-based indicators such as distance to roads, distance to built-up areas, and distance to paddy-processing facilities or markets. In the land economics literature, these measures are widely interpreted as proxies for land-value gradients and market accessibility, where locations closer to transport infrastructure and urban centers tend to experience higher land values and stronger incentives for land-use conversion away from agriculture [22].

Empirical studies of land-use and land-cover change show that improved accessibility via road networks and proximity to settlements significantly increases the likelihood that agricultural land, including paddy fields, will be transformed into non-agricultural uses such as housing, industry, and services. In paddy-growing regions, shorter distances to paddy mills and other agro-processing or marketing facilities also reshape farmers’ production and land-use decisions by altering transaction costs and expected returns, thereby reinforcing spatial patterns of land-use change along accessibility gradients [23].

Economic variables were included to represent accessibility, urban expansion pressure, and agricultural economic connectivity. Proximity to roads, built-up areas, and rice milling industries may influence market accessibility, logistics efficiency, development pressure, and the economic viability of maintaining paddy field systems.

2.3. Spatial Data Preparation

All spatial datasets were transformed to a common coordinate reference system and harmonized to a uniform grid resolution to ensure spatial consistency across layers. Vector data were converted to raster format, and continuous surfaces were resampled to match the analytical grid resolution, in line with widely adopted guidelines for preparing multi-source geospatial datasets for spatial analysis and modeling [24].

The spatial preprocessing workflow included coordinate system harmonization, data cleaning, raster harmonization, buffering analysis, slope modelling, Topographic Wetness Index (TWI) derivation, distance analysis, and spatial data integration prior to modelling (Figure 3). All environmental spatial layers were standardized into a common analytical grid to ensure spatial consistency among variables used in the GWLR analysis.

The spatial resolution used in this study was 25 m × 25 m. This grid size was selected primarily to maintain consistency with regional spatial planning map standards commonly applied at the regency level (scale 1:50,000). In addition, the selected resolution represented a compromise between preserving sufficient spatial detail and maintaining computational efficiency for local spatial modelling. The selected grid size also helped reduce excessive artificial precision that may arise when integrating datasets originating from multiple spatial resolutions.

The population density variable was initially derived from village-level tabular population data representing the total population within each administrative village unit. To spatially distribute demographic influence, built-up area maps within each village were used as a proxy for population concentration under the assumption that population distribution is relatively associated with the spatial distribution of built-up areas.

Population density for each village was calculated by dividing the total village population by the total built-up area within the corresponding administrative unit. Subsequently, the spatial influence of population density on surrounding locations was modelled using an inverse-distance approach, where the influence decreases with increasing distance from built-up concentrations (Figure 4).

The resulting influence values were transformed into a continuous spatial influence surface to represent the spatial distribution of population density effects across the study area. A similar spatial transformation approach was also applied to other social variables. In contrast, economic variables were primarily represented through spatial proximity effects rather than density-based influence modelling.

Attribute values were then extracted at the sampling locations, and each variable was normalized to a comparable scale to minimize the influence of differing units and value ranges. Prior to model estimation, multicollinearity among predictor variables was assessed and controlled, following recommendations for regression-based spatial modeling workflows that emphasize the importance of diagnosing inter-variable dependence in geographically weighted or spatial regression frameworks [25].

Spatial data preprocessing, spatial analysis, and map visualization in this study were conducted using ArcGIS software version 10.8. The GWLR analysis was performed using GWR4 software, while Random Forest (RF) and Logistic Regression (LR) analyses were conducted using RapidMiner. No custom programs or scripts were developed in Python for the analyses presented in this study.

2.4. Sampling Design and Data Partitioning

2.4.1. Training and Testing Samples

A stratified random sampling strategy with proportional allocation was implemented to obtain a representative dataset for model calibration and validation. Sample size was determined using the Slovin formula [26]:

n = N/(1 + N × e²)

(1)

where n is the required sample size, N is the population size, and e is the margin of error (set at 5%). This calculation yielded an optimal sample size of 400 points. The adequacy of the sample size was also evaluated using the Isaac and Michael sample size reference, which indicates that for very large populations, the required sample size tends to converge at approximately 349 samples at the 5% significance level. Therefore, the use of 400 sample points in this study was considered statistically sufficient for representing the spatial population characteristics of the study area.

The 400 samples were stratified by land use type with proportional allocation reflecting the actual landscape composition in the study area, where paddy fields constitute approximately 53% and non-paddy areas comprise 47% of the total land cover. Sampling locations within each stratum were selected using simple random sampling to ensure spatial representativeness across both Indramayu and Majalengka regencies.

In addition to statistical adequacy, spatial representativeness was considered during the sampling process. Sample points were spatially distributed across diverse landscape characteristics, including irrigated lowland paddy fields, upland heterogeneous areas, coastal aquaculture zones, and peri-urban transition regions. This distribution was intended to support bandwidth optimization and improve the stability of local coefficient estimation in the GWLR analysis.

Figure 5 shows the spatial distribution of the training and testing samples that demonstrates broad spatial coverage across Indramayu and Majalengka Regencies, including irrigated lowland paddy areas, heterogeneous upland landscapes, coastal zones, and peri-urban transition regions. This spatial distribution was intended to improve the representativeness of heterogeneous landscape conditions and support the stability of local coefficient estimation in the GWLR modelling process.

The sampled observations were subsequently partitioned into training (80%, n = 320) and testing (20%, n = 80) subsets using stratified random split. The training set comprised 163 paddy field locations (50.9%) and 157 non-paddy locations (49.1%), while the testing set consisted of 50 paddy field points (62.5%) and 30 non-paddy points (37.5%). Both subsets maintained proportional representation approximating the 53:47 landscape composition, ensuring that model calibration and validation reflect actual land use patterns in the study area.

2.4.2. Spatial Prediction Grid

For generating spatially continuous probability surfaces and comprehensive spatial classifications, a systematic grid of 10,000 prediction points was created across the entire study area. These prediction points were distributed at approximately 295 m spacing to ensure adequate spatial coverage and resolution for probability mapping and typology classification.

Unlike the training and testing samples, the prediction grid was not used in model estimation or accuracy assessment. Instead, it served as the spatial framework for applying calibrated models to generate wall-to-wall predictions across the landscape, enabling the derivation of spatially explicit outputs that support place-based land-use planning and agricultural protection strategies.

The 400 sample points were used specifically for model calibration and validation, whereas the 10,000 systematically distributed prediction points were used exclusively for generating continuous spatial probability surfaces and spatial typology outputs across the study area.

This dual-component sampling design—combining stratified random samples with proportional allocation for model development and systematic prediction points for spatial inference—enhances both statistical robustness and spatial generalization, aligning with current recommendations for spatial predictive modeling workflows that emphasize representative sampling, explicit validation, and spatially explicit probability mapping [27].

2.5. Modelling Framework

To assess the spatially varying effects of environmental, social, and economic factors on paddy field sustainability, three modeling approaches were applied: global Logistic Regression, Random Forest, and Geographically Weighted Logistic Regression (GWLR). Logistic Regression and Random Forest provide global estimates of factor importance and prediction accuracy, whereas GWLR extends logistic regression by allowing regression coefficients to vary across space, thereby capturing localized relationships between predictors and paddy field outcomes [28]. The use of multiple modeling approaches for spatial prediction is consistent with previous studies that have demonstrated improved representation of land-use dynamics through the integration and comparison of different modeling techniques [29]. A concise overview of the characteristics, assumptions, and analytical roles of the three models is presented in

Table 2. Summary of the three modeling approaches applied in this study, outlining their model structure, analytical purpose, key assumptions, and primary outputs.

Model	Model Type	Primary Purpose	Key Assumption	Main Outputs
Random Forest (RF)	Non-parametric machine learning	Benchmark classification and variable importance under relatively stable biophysical conditions	No parametric form; assumes sufficient training data	Classification map; variable importance
Global Logistic Regression (LR)	Parametric global regression	Baseline estimation of average relationships between predictors and paddy field presence	Spatial stationarity of coefficients	Global coefficients; classification map
Geographically Weighted Logistic Regression (GWLR)	Local spatial regression	Capture spatial non-stationarity and local variation in predictor effects	Relationships vary continuously across space	Local coefficients; probability surfaces; spatial classification

to clarify their comparative functions in this study.

This comparative modeling framework is in line with recent work that contrasts global statistical and machine learning models with spatially explicit or locally weighted approaches to evaluate whether accounting for spatial heterogeneity improves model performance and interpretability. Studies comparing global and local models have shown that geographically weighted and other spatially aware techniques can yield higher predictive accuracy and richer insights into spatially varying drivers than purely global implementations of regression or Random Forest, supporting their use in spatial predictive modeling of land-use processes [30].

2.5.1. Global Logistic Regression

Global logistic regression was implemented as a baseline model to estimate average relationships between the predictor variables and the binary paddy field indicator, implicitly assuming spatial stationarity in the effects of the covariates. Under this assumption, a single set of coefficients summarizes the association between environmental and socio-economic predictors and the probability of paddy field occurrence across the entire study area, providing a useful reference for evaluating the added value of spatially explicit or locally varying modeling approaches [31].

Logistic regression remains one of the most widely applied techniques for modeling binary land-use outcomes because of its clear probabilistic interpretation, the straightforward estimation of odds ratios, and the availability of well-established procedures for model diagnostics and inference. These properties make it a statistically robust and transparent benchmark against which more complex spatial or machine learning models can be compared in land-use and land-cover change studies [32].

2.5.2. Random Forest Model

Random Forest was implemented as a non-parametric benchmark model capable of capturing non-linear relationships and complex interactions among predictor variables in the paddy field dataset. Previous studies have shown that variable importance measures derived from the Random Forest model can be used to assess and compare the relative contribution of environmental, social, and economic predictors to paddy field sustainability [33].

Random Forest has become a standard tool in agricultural and land-use modeling because it delivers high predictive accuracy, handles high-dimensional and noisy data, and provides robust classifications without strong distributional assumptions. These characteristics, originally highlighted in the seminal formulation of the algorithm and reinforced by its widespread application in agricultural and land-use/land-cover studies, justify its use as a strong benchmark alongside more traditional statistical models [34].

2.5.3. Geographically Weighted Logistic Regression (GWLR)

Geographically Weighted Logistic Regression (GWLR) formed the core analytical framework of this study, enabling the modeling of spatially varying relationships between paddy field presence and its environmental, social, and economic determinants. In contrast to global regression models that impose a single set of coefficients for the entire study area, GWLR calibrates a separate local logistic model at each observation location, allowing regression parameters to vary smoothly over space. By adopting GWLR alongside global models, this study aligns with a growing body of research that uses geographically weighted approaches to reveal localized effects that would be obscured under the assumption of spatial stationarity [35].

Local parameter estimates were obtained using a spatial kernel weighting scheme, in which nearby observations exert greater influence on the local regression fit than distant ones, with the kernel bandwidth optimized to balance bias and variance. This framework has been widely recommended for detecting and visualizing spatial non-stationarity in regression relationships, and has been successfully applied in diverse socio-environmental settings, including poverty mapping, health outcomes, and environmental risk assessment [36].

Local coefficients from the GWLR model provide location-specific estimates of how the sign and strength of each predictor’s effect on paddy field presence vary across geographic space. Mapping these coefficients reveals zones where environmental, social, or economic variables exert stronger positive or negative influences, thereby making spatial heterogeneity in driving factors explicit rather than assumed uniform [37].

Recent applications of GWR-type models in land-use analysis similarly interpret spatially varying coefficients to understand how the determinants of land-use change differ across regions, and show that local parameter estimates offer richer insight than global models into place-specific land-use dynamics. These studies demonstrate that geographically weighted approaches can uncover spatial patterns in coefficient magnitude and direction that are crucial for targeted land-use planning and policy design [38].

2.6. Model Evaluation and Validation

Model performance was evaluated using standard classification metrics, with primary emphasis on overall accuracy as a key indicator of model effectiveness in classifying observations. Overall accuracy provides an intuitive measure of the proportion of correctly classified observations across the dataset, reflecting the model’s general predictive capability [39].

Comparative analysis of global versus local models was conducted to assess whether accounting for spatial non-stationarity leads to improvements in predictive performance and explanatory power, following established practices in spatial regression and geographically weighted modeling. In line with recent spatial predictive modeling studies, this comparison focuses on whether local, spatially explicit models can outperform global specifications in both accuracy metrics and the ability to reveal spatially varying relationships relevant for land-use planning [40].

2.7. Spatial Outputs and Interpretation

The final outputs of the analysis included spatially explicit probability surfaces representing the predicted likelihood of paddy field sustainability across the landscape, together with maps of local GWLR coefficients and a derived spatial typology of paddy field priority classes. These products make it possible to visualize how the strength and direction of environmental, social, and economic drivers vary spatially, and to delineate zones where different combinations of suitability, social pressure, and economic accessibility create distinct vulnerability or priority patterns [41].

Such spatially explicit outputs are consistent with land-use and agricultural planning literature that advocates place-based approaches to sustainability, in which policies and protection strategies are geographically differentiated according to local biophysical conditions and socio-economic contexts. By integrating probability mapping, local coefficient surfaces, and a priority typology, the framework supports the design of targeted land-protection and management interventions tailored to specific areas rather than applying uniform measures across the entire region [42].

3. Results

3.1. Model Performance Comparison

The performance of Random Forest (RF), global Logistic Regression (LR), and Geographically Weighted Logistic Regression (GWLR) was evaluated using standard classification metrics and spatial diagnostics. The RF model achieved training, testing, and prediction accuracies of 71.50%, 62.50%, and 61.84%, respectively, while the global LR model produced accuracies of 62.50%, 63.75%, and 62.86%. These performance differences are consistent with the strengths of non-parametric ensemble methods in capturing non-linearities and variable interactions, while logistic regression provides stable global estimates under linearity assumptions [43]. A complete summary of these performance metrics, including accuracy values and spatial diagnostic indicators for all three models, is presented in

Table 3. Summary of performance metrics and spatial diagnostics for the Random Forest (RF), global Logistic Regression (LR), and Geographically Weighted Logistic Regression (GWLR) models. The table reports accuracy-based measures for global models (RF and LR) and spatial diagnostic indicators for GWLR, highlighting key differences in model behavior and their ability to capture spatial non-stationarity.

Aspect	RF	LR	GWLR
Model type	Global, non-parametric	Global, parametric	Local spatial model
Accuracy (train/test)	71.50/62.50	62.50/63.75	Not applicable
Prediction accuracy (%)	61.84	62.86	Not applicable
Spatial diagnostics	None	Deviance explained (7.4%)	Deviance explained (25.5%)
		AIC: 433.360	AIC: 401.272
		AICc: 434.217	AICc: 410.362
Captures spatial non-stationarity	No	No	Yes
Interpretability	Moderate	High (global coefficients)	Very high (local coefficients)

. RF and LR are compared using classical accuracy metrics. LR and GWLR are compared using spatial model diagnostics (AIC, deviance explained) and interpretability. GWLR is not intended to maximize classification accuracy but to reveal spatially varying relationships that global models cannot capture.

3.2. Spatial Classification Patterns

Spatial comparison of classification maps shows distinct error behaviors among the three models. The spatial distribution of correctly and incorrectly classified locations for each model is shown in Figure 6. RF tends to over-predict paddy fields in coastal aquaculture zones, likely due to its sensitivity to dominant training patterns—a phenomenon commonly documented in RF-based land classification [44]. In contrast, global LR under-predicts paddy fields in intensively cultivated areas, aligning with the model’s known conservatism under spatial heterogeneity [45].

GWLR demonstrates a more balanced spatial error distribution, especially in transition zones between agricultural and non-agricultural areas. This improved performance reflects the ability of local models to account for contextual land-use dynamics, consistent with findings from spatially explicit agricultural land studies [9].

3.3. GWLR Kernel Selection and Model Diagnostics

Four geographic kernels were evaluated: Fixed Gaussian, Fixed bi-Square, Adaptive bi-Square, and Adaptive Gaussian. A full comparison of kernel characteristics and diagnostic metrics is presented in

Table 4. Comparison of GWLR kernel configurations, including weighting functions, bandwidth characteristics, and model diagnostic measures (deviance, AIC, AICc, BIC/MDL, and deviance explained). The table summarizes the performance of four alternative kernels evaluated in the study.

Criterion	Fixed Gaussian	Fixed bi-Square	Adaptive bi-Square	Adaptive Gaussian
Bandwidth	Distance based	Distance based	Nearest neighbor based	Nearest neighbor based
Weighting	Exponentially decreases with distance	Quadratically decreases and becomes zero beyond a certain distance	Quadratically decreases and reaches zero beyond a certain neighborhood	Exponentially decreases without a clear cutoff
Characteristic	Exponential functions characterized by rapid changes in magnitude	Quadratic functions characterized by gradual and consistent changes in values	Places strong emphasis on local influence within a defined spatial range	Allows for a broader and more gradual influence from distant data points
Bandwidth size	15,008.583	50,864.169	6.000	72.000
Deviance	330.461	363.677	360.788	355.676
Classic AIC	401.272	413.052	411.872	407.703
AICc	410.363	417.361	416.492	412.499
BIC/MDL	534.693	506.081	508.122	505.730
Percent deviance explained	0.255	0.180	0.187	0.198

to summarize their weighting functions, bandwidth parameters, and model performance indicators. The Fixed Gaussian kernel produced the lowest deviance (330.461), AIC (401.272), AICc (410.363), and BIC/MDL (534.693), along with the highest deviance explained (25.5%). The superior performance of the Fixed Gaussian kernel suggests a continuous spatial decay function, aligning with theoretical expectations that gradual weighting functions perform better in homogeneous and highly connected landscapes [46].

The relative underperformance of adaptive kernels may reflect the landscape’s ecological continuity and administrative integration, which favor distance-based smoothing rather than neighborhood-based kernel adaptation, as observed in other multiscale GWR applications [47].

To further evaluate the spatial performance of the GWLR model, Moran’s I analysis was conducted on the residuals associated with the environmental, social, and economic variable groups. The residuals exhibited relatively weak positive spatial autocorrelation, with Moran’s I values ranging approximately from 0.05 to 0.08 and z-scores around 2.0–2.35 (Figure 7). These results indicate limited residual spatial clustering, suggesting that the GWLR model successfully captured the major spatial structure present in the data, although a relatively low level of residual spatial dependency remained. Such residual conditions are relatively common in complex land-use systems where certain localized processes and unobserved factors may not be fully represented within the modelling framework.

3.4. Spatial Probability Surfaces

Spatial probability surfaces generated using GWLR reveal distinctive patterns for each variable group. These probability surfaces for environmental, social, and economic variable groups are illustrated in Figure 8. Environmental variables exhibit smooth and structured gradients aligned with physiographic conditions, consistent with prior observations in environmental suitability modeling. Social variables produce fragmented probability surfaces marked by sharp local contrasts, indicating strong spatial heterogeneity—a characteristic commonly identified in socio-demographic land-use drivers [48].

Economic variables display intermediate gradients, with patterns shaped by accessibility and development pressure. This reflects well-established spatial economic theories linking distance-based indicators to land conversion risks. These multi-scale probability structures confirm that environmental, social, and economic drivers operate at different spatial resolutions.

3.5. Local Coefficient Patterns

Local GWLR coefficients show strong spatial variability in both magnitude and direction across all variable groups, confirming the presence of spatial non-stationarity in the determinants of paddy field sustainability. To illustrate this spatial heterogeneity, three variables were selected for detailed visualization based on the stability, magnitude, and spatial contrast of their local coefficient surfaces (Figure 9).

Soil texture was selected to represent environmental variables because it exhibits the highest spatial smoothness and strongest biophysical gradient structure, with distinct coefficient clusters aligned with physiographic zones. Population density was chosen from the social group due to its pronounced coefficient variability, including sign reversals across rural–urban transitions that indicate high sensitivity to localized demographic pressures. Distance to roads was selected from the economic group because it generates the steepest spatial gradients in coefficient values, capturing accessibility-driven development pressure and market proximity effects with minimal noise. These three variables collectively provide the clearest technical evidence of GWLR’s ability to resolve local parameter variation across heterogeneous landscapes.

Environmental predictors—including soil texture, permeability, rainfall, slope, and elevation—exhibit geographically varying influence patterns consistent with agro-ecological zonation principles [49]. Soil texture coefficients show positive values in lowland irrigated zones but negative values in upland areas, reflecting differential soil-water-crop interactions across topographic gradients. Social variables demonstrate dual effects, with population density alternating between positive coefficients in areas with agricultural intensification and negative coefficients in peri-urban zones experiencing conversion pressure, consistent with documented spatial disparities in demographic land pressures [50].

Economic variables show the highest contextual dependency, particularly for distance-based indicators linked to roads, built-up areas, and paddy mills. Distance to roads displays positive coefficients in remote agricultural areas where isolation provides protection from development, but negative coefficients near urban centers where accessibility increases land values and conversion risk. These spatial shifts in coefficient sign and strength reflect development-driven land-value gradients, as noted in recent spatial economic modeling studies [51].

The overall distribution of local coefficients across all variable groups reinforces the presence of spatial non-stationarity and validates the necessity of local modeling frameworks for capturing heterogeneous land-use processes [40].

3.6. Spatial Typology of Paddy Field Sustainability

Integration of environmental, social, and economic probability outputs with existing paddy field data produced a four-dimensional typology comprising sixteen possible combinations. A detailed classification of all sixteen spatial combinations and their corresponding priority levels is presented in

Table 5. Spatial typology of paddy field sustainability based on the integration of existing paddy fields with environmental, social, and economic suitability layers. The table lists all sixteen land-suitability combinations and their corresponding protection or development priority classes.

No	Land Suitability Combination (Existing-Env-Soc-Eco)	Number of Points	Description
1	1-1-0-1	557	Paddy field protection Priority 1
2	1-1-1-0	143	Paddy field protection Priority 1
3	1-1-1-1	2259	Paddy field protection Priority 2
4	1-0-1-1	700	Paddy field protection Priority 3
5	1-1-0-0	81	Paddy field protection Priority 3
6	1-0-0-1	750	Paddy field protection Priority 4
7	1-0-1-0	289	Paddy field protection Priority 4
8	1-0-0-0	503	Paddy field protection Priority 4
9	0-1-1-1	450	Paddy field development Priority 1
10	0-1-0-1	153	Paddy field development Priority 2
11	0-1-1-0	468	Paddy field development Priority 2
12	0-1-0-0	287	Paddy field development Priority 3
13	0-0-1-1	427	Paddy field development Priority 3
14	0-0-0-1	781	Paddy field development Priority 4
15	0-0-1-0	652	Paddy field development Priority 4
16	0-0-0-0	1500	Paddy field development Priority 4

. These were aggregated into priority classes for paddy field protection and potential expansion. Areas with strong multi-dimensional support exhibit the highest sustainability and align with findings that multi-factor agricultural stability enhances long-term land retention [52].

Priority determination in this study follows two complementary logics: protection of existing paddy fields and expansion of new paddy areas. For existing paddy fields, protection priority is defined by the interaction between intrinsic sustainability (primarily environmental suitability) and socio-economic pressures, whereby highly suitable areas under emerging conversion pressure receive the highest priority due to their elevated risk of loss. Conversely, for non-paddy areas, expansion priority hinges on feasibility, with environmental suitability as a prerequisite and socio-economic factors indicating implementation readiness. Areas with strong multi-dimensional support are prioritized for expansion, whereas those with substantial constraints are considered unsuitable. This integrated framework enables spatially explicit decision-making that simultaneously safeguards existing paddy systems and guides sustainable agricultural expansion. The resulting spatial typology of paddy field sustainability is illustrated in Figure 10.

4. Discussion

4.1. Added Value of Local Spatial Modelling

The results demonstrate that global and non-spatial models, such as Logistic Regression and Random Forest, are limited in their ability to capture spatial heterogeneity in paddy field sustainability. While these models provide reasonable overall accuracy, their uniform parameterization assumes spatial stationarity, which is rarely satisfied in heterogeneous agricultural landscapes. Similar findings have been documented in land-use models where global estimators oversimplify spatially varying processes [7].

In contrast, GWLR explicitly accommodates spatial non-stationarity by allowing relationships between predictors and paddy field presence to vary locally. This capability proves particularly valuable in regions where environmental suitability, social pressure, and economic accessibility interact differently across space. The improvement observed in GWLR is therefore not solely reflected in accuracy metrics, but more importantly in its ability to reveal spatially differentiated processes. This reinforces earlier work highlighting the superiority of local regression approaches for uncovering fine-scale land-use dynamics in complex geographical systems [49].

4.2. Differential Spatial Roles of Environmental, Social, and Economic Factors

The spatial probability surfaces and local coefficient maps indicate that environmental, social, and economic factors exhibit distinct patterns of spatial variability. Environmental variables produce relatively continuous spatial patterns, reflecting gradual changes in biophysical conditions such as soil properties, rainfall, and topography. These findings are consistent with ecological gradient theory and previous studies on environmental suitability for paddy ecosystems [53].

In contrast, social variables exhibit highly fragmented spatial patterns, suggesting strong local dependency. Population density has been widely recognized as an important driver of land-use dynamics and spatial land-use patterns [54]. Population density and socio-economic vulnerability influence paddy field sustainability in a context-specific manner, where similar demographic pressures may result in different land-use outcomes depending on local governance, land tenure, and institutional settings—patterns widely observed in rapidly transforming agricultural regions [55].

Economic variables show intermediate spatial behavior, with distance-based indicators capturing development gradients that vary across accessibility corridors and urban influence zones. This is aligned with land economics literature emphasizing that accessibility and market proximity strongly influence land conversion incentives [56].

Taken together, these findings underscore the inadequacy of single-scale modeling approaches and highlight the importance of spatially adaptive methods for land-use analysis [57].

Several sources of uncertainty should be acknowledged in this study. These include differences in raster resolution among datasets, the use of village-level administrative social data, spatial influence variables derived from distance-based analysis, and the integration of multi-source spatial datasets with different temporal references. To reduce these uncertainties, preprocessing and harmonization procedures were applied, including coordinate system standardization, spatial grid standardization, raster harmonization, and proportional spatial sampling.

This study employed a spatial cross-sectional modelling framework and did not explicitly incorporate temporal or spatiotemporal change analysis into the calculations. Therefore, the datasets do not represent fully synchronized temporal conditions, but rather a combination of the most relevant and available datasets representing relatively comparable regional conditions. Consequently, the results should be interpreted primarily as a spatial representation of paddy field sustainability conditions rather than as a dynamic temporal change model.

4.3. Interpreting Local Coefficients and Spatial Non-Stationarity

The substantial spatial variation observed in GWLR coefficients confirms the presence of spatial non-stationarity across all variable groups. The direction and magnitude of variable effects differ markedly between locations, indicating that paddy field sustainability cannot be explained by uniform relationships—a result frequently found in non-stationary geographic processes [58]. For example, proximity to infrastructure may enhance paddy field persistence in areas with strong irrigation networks, while accelerating conversion in rapidly urbanizing zones, consistent with contrasting rural–urban interface dynamics noted in prior studies [59].

This dual behavior illustrates how identical variables can exert contrasting influences depending on local spatial context. Such insights cannot be obtained from global models and represent a key methodological contribution of this study. By mapping local coefficients, GWLR provides an interpretable framework for understanding place-specific land-use processes, consistent with the growing emphasis on spatial explainability in contemporary geographical analysis [60].

4.4. Implications for Spatial Classification and Priority Mapping

The spatial typology derived from integrating environmental, social, and economic probability outputs demonstrates the analytical advantage of combining multiple dimensions within a spatial modeling framework. Multidimensional classification approaches have been increasingly recommended for agricultural land assessment because single-variable suitability maps often mask complex spatial trade-offs [61].

Rather than classifying paddy fields based solely on physical suitability or conversion risk, the typology captures local sustainability conditions shaped by both biophysical and socio-economic drivers. This allows more nuanced spatial differentiation, distinguishing areas requiring strict protection from those where adaptive management strategies may be appropriate. Spatial multi-criteria typologies such as this one are consistent with contemporary spatial planning frameworks emphasizing place-based agricultural governance [62].

Importantly, the typology is not intended as a rigid zoning instrument, but as a spatial decision-support tool that reflects underlying geographic complexity—a principle aligned with recent recommendations in sustainable land-use planning [63].

The spatial typology results also suggest that geographically differentiated governance strategies may be more appropriate than uniform agricultural protection policies. In the study area, paddy field sustainability is shaped not only by environmental suitability, but also by varying socio-economic pressures and development trajectories across locations. Therefore, conservation and agricultural planning strategies should be adapted to the dominant local characteristics of each typology class.

This finding is particularly relevant in the context of existing agricultural land protection policies in Indonesia, including the Sustainable Agricultural Land Protection policy (LP2B), which aims to prevent uncontrolled paddy field conversion. In rapidly developing areas, especially peri-urban zones influenced by infrastructure expansion and accessibility growth, environmentally suitable paddy fields may still face high conversion pressure due to socio-economic and market factors. In such cases, protection-oriented strategies supported by spatial zoning regulations and agricultural incentives become increasingly important.

For example, the 1-1-1-1 typology represents existing paddy fields supported simultaneously by environmental suitability and favorable social and economic conditions. These areas may be interpreted as relatively stable agricultural landscapes where long-term conservation strategies should be prioritized. In contrast, the 1-1-0-0 typology represents existing paddy fields with strong environmental suitability but weak social and economic support. Although these areas remain physically suitable for paddy cultivation, they may become vulnerable to land conversion due to limited socio-economic resilience. Consequently, policy interventions such as LP2B protection, agricultural incentives, and strengthening of local agricultural economic infrastructure may help reduce conversion pressure and improve sustainability.

Meanwhile, typologies such as 1-0-1-1 indicate situations where social and economic conditions remain supportive, but environmental suitability is relatively constrained. These areas suggest the need for more detailed investigation into limiting environmental factors affecting paddy cultivation suitability, such as topography, hydrological conditions, or soil characteristics. Although environmental constraints are generally more difficult to modify directly, identifying the dominant limiting factors may support more adaptive and locally appropriate agricultural management strategies.

4.5. Methodological Limitations and Scope

While GWLR offers substantial advantages in capturing spatial heterogeneity, it also entails limitations. The explanatory power, as measured by deviance explained, remains moderate, reflecting the inherent complexity of land-use systems influenced by unobserved institutional, cultural, and policy factors. Similar levels of explanatory power have been reported in other spatial logistic models applied to heterogeneous agricultural landscapes [64].

Moreover, the selective application of RF and global LR as benchmark models for environmental variables represents a deliberate methodological choice aimed at isolating the contribution of local spatial modeling under relatively stable biophysical conditions. Alternative configurations—such as multi-scale GWLR or spatial machine learning hybrids—may further enhance explanatory performance, as suggested by recent advances in spatial modeling [65].

Future research may explore multi-scale extensions of GWLR or integrate temporal dynamics to further enhance explanatory capacity. Nevertheless, the current framework provides a robust foundation for spatially explicit analysis of paddy field sustainability.

4.6. Contributions to Geographical Systems Research

This study contributes to geographical systems research by demonstrating how local regression techniques can be applied to model agricultural land sustainability within a multidimensional spatial context. By integrating environmental, social, and economic factors and explicitly addressing spatial non-stationarity, the proposed framework advances methodological practice in spatial land-use modeling.

Beyond the specific case of paddy fields, the approach is transferable to other land-use systems characterized by heterogeneous drivers and localized interactions. Similar findings have emerged in recent geographical systems research emphasizing the need for spatially adaptive modeling in complex socio-ecological systems [66]. As such, the study reinforces the relevance of spatially adaptive techniques in understanding and managing geographically complex landscapes.

5. Conclusions

This study demonstrates that paddy field sustainability is governed by spatially heterogeneous processes that cannot be captured by global models. Environmental variables generate continuous spatial patterns aligned with physiographic conditions, social variables exhibit strong local heterogeneity reflecting demographic pressures, and economic variables display context-dependent dual behavior—supporting sustainability in some areas while inducing conversion elsewhere. This spatial variation necessitates place-based interpretation of land-use sustainability.

GWLR with a Fixed Gaussian kernel outperforms global models (Random Forest, Logistic Regression) by capturing spatial non-stationarity, improving deviance explained from 7.4% to 25.5%. Critically, aggregate accuracy metrics inadequately evaluate spatial models; local coefficient patterns and error distributions provide more substantive insight. The resulting spatial typology integrates probability surfaces across variable dimensions to distinguish stable paddy fields, vulnerable areas, and development potential zones, functioning as a decision-support framework.

For geographical systems research, this study advances local regression techniques for agricultural sustainability modeling. For policy, results emphasize the need for place-based approaches aligned with locally specific conditions rather than uniform regulations. Future research should incorporate temporal dynamics, institutional variables, and multi-scale models.