Hierarchical Linear Model And Study On The Hierarchical Characteristics Of Water Resources In The Yangtze River Basin

The linear regression model is a statistical method which requires that the independent sample is selected from the same population, and the variance is homogeneous. However, the individuals (namely, the sample)tend to be hierarchical in many practical problems. That is, the structure of observed data is nested. At this point, the use of hierarchical linear model will be more reasonable to study the individual indicators. This is because that the hierarchical model breaks the limitations of the typical linear model techniques in the analysis of nested structures, which includes:sample can be from different populations; there can be a significant difference between the individuals in variances statically, which is generally limited between different populations.The Yangtze River Basin bulletin of water resource is in an important position in the annual statistics of the hydrology and water resource in China. Because of geographical, historical, administrative and other reasons, the water resources data of the rivers in Southwest China is usually collected and reorganized together with the Yangtze River Basin. The statistical units are divided into provincial division and second-grade river basins. Water consumptions in subareas are important and artificial controllable statistical indices among the various indicators of the water resource bulletin. What’s more, water consumption plays a pivotal role in the community economy, resident life, industrial and agricultural production, and so on.In this paper, the theoretical method, parameter estimation and hypothesis testing of the general linear model were summarized firstly, after which the principle, the process, and the test of hierarchical model were elaborated. The steps of establishing and calculating the hierarchical model with HLM software were proposed at the same time. Then, we collected and collated the data of the Yangtze River Basin and the Southwest Rivers bulletin in water resource over the past years (from 1998 to 2012), and also studied the yearly change of water consumptions in subareas from the bulletin of water resource above, from two types of partitions. Based on the cluster analysis and the selection of the variables in hierarchical linear model using correlation method, the hierarchical development models of water consumptions in subareas were established respectively. And then we calculated the parameters and tested the models with HLM. The established models described the changing trend of water consumptions of subareas in the Yangtze River Basin and the Southwest Rivers. Finally, the general regression was used for the new analysis of water consumptions, and its purpose was to make a comparison between its results and the results of hierarchical model. The two kinds of models described the changing trend of water consumptions in different subareas respectively from different aspects. The results of all analysis provide some foundations for further study of some indicators in water resources and utilization planning in the Yangtze River Basin and the Southwest Rivers.