Statistical Diagnostics In Geographically And Temporally Weighted Regression Models

Geographically and temporally weighted regression model is a new spatial analysismethod recently, which is based on geographically weighted regression model. Spatialand temporal characteristics of data structure are involved in geographically andtemporally weighted regression model, in order to exploring the nonstationarity ofspatial and temporal. With the expanding range of statistical applications, as a kind ofsimple and effective date to solve the problem of date in time and space characteristics,this method is studied and applied more and more because it is easy to construct amodel, but also able to choose a set of statistical inferential approaches to dosignificance test of parameter estimation. The fitting method and statistical diagnosticsof geographically and temporally weighted regression model have been researched inthis article.Firstly, the basic principle of the geographically and temporally weightedregression model is illustrated; the fitting method of geographically and temporallyweighted regression model is given based on the theory of weighted least squaresestimate. The expression of residual sum of squares and the unbiased estimate of thevariance are obtained. The choice of spatial weighting function, bandwidth selection,and adaptive spatial kernels are discussed in detail.Secondly, the stable empirical regression equation in statistical analysis is gained.However, when the date set are applied to estimate the model parameters, if some datapoints of the data set have abnormal effect on parameter estimation or away from themain body of data set, the fitting results of model will be poor. Based on thisconsideration, the statistics diagnosis of the geographically and temporally weightedregression model is mainly studied in this paper. In this section, the fitting influence degree of each observational date is discussed upon the case deletion model and theCook distance, W-K statistics and Leverage value were given. Show that the casedeletion model is equivalent to the mean shift outlier model for diagnostic purpose, andsome test statistics for testing whether a given observation is an outlier to the modelbased on the mean shift outlier model were constructed.Finally, through the simulating experimental by using R software, based on Cookdistance and W-K statistics，it proved that the testing method is effective and feasible.