Nonparametric Spline Regression Research Articles

Modeling of poverty in Kalimantan with nonparametric spline regression approach

Poverty is a problem that is always present in any country, including Indonesia. Kalimantan is one of the islands in Indonesia that has not been free from poverty. Therefore, more effective efforts to further reduce poverty are needed. The purpose of the is study was to develop a model that can explain significant factors to poverty in Kalimantan. To achive the objective, first, factors that may have significant influence to the changes in the percentage of poor people should be identified, using regression analysis. In this study, nonparametric regression analysis was used with a spline approach since the relationship between poverty and the explanatory factors did not have a particular pattern. The results of this study showed that, the best was using three knot points, where Open Unemployment Rate (OUR), Human Development Index (HDI), and Economic Growth have a significant effect on poverty in Kalimantan.

Spline Nonparametric Regression Model for Local Revenue in Central Sulawesi

Local Own-source Revenue (LOR) is all regional revenue that comes from the region's original economic resources. It is very important to identify it by researching and determining the Regional Local Own-source Revenue (LOR) by properly researching and managing the source of revenue so as to provide maximum results. Central Sulawesi Province itself has Local Own-source Revenue (LOR) in the Regional Revenue and Expenditure Budget of the 2018 Budget Year has reached Rp1 trillion. The increase or decrease in growth of local revenue is influenced by the amount and type of tax, levies collected by local governments and the lack of incentives for the management apparatus to carry out tax collection and levies. This study uses spline regression analysis because the data of the Local Own-source Revenue (LOR) in Central Sulawesi in 2018 does not have a pattern so that it fits perfectly with that method. Then after processing the data obtained the results of spline nonparametric regression modeling using the optimal knots point obtained from the minimum GCV value. The best spline nonparametric regression model is written as follow . It can be concluded that in Central Sulawesi in 2018 the lowest Local Own-source Revenue (LOR) value was Banggai Laut Regency with 21,776 billion rupiahs and the highest Local Own-source Revenue (LOR) value was Palu City at 267,402 billion rupiahs.

PEMODELAN RATA-RATA LAMA SEKOLAH MENGGUNAKAN PENDEKATAN REGRESI NONPARAMETRIK SPLINE MULTIVARIABLE

Mean years school (MYS) is one of the indicators used in calculating the human development index (HDI). The value of MYS Indonesia in 2019 is 8,75 which is still low. Therefore it still needs to be improved. In this research, MYS modeling will be carried out using six factors that are thought to influence MYS. This research uses multivariable spline nonparametric regression to modeling MYS Indonesia in 2019. The best model is selected based on the minimum value of Generalized Cross Validation (GCV). Based on this research, the best model obtained is a linear orde (orde 2) spline model with four knots. The model has value of 99,91%.

The Effect of Human Development Index on Poverty Model in Indonesia using Penalized Basis Spline Nonparametric Regression.

Poverty is an issue of special concern to various countries in the world, including Indonesia. One factor that can affect poverty is the Human Development Index (HDI). The aim of this study is to model of the problem of poverty based on HDI. Using nonparametric spline regression was used with the penalized basis spline (PB-Spline) approach, which can overcome the problem of selecting many knot points and the location of knots in spline regression. This study was obtained three models, i.e. model with one knot point, model with two knot points, and model with three knot points. Based on indicators of the value of Generalized Cross Validation (GCV) and the value of Mean Square Error (MSE), the best model was a model with three knots, with smoothing parameter value of 1000, 11.26236 value of GCV and 11.08420 value of MSE.

Generalized Cross Validation (GCV) in Smoothing Spline Nonparametric Regression Models

A nonparametric regression model is utilized if the the regression curve does not contain information about the accepted shape and accepted curve is exist in a function. If any curve is given without the limitation of a certain functional form, a rough and non-unique curve will result. The smoothing spline can be utilized to remove rough curves in some segments by following a curve pattern. An approach that combines nonparametric regression and smoothing spline is known as the smoothing spline nonparametric regression model. The problem in estimating is the selection and determination of smoothing parameters obtained by taking into the sum of knots used and the position of the knots so that the Generalized Cross-Validation (GCV) method is required. A study was conducted on the smoothing spline nonparametric regression model on GCV. The method used in research is a literature study obtained from some articles, journals, and books that support research achievement. The results showed that with the GCV method the minimum GCV value was obtained which would determine how well the smoothing parameters shown by the estimator did not change significantly even though the number and position of the knots varied.

Pemilihan Titik Knot Optimal Model Spline Truncated Dalam Regresi Nonparametrik Multivariabel dengan GCV

One of the most frequently studied nonparametric regression model approaches is the spline truncated. This method is applied to cases of Maternal Mortality Rate because in various cases there is an increase in maternal mortality problems so that the government is expected to be more serious in dealing with and suppressing the MMR value through the programs launched or by overcoming the factors that significantly influence the high MMR value. This study aims to examine the determination of the optimal knot point of the multivariable nonparametric spline regression model using the GCV method as the optimal knot point selection method. The criteria for selecting the best model in this study using the MSE value. The results obtained are the best model suitable for AKI 2017, namely by using the GCV method which is located in the three knot linear spline, which is 0.07722 and an MSE value of 0.018. The variables that have an effect on the model are the percentage of deliveries performed with the help of medical personnel (x1), the percentage of pregnant women who receive Fe1 tablets (x2), the percentage of pregnant women implementing the K1 (x3), and the percentage of pregnant women implementing the K4 (x4).

REGRESI NONPARAMAETRIK SPLINE PADA DATA LAJU PERTUMBUHAN EKONOMI DI KALIMANTAN

The Economic Growth Rate (EGR) is an important indicator to measure the success of economic development.The welfare and progress of an economy is determined by the amount of growth shown by changes in the quantity of goods and services produced nationally. High economic growth is a goal that is expected to be achieved in a developing country. Many factors affect EGR in Kalimantan, so it is necessary to do modeling to find out the factors that significantly affect EGR. This study uses 6 factors that are suspected to influence EGR, namely the labor force participation rate, the number of large and medium industries, the average length of schooling, regional income and expenditure budgets, general allocation funds and rice productivity. The data is 2017 data obtained from the Central Statistical Agency (CSA) in 5 provinces in Kalimantan. The method used to model EGR is spline nonparametric regression and obtained the optimal knot point with the smallest GCV (Generalized Cross Validation) value of three knots. Based on the research results obtained an R2 of 82.15 percent which shows that the model formed is suitable to be used to model data patterns and there are 6 variables that have a significant effect on EGR namely labor force participation rates, number of large and medium industries, average length of schooling, regional income and expenditure budgets, general allocation funds and rice productivity.

Pemodelan Regresi Nonparametrik Spline Linear Persentase Penduduk Miskin di Kalimantan

Poverty is a social problem faced in almost every country. Based on BPS data published in 2018, East Kalimantan Province has a population of poor people of 222.39 thousand people or around 6.06 percent. In March 2018, the number of poor people was 218.90 thousand people or about 6.03 percent, which means the number of poor people had increased by an absolute 3.49 thousand people, this caused the percentage of poor people to rise 0.03 percent. In this study identified factors that influence the percentage of poor population using a linear spline nonparametric regression model. The data used in this study are data from the Central Statistics Agency (BPS) in 5 provinces in Kalimantan. In the nonparametric linear spline regression method using the optimal knot point based on the smallest GCV value. The results obtained an R2 value of 74.48% which shows that the model formed is feasible to be used to model the data pattern and there are 5 variables that have a significant effect on the Percentage of Poor Population, namely Population Growth Rate, School Length Average, School Old School Expectancy Rate, Level Open Unemployment, Labor Force Participation Rate.

Optimal knot selection in spline regression using unbiased risk and generalized cross validation methods

Spline regression is a nonparametric regression method that estimates data patterns that do not form certain patterns with the help of knots. The best model is obtained from the optimal knot. There are several methods that can be used to select optimal knots, including Generalized Cross-Validation (GCV) and Unbiassed Risk (UBR). The best model selection criteria used are based on the Mean Squared Error (MSE) and R-Square values. This study discusses the comparison of spline regression models using the UBR and GCV methods as a method for selecting optimal knots in data generation simulations. This research resulted in the best nonparametric spline regression model from the UBR method obtained by using three knots which produced an MSE value of 738.67 and R -Square of 85.65%. Whereas, the best nonparametric spline regression model of the GCV method was obtained using three knots which produced an MSE value of 121.43 and R-Square of 97.64%. It can be concluded that the more appropriate method used for the selection of optimal knot is the GCV method because it produces a smaller MSE value and a larger R-Square compared to the UBR method.

Estimating mean arterial pressure affected by stress scores using spline nonparametric regression model approach

An average arterial blood pressure needed for blood circulation to the brain is called as mean arterial pressure (MAP). Blood circulation to the brain supplies food and oxygen to the brain for nutrition and brain activity. If the MAP is too low, it can cause diseases such as tachycardi heart rate and hypotension. In contrast, if MAP is too high, it can cause brain blood vessel rupture and hypertension. Stress is believed to has a relationship with hypertension. This is thought to be through sympathetic nerve activity which can increase blood pressure intermittently. Also, stress can stimulate kidneys to release adrenaline hormone and stimulate the heart to beat faster and stronger, so that blood pressure will increase. An increase in stress scores can be followed by an increase in MAP as well. In this study, we are interested to investigate the aftermath of changes in the stress scores on MAP by using spline nonparametric regression model approach which can accommodate changes in data patterns, and then compare it with the parametric regression model approach. The results showed that based on the mean square error values, the nonparametric regression model approach based on spline estimator is better than the parametric regression model approach. The estimated model that we got can be used to predict and interpret the values of MAP affected by stress scores as an effort to prevent hypertension.

PEMODELAN REGRESI NONPARAMETRIK SPLINE TRUNCATED PADA FAKTOR-FAKTOR YANG MEMPENGARUHI PERTUMBUHAN EKONOMI DI PROVINSI MALUKU

Economic growth is a benchmark for the success of a region's development, especially in the economic field. The purpose of economic development in an area is basically to improve the welfare and prosperity of the community. Economic growth in Maluku Province experienced a positive increase. However, there is still a disparity between districts/cities in Maluku Province, which has an impact on increasing unemployment and an increasingly poor population. This is inseparable from the influencing factors so that it can be precisely done by modeling these factors using the truncated nonparametric spline regression method. the advantages of this method occur because in nonparametric spline truncated regression has knot points, which are joint fusion points that indicate changes in data behavior patterns. Besides, this method can be used to model data patterns that change at certain sub-intervals. The best model is very dependent on determining the optimal knot point by using the minimum Generalized Cross-Validation (GCV) value. The results obtained in this study were the highest percentage of economic growth in Maluku Province, Ambon City with a percentage of 6.17%, and the lowest economic growth was in the East Seram District (SBT) with a percentage of 5.03%. Furthermore, the best model is obtained with a model with three knots and a GCV value of 11.61, a value of 2 of 0.94 and an MSE value of 0.005. This means that statistically, the variables used in this study affect economic growth by 94%. While the rest is influenced by other variables outside the research.

Simultaneous Hypothesis Testing of Multivariable Nonparametric Spline Regression in the GWR Model

In this research, studied multivariable nonparametric geographically weighted regression use truncated spline approach. The model is an expansion of nonparametric truncated spline regression that takes into account geographical or spatial factors. The purpose of this study was to find statistics test and distribution for the simultaneous hypothesis test. This study obtains the statistic test used the maximum likelihood ratio test (MLRT) method. Results of the research obtained statistics test based on the ratio between the maximum of the likelihood function under the set of H_0  and the maximum of the set likelihood function below the population with each have a spatial factor. Distribution of statistical tests has been proven to have a distribution of F. The modeling application used the percentage of the death of Dengue Hemorrhagic Fever (DHF) in 38 districts/cities in East Java Province. The modeling resulted in the determination coefficient of 80.7% and SSE value that is 0.0043.

Smoothing parameters of penalized spline nonparametric regression model using linear mixed model

Nonparametric regression is method of regression approach for data patterns of which regression curve is unknown. Meanwhile, spline is a type of segmented polynomial piecewise. Such segmented nature gives more flexibility than common polynomial models so that spline can adapt more effectively to local characteristics of function or data. The use of spline focuses on presence of behavior and patterns of data which in certain area has different characteristics from other areas. Data matching can be done by observing points on data in which an extreme change occurs in an area and consequently data patterns in each area differ. One approach using nonparametric regression is spline regression with penalized spline (P-spline). It is defined as a regression determined using method of least squares and roughness penalty. The article examines smoothing parameters of penalized spline nonparametric regression model. P-spline can be represented in linear mixed model with components of variance to control nonlinearity level of estimators of smooth functions. P-spline using linear mixed model approach can be estimated using either maximum likelihood or residual maximum likelihood. The results of research show that smooth function of best linear unbiased predictor in linear mixed model is equivalent to estimators of penalized spline regression.

A New Method of Hypothesis Test for Truncated Spline Nonparametric Regression Influenced by Spatial Heterogeneity and Application

This study developed a new method of hypothesis testing of model conformity between truncated spline nonparametric regression influenced by spatial heterogeneity and truncated spline nonparametric regression. This hypothesis test aims to determine the most appropriate model used in the analysis of spatial data. The test statistic for model conformity hypothesis testing was constructed based on the likelihood ratio of the parameter set under H0 whose components consisted of parameters that were not influenced by the geographical factor and the set under the population parameter whose components consisted of parameters influenced by the geographical factor. We have proven the distribution of test statistics V and verified that each of the numerators and denominators in the statistic test V followed a distribution of χ2. Since there was a symmetric and idempotent matrix S, it could be proved that Y~TS Y~/σ2~χn-lm-12. Matrix Dui,vi was positive semidefinite and contained weighting matrix Wui,vi which had different values in every location; therefore matrix Dui,vi was not idempotent. If Y~TDui,viY~≥0 and Dui,vi was not idempotent and also Y~ was a N0,I distributed random vector, then there were constants k and r; hence Y~TDui,viY~~kχr2; therefore it was concluded that test statistic V followed an F distribution. The modeling is implemented to find factors that influence the unemployment rate in 38 areas in Java in Indonesia.

MODEL REGRESI NONPARAMETRIK SPLINE TRUNCATED PADA JUMLAH KASUS TUBERKULOSIS DI PROVINSI BALI TAHUN 2016

Tuberculosis is a contagious disease caused by Mycobacterium tuberculosis. Based on data from the health office of Bali Province, in 2015 tuberculosis cases found 0,96%, while in 2016 tuberculosis cases increase to 1,05%. This research used truncated spline nonparametric regression to model tuberculosis cases in Bali Province in 2016. This method was used because truncated spline has high flexibility compared to other polynomial models. The truncated spline function has a connecting point called knots. The best estimation of truncated spline regression model is obtained from optimal knot point selection by calculating minimum generalized cross validation. The estimated truncated model is linear with one knot point with determination coefficient equals to 70,48 %. In addition, it is also found in order to reduce tuberculosis cases the government of Bali Province should increase percentage of family who lives clean and healthy.

PEMODELAN INDEKS HARGA SAHAM GABUNGAN MENGGUNAKAN REGRESI SPLINE MULTIVARIABEL

The Composite Stock Price Index (CSPI) is a composite index of all types of shares listed on the stock exchange and their movements indicate the conditions occurring in the stock market. CSPI movement is an important indicator for investors to determine whether they will sell, hold, or buy a stock. One of the factors that influence the movement of CSPI is Inflation (X1), Exchange Rate (X2) and SBI rate (X3). This study aims to obtain the best CSPI model using a multivariable nonparametric spline regression approach. The approach is done by nonparametric regression because the regression curve obtained does not show a certain relationship pattern. Spline is very dependent on the order and location of the knot point. The best spline model is the model that has the minimum MSE (Mean Square Error) value. In this study, the best spline regression model is when X1 is 4 order, X2 is 2 order and X3 is 2 order. The number of knots on X1 is 1 knot at 8.22, X2 is 2 knots at 13066.82 and 13781.75 While X3 is 2 knots at 6.6 and 6.67 with value of MSE equal to 6686.85.Keywords: Composite Stock Price Index, Multivariable Spline Regression, MSE

Retrieval of fractional snow covered area from MODIS data by multivariate adaptive regression splines

In this paper, a novel approach to estimate fractional snow cover (FSC) from MODIS data in a complex and heterogeneous Alpine terrain is represented by using a state-of-the-art nonparametric spline regression method, namely, multivariate adaptive regression splines (MARS). For this purpose, twenty MODIS - Landsat 8 image pairs acquired between April 2013 and December 2016 over European Alps are used. Fifteen of the image pairs are employed during model training and five images are reserved as an independent test dataset. MARS models are trained by using MODIS top-of-atmosphere reflectance values of bands 1–7, normalized difference snow index, normalized difference vegetation index and land cover class as predictor variables. Reference FSC maps are generated from higher spatial resolution Landsat 8 binary snow cover maps. Multilayer feedforward artificial neural network (ANN) models are also trained by using the same input data. During the training and the testing, the effects of the training data size and the sampling type on the predictive performance of ANN and MARS models are investigated. An additional search is also conducted to reveal whether the choice of the transfer function used in the output layer of ANN has a significant contribution to the network's FSC mapping performance. The final ANN and MARS FSC products are at 500m spatial resolution. The results on the independent test scenes indicate that the developed ANN models with linear and hyperbolic tangent transfer functions in the output layer and the MARS models are in good agreement with reference FSC data with the same average values of R=0.93. In contrast, the standard MODIS snow fraction product, namely, MOD10 FSC, exhibits slightly poorer performance with average R=0.88. The proposed MARS approach is statistically proven to have the same performance with ANN, yet it is computationally more efficient in model building.

ESTIMATION OF SUBPIXEL SNOW-COVERED AREA BY NONPARAMETRIC REGRESSION SPLINES

Abstract. Measurement of the areal extent of snow cover with high accuracy plays an important role in hydrological and climate modeling. Remotely-sensed data acquired by earth-observing satellites offer great advantages for timely monitoring of snow cover. However, the main obstacle is the tradeoff between temporal and spatial resolution of satellite imageries. Soft or subpixel classification of low or moderate resolution satellite images is a preferred technique to overcome this problem. The most frequently employed snow cover fraction methods applied on Moderate Resolution Imaging Spectroradiometer (MODIS) data have evolved from spectral unmixing and empirical Normalized Difference Snow Index (NDSI) methods to latest machine learning-based artificial neural networks (ANNs). This study demonstrates the implementation of subpixel snow-covered area estimation based on the state-of-the-art nonparametric spline regression method, namely, Multivariate Adaptive Regression Splines (MARS). MARS models were trained by using MODIS top of atmospheric reflectance values of bands 1-7 as predictor variables. Reference percentage snow cover maps were generated from higher spatial resolution Landsat ETM+ binary snow cover maps. A multilayer feed-forward ANN with one hidden layer trained with backpropagation was also employed to estimate the percentage snow-covered area on the same data set. The results indicated that the developed MARS model performed better than th

ANALISIS REGRESI NONPARAMETRIK SPLINE MULTIVARIAT UNTUK PEMODELAN INDIKATOR KEMISKINAN DI INDONESIA

The aim of this study is to obtain statistics models which explain the relationship between variables that influence the poverty indicators in Indonesia using multivariate spline nonparametric regression method. Spline is a nonparametric regression estimation method that is automatically search for its estimation wherever the data pattern move and thus resulting in model which fitted the data. This study, uses data from survey of Social Economy National (Susenas) and survey of Employment National (Sakernas) of 2013 from the publication of the Central Bureau of Statistics (BPS). This study yields two models which are the best model from two used response variables. The criterion uses to select the best model is the minimum Generalized Cross Validation (GCV). The best spline model obtained is cubic spline model with five optimal knots.

PEMODELAN REGRESI SPLINE (Studi Kasus: Herpindo Jaya Cabang Ngaliyan)

Regression analysis is a method of data analysis to describe the relationship between response variables and predictor variables. There are two approaches to estimating the regression function. They are parametric and nonparametric approaches. The parametric approach is used when the relationship between the predictor variables and the response variables are known or the shape of the regression curve is known. Meanwhile, the nonparametric approach is used when the form of the relationship between the response and predictor variables is unknown or no information about the form of the regression function. The aim of this study are to determine the best spline nonparametric regression model on data of quality of the product, price, and advertising on purchasing decisions of Yamaha motorcycle with optimal knots point and to compare it with the multiple regression linear based on the coefficient of determination (R2) and mean square error (MSE). Optimal knot points are defined by two point knots. The result of this analysis is that for this data multiple regression linear is better than the spline regression one.