Spatial Analysis Using Geographically Weighted Ordinary Logistic Regression (GWOLR) Method for Prediction of Particle-Size Fraction in Soil Surface

Spatial analysis is a method used to understand the spatial variation of geospatial data. In this study, the Geographically Weighted Ordinary Logistic Regression (GWOLR) method was used in spatial analysis to predict the particle size fraction of the surface soil. The particle size fraction of the surface soil is an important parameter in determining soil productivity and environmental quality. However, the particle size fraction in surface soils can vary spatially and is influenced by geographical factors such as elevation, rainfall, and soil texture. This study will be carried out by collecting particle size fraction data and geospatial data at randomly selected locations. Accurate modelling of soil texture is necessary because it‘s a crucial factor in determining how soil management will go. However, because soil texture is a compositional data set, it is one of the soil attributes that is more challenging to model. The challenge presented by this compositional data set is the imposition of constant quantities, specifically the requirement that the total of the fractions of clay, silt, and sand be 100%. Topographical variability can be derived from DEM data, making it an independent variable or predictor for soil texture prediction. The data will then be analyzed using the GWOLR method to predict the particle size fraction at locations that have not been observed before. The resulting prediction model will then be evaluated using cross-validation to check the accuracy of the model. This study will provide benefits for land management and natural resource management and can improve understanding of the spatial variation of particle size fractions in surface soils and the spatial and geographical factors that influence them. The GWOLR model for predicting particle size fractions in surface soils was carried out with a fixed bi-square weight and a bandwidth of 0.28895. The GWOLR model classification accuracy value is 94 percent, this shows that the GWOLR model for predicting soil particle size is more suitable than the ordinal logistic regression model with a classification accuracy of 90 percent. The aims of this study are to: (1) Establish a soil texture prediction model using the GWOLR method; and (2) Test the reliability of the model in predicting surface soil texture.


Introduction
In the past few decades, there has been an acceleration in the development of spatial modeling for soil properties.This is an answer to the problem of the critical need for spatial data on soil in order to accomplish the acceleration of precision farming operations.The practice of precision farming involves utilizing novel technology to enhance agricultural productivity and financial gain while reducing the usage of conventional inputs such as soil, water, fertilizers, pesticides, and herbicides.Put differently, farmers that utilize precision farming maximize yield by utilizing less resources.Here, modeling provides a means of obtaining fundamental quantitative data for guiding land management decisions.
Accurate modeling of soil texture is necessary because it's a crucial factor in determining how soil management will go.It is impossible to overstate the significance of soil texture.The shape and stability of the soil structure, as well as the passage of water, heat, and nutrients, are all influenced by the texture and, of course, the distribution of particle sizes in the soil [1].On the other hand, because soil texture is a compositional data set that specifies the particle size of the soil mineral fraction with variables for sand, silt, and clay, it is a relatively challenging soil attribute to model [2].This compositional data set presents a challenge because it only includes constant numbers, such as the total of the fractions of sand, silt, Particle-size fraction is the size of soil particles that is used to distinguish various types of soil.Predicting the particle-size fraction of surface soils can help farmers and agricultural scientists understand the optimal soil conditions for plant growth and plan appropriate soil management strategies [3].However, conventional analysis cannot take into account the spatial factors that contribute to differences in particle-size fractions at different locations.Therefore, a more accurate and effective spatial analysis approach is needed to understand and predict differences in particle-size fraction in surface soils [4].
Geographically Weighted Ordinary Logistic Regression (GWOLR) is a spatial analysis method that can be used to combine spatial and statistical information in geographic data analysis.In the context of the prediction of particle-size fraction in surface soils, GWOLR can help identify geographical factors that contribute to differences in particle-size fraction in different locations.
Spatial analysis using the Geographically Weighted Ordinary Logistic Regression (GWOLR) method is a geographic data analysis technique used to study the relationship between spatial variables and events or phenomena observed at different locations [5].The GWOLR method combines logistic regression techniques with spatial analysis techniques, thereby enabling researchers to combine statistical and spatial information in geographic data analysis more accurately and effectively [6].
In the GWOLR method, logistic regression is used to model the relationship between independent variables (e.g., soil water content, altitude, and soil type) and observed events or phenomena (e.g., human population density or soil quality).Then, spatial analysis techniques are used to consider the effect of spatial variables on the regression model, making it possible to obtain more accurate and detailed results [7] [8].
The GWOLR method has several advantages over other spatial analysis methods.One of these advantages is the ability to consider the effect of spatial variables on the regression model specifically at each location, making it possible to obtain more accurate and detailed results [9].In addition, the GWOLR method can also be used to study the relationship between spatial variables and events or phenomena that cannot be explained by conventional regression models.
In this study, there are several novelties, namely using a more accurate and effective spatial analysis method: The GWOLR method allows researchers to combine spatial and statistical information in geographic data analysis more accurately and effectively [10].This opens up opportunities to gain a better understanding of the spatial factors that contribute to differences in soil characteristics at different locations.Emphasis on the prediction of particle-size fractions on surface soil: The prediction of particle-size fractions on surface soil is the main focus of this proposal.This is very important because soil characteristics such as nutrient content and soil structure greatly affect plant growth and agricultural productivity.Making a new contribution to research on soil characteristics: Research on soil characteristics is an important and always relevant topic.
Provide more appropriate and effective soil management recommendations: The results from the GWOLR analysis can provide more appropriate and effective soil management recommendations to farmers and agricultural scientists.This will help increase crop productivity and farmer welfare.
Through this research, researchers intend to apply the GWOLR method in spatial analysis to predict the particle-size fraction of surface soils in a certain area [11].The results of this study are expected to provide a better understanding of the spatial factors that contribute to differences in particle-size fraction in surface soils as well as recommendations for more appropriate and effective soil management for farmers and agricultural scientists.
This research aims to construct a soil texture prediction model using the GWOLR model for the particle size fraction of the surface soil.Both GWOLR methods identify and spatially map particle size fractions in surface soils using primary data collected from the field.The third test tests the validity and accuracy of the spatial prediction model developed using the cross-validation method and determines the factors that contribute to the spatial distribution of particle size fractions in surface soils.
This research is expected to provide a better understanding of the spatial distribution of particle size fractions in surface soils and the factors that influence them.In addition, by using the GWOLR method as a spatial analysis tool, it is hoped that a more accurate spatial prediction model will be obtained and be able to provide useful information for decision-makers regarding land and natural resource management.

Data
In this study, the data used are primary data from soil texture measurements in the field and primary data obtained from digital terrain modeling analysis.Field data in this study is used to form a model (training data), and the data is used to validate the model obtained.The training data used is 50 observations.While the data tested as many as 10 observations.The data is in the form of results from soil texture analysis in the Kalikonto watershed.The variables in this study consist of eight local morphologic variables (LMV), which show the curvature of a topography [2].The LMV consists of: 6. Eastness Aspects (Ae) In this study, data was collected at the Kalikonto Watershed in Malang Regency, which consisted of 50 location points.Consists of 8 independent variables (X), and the dependent variable is divided into 3 categories, namely silt, sand, and clay.The data was taken in 2023.Map of the research location in Figure

Ordinal Logistic Regression
An extension of binary logistic regression is called ordinal logistic regression.In ordinal logistic regression, the response variable is an ordinal scale with three or more categories, and the predictor variable is either a factor (if using a nominal or ordinal scale) or a covariate (if using an interval or ratio scale) [12].
Ordinal logistic regression is a statistical method for analyzing response (dependent) variables that have ordinal data scales consisting of three or more categories.predictor variables (independent) that can be included in the model in the form of categorical or continuous data consisting of two or more variables [13].
The definition of an ordinal logistic regression model is a cumulative logit model.In this logit model, the ordinal nature of the Y response is expressed in cumulative probabilities.Logistic regression is formed by expressing the value of P(Y=1|x) as (x), which is denoted as follows [14]: The logistic regression model is included in the generalized linear models.The model used for ordinal logistic regression is the cumulative logit model.

Geografically Weighted Ordinary Logistic Regression
The GWOLR model is a combination of the GWR (geographically weighted regression) model and the ordinal logistic regression model.The GWOLR model is used to model the relationship between response variables with ordinal scales and predictor variables, each of which has a regression coefficient depending on the location where the data is observed.
It can also be said that GWOLR is a local form of a logistic regression model where the effect of location is taken into account.In the GWOLR technique, geographic location is entered into the model through a weighting function.A weight is given to each observation.Suppose the response variable consists of G categories, then the GWOLR model for location I can be written as follows [15]: where g = category (1,2,....., G-1 ), where {  ( ,  ) } is an intercept parameter and satisfies the condition T is the regression coefficient vector for the i location, while ( , ) is the coordinates (longitude, latitude) of the i-th location.

Weights
One factor that affects the outcomes of the spatial analysis is the choice of weighting function.In order to create the weighting matrix, which assigns a weight to each location based on the distance between it and the observed location, the weighting function was selected since it incorporates the distance between observed locations, whose values are continuous.Fixed Bisquare Kernel weights were employed in this investigation.Every location is assumed to have a single optimal bandwidth when using the Fixed Bisquare Kernel weighting algorithm.Determining the ideal bandwidth is one crucial step.The parameter known as bandwidth regulates the circumference of a circle of influence for every observation.One method for determining the optimum bandwidth is the bandwidth that produces the minimum AIC value [19].
In order to create a weighting matrix where each location is assigned a weight based on the distance between it and the observed location, the bi-square weighting function is utilized since it incorporates components of the distance between observed locations whose value is continuous [20].

Spatial Effect Testing
Spatial effect testing was carried out to find out whether there is a location effect in the model studied [21].This test was carried out using Moran's I. Moran's I is a statistical test to see the value of spatial autocorrelation, which is used to identify the location of spatial grouping or spatial autocorrelation globally [22].This method can detect the onset of global spatial randomness.This spatial randomness can indicate patterns that cluster or form trends in space [23].The calculation of spatial autocorrelation using Moran's I formula with a weighting matrix in the form of a standardized matrix is as follows [24]:

Best Model Selection
To get the best regression model, it is done by comparing the results of ordinal logistic regression models and GWOLR.One of the criteria used to determine the best model is the model that has the greatest classification accuracy value [25]

Ordinary Logistic Regression Analysis
Ordinal logistic regression analysis was carried out to investigate the variables that affect particle-size fraction.The particle-size fraction data used is interval-scale category data, with more than two particlesize fraction categories used, so that it can be continued with ordinal logistic regression analysis.Next, an ordinal logistic regression logit model will be created based on the parameter estimates as follows: Logit [ ̂( ≤ 1|)] = 0,803 + 21,845 X1 -202,102 X2 + 247,059 X3 + 161,852 X4 -165.497X5 -0.016 X6 + 0.108 X7-0.525X8 Logit [ ̂( ≤ 2|)] = 2,079 + 21,845 X1 -202,102 X2 + 247,059 X3 + 161,852 X4 -165.497X5 -0.016 X6 + 0.108 X7-0.525X8 The negative sign on the variable coefficient (X2) indicates that the lower the X1 value of a location point, it tends to be related to the lower the soil particle size, namely the clay category.Every time the X2 variable decreases by 0.01, there will be an opportunity to increase the content of soil particle size, namely clay.While the positive sign on the variable coefficient (X7) indicates that the higher the quality of X7 at a location point, it tends to relate to the quality of the dominant soil particle size content, namely sand content.

Accuracy of Ordinal Logistic Regression Classification
Calculation of the accuracy of the particle-size fraction classification results in the Kalikonto watershed area of Batu City in 2023 using an ordinal logistic regression model The results of calculating the odds for each category can be seen in the following table attachment ) x 100 % = 90% Based on the calculation of the accuracy of the Particle-size Fraction classification in Table 1, it can be seen that the percentage of accuracy of the logistic regression model in classifying is 90%.This figure is quite good because the classification accuracy is more than 50%.

Morans I Test
In testing with the OLR method, it was found that there were cases of the effect of particle-size fraction.Thus, it is followed by an analysis using the Geographically Weighted Ordinary Logistic Regression method.To test whether there is a spatial effect, the spatial dependency test is continued through the Moran's I test, aiming to see the spatial effect or the effect of location on each variable by looking at the p-value and comparing the value with α (0.05); if the p-value < α (0.05) there is a spatial effect on this variable.In testing the spatial effects with Moran's, I test whether the weights used are distance weights or distance weights with the calculation   = 1   .The distance weighting used is fixed kernel bisquare with an optimum bandwidth of 7.2154.For the Moran's I test, the results obtained are: From Table 2, it can be seen that all variables have a p-value <α (0.05), meaning that the 8 variables above have a spatial effect and need to be followed up with a GWOLR analysis.This test concludes that 1299 (2024) 012005 IOP Publishing doi:10.1088/1755-1315/1299/1/0120059 there is spatial autocorrelation in the independent variables.This means that the values of each variable between adjacent location points in the Kalikonto Basin influence each other.So this research can be continued with GWOLR analysis.

Geografically Weighted Ordinary Logistic Regression
The GWOLR parameter estimation results form a local model.Each location has a different model for the 50 location points.The former model will produce predictions of opportunities for each category.For example, the model for the first location point is located at coordinates (ui,vi).The GWOLR model formed is: Probability per category. 1 ( The probability of the category index of air pollution standards is influenced by the value of each independent variable; for example, the parameter  1 has a positive value, meaning that the higher the quality of X1 (Eastness Hill Aspect) at a location point, the higher the particle size of the soil, namely the content of sand in the soil.Likewise with other variables.
And parameter  5 is negative, meaning the lower the value of variable X5 (minimum curvature) at a location point, the more it tends to be related to the particle size of the soil, namely the content of silt and clay in the soil.
From Figure 2, the predicted probability value for each location is obtained, the resulting opportunity value is multiplied by 100 to get the soil content value for each location.

GWOLR Classification Accuracy
Calculation of the accuracy of the Particle Size classification results of soil in the Kalikonto Watershed Area, Batu City in 2023 using the GWOLR model.With the results of calculating the probability of each category of soil particle size, it can be seen in Table 3 with the following classification accuracy: x 100 % = 94% Based on the calculation of the accuracy of the soil particle size classification in Table 3, it can be seen that the percentage accuracy of the GWOLR model in classifying is 94%.This figure is quite good because the classification accuracy is greater than 50%.

Comparison of Ordinary Logistic Regression Models and GWOLR
Comparison between the ordinal logistic regression model and the geographically weighted ordinal logistic regression model to determine a better model for describing the particle size of soil in the  From the results of the analysis in Table 4, it can be seen that the accuracy of the particle size classification results of soil in the Kalikonto Watershed of Batu City using ordinal logistic regression models and GWOLR yield values of 90% and 94% Based on the classification accuracy value, the GWOLR model is the best because it has a model classification accuracy value of 94% greater than ordinal logistic regression.This is influenced by the influence of location on the GWOLR model.

Conclusion
Based on the data analysis process and discussion of soil particle size as the response variable in the Kalikonto watershed area of Batu City in 2023 using the ordinal logistic regression method and Geographically Weighted Ordinary Logistic Regression (GWOLR), it can be seen that Geographically Weighted Ordinary Logistic Regression (GWOLR) has the greatest classification accuracy of 94% compared to the ordinal logistic regression classification accuracy of 90%.This indicates that in these data, the GWOLR model is better than the logistic regression model.

Figure 1 .
Figure 1.Map of Research Locations

Table 1 .
: Accuracy of the Logistic Regression Model Classification

Table 3 .
Accuracy of GWOLR Classification Kalikonto watershed area in 2023The criterion for the goodness of the model used is the value of the classification accuracy.In this study, the best model is the one that has the greatest classification accuracy value.

Table 4 .
Model Comparison Values