System Clustering Analysis Of Multivariable Panel Data Via Probability Link Function And Its Application

This paper investigates two essential problems in the system clustering analysis of the multivariable panel data. One is what the similarity index to adopt, which means the algorithm of clustering analysis. The other is the methods of system clustering analysis relied on the similarity index that is the procedure of clustering analysis. Bonzo and Hermosilla (2002) proposed a new method to do the clustering analysis of panel data via the probability link function instead of the usual distance function. It can preserve the probabilistic structure perfectly, while the usual distance methods of PAC (Principal component analysis) and the sum of all the variables can't. This paper considers the probability link function as the algorithm of clustering analysis, and studies the approaches of system clustering analysis via the probability link function.This paper reviews the probability link function of Bonzo and Hermosilla (2002), and also investigates its property. However, Bonzo and Hermosilla (2002) assume the covariance matrix of a pair of the cross-section units in the same cluster equals to the variance matrix of themselves. This often can't be met in reality. Zhao and Hang (2010) assume all the cross-section units in panel data are independent, and redefine the new probability link function in the panel data with independent the cross-section units. Therefore, in this paper we also introduce the probability link function of Zhao and Hang (2010).This paper considers the more general situation that the covariance matrix of a pair of the cross-section units in the same cluster doesn't equal to the variance matrix of themselves and that the cross-section units in panel data are not independent. We redefine the new probability link function in this situation, and study its property. We find that the situation of Zhao and Hang (2010) is a special example of the situation this paper considers.What's more, Bonzo and Hermosilla (2002) haven't applied this method of the probability link function in multivariate statistics, so this paper should also consider how use this method to do the system clustering analysis and so on. Zhao and Hang (2010) consider how to apply the probability link function in system clustering analysis by the Centroid hierarchical method, when all the cross-section units in panel data are independent. Then, this paper also considers how to apply the probability link function in system clustering analysis basing the Centroid hierarchical method of Zhao and Hang (2010), in the condition that the covariance matrix of a pair of the cross-section units in the same cluster do not equal to the variance matrix of themselves and that the cross-section units in panel data are not independent. Besides the Centroid hierarchical method, we also propose3other approaches of system clustering analysis via this probability link function:the Single linkage method, the Complete link method and the Average linkage method.In this paper, we do some simulation experiments of the proposed4approaches of system clustering analysis for multivariable panel data via this probability link function. By the result of the Monte Carlo simulation experiments, we can see that the Centroid hierarchical method and the Average linkage method are robust and valid in different conditions, but the Single linkage method and the Complete link method are not good.We also do an empirical analysis of the urban average household consumption of the31Provinces from2000to2009. In this paper, we do the system clustering analysis of31Provinces by the Centroid hierarchical method. The result of the system clustering is rational. We consider classifying these Provinces into3clusters, and we also compare and analyze these3clusters.