Non-monoton Nonparametric Variogram to Model the Land Price of Manado City with Hole Effect Periodicity Structure

Abstract

Abstract In spatial analysis, the experimental variogram fitting generally uses a mathematical variogram model such as monotonous spherical, exponential Gaussian along with increasing distance lag. However, there are certain cases, in this case the land price in Manado which raises experimental variogram in the form of non-monotonous (hole effect) as well as sinusoidal waves. This means that experimental variogram matching must be done as well as possible based on the positive definite function or at least following the hole effect pattern at the first peak. This study offers a variogram multiplicative-additive operation to combine monotonous and non-monotonous models in a nonparametric manner. The monotonous model used is a Gaussian-type for the amplitude of the hole effect, while the non-monotonous model is the first order zero-form Bessel function to indicate the wavelength. Based on measurements of the accuracy of RMSE (Root Mean Square Error) and MAE (Mean Absolute Error), combining the two models is relatively good and successful in fitting experimental variograms of land prices that have indicators of hole effect with periodicity. The hybrid composition of these models (non monotonous and monotonous models) provides a better approach to the experimental variogram compared to the previous mathematical monoton variogram models. To model Manado’s land price which has a hole effect, it would be more appropriate to use the Bessel composition model on the basis of p = 1 and the Gaussian-type model at m = 1 (or Exponential).