In spatial analysis, it is important to identify the nature of the relationship that exists between variables. Normally, it is done by estimating parameters with observations which taken from different spatial units that across a study area where parameters are assumed to be constant across space. However, this is not so as the spatial non-stationarity is a condition in which a simple model cannot explain the relationship between some sets of variables. The nature of the model must alter over space to reflect the structure within the data. Non-stationarity means that the relationship between variables under study varies from one location to another depending on physical factors of the environment that are spatially autocorrelated. Geographically Weighted Regression (GWR) is a technique in which it applied to capture the variation by calibrating a multiple regression model, which allows different relationships to exist at different points in space. A robust algorithm has been successfully used in spatial analysis. GWR can theoretically integrate geographical location, altitude, and other factors for spatial analysis estimations, and reflects the non-stationary spatial relationship between these variables. The main goal of this study is to review the potential of the GWR in modelling the spatial relationship between variables either dependent or independent and its used as the spatial prediction models. Based on the application of GWR such as house property indicates that GWR is the best model in estimating the parameters. Hence, from the GWR model, the significance of the variation can also be tested
Rainfall is an interesting phenomenon to investigate since it is directly related to all aspects of life on earth. One of the important studies is to investigate and understand the rainfall patterns that occur throughout the year. To identify the pattern, it requires a rainfall curve to represent daily observation of rainfall received during the year. Functional data analysis methods are capable to convert discrete data intoa function that can represent the rainfall curve and as a result, try to describe the hidden patterns of the rainfall. This study focused on the distribution of daily rainfall amount using functional data analysis. Fourier basis functions are used for periodic rainfall data. Generalized cross-validation showed 123 basis functions were sufficient to describe the pattern of daily rainfall amount. North and west areas of the peninsula show a significant bimodal pattern with the curve decline between two peaks at the mid-year. Meanwhile,the east shows uni-modal patterns that reached a peak in the last three months. Southern areas show more uniform trends throughout the year. Finally, the functional spatial method is introduced to overcome the problem of estimating the rainfall curve in the locations with no data recorded. We use a leave one out cross-validation as a verification method to compare between the real curve and the predicted curve. We used coefficient of basis functions to get the predicted curve. It was foundthatthe methods ofspatial prediction can match up with the existing spatial prediction methods in terms of accuracy,but it is better as the new approach provides a simpler calculation.
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