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# Hierarchical Linear Model and Its Research on Hierarchical Characteristics of Rainfall

Author: JiangGaoXia
Tutor: ZhuYongHua
School: North China Electric Power University
Course: Applied Mathematics
Keywords: hierarchical linear model(HLM) monthly rainfall seasonal effects regional differences proportion reduction in variance
CLC: P426.6
Type: Master's thesis
Year: 2012
Quote: 0

### Abstract

 Most natural disasters have close relationship with the rainfall, which has an important impact on the people’s production, living and the environment. It is found that there are some statistical correlations between rainfall, which showed some seasonal periodicity and geographical differences, and other meteorological factors, like temperature, sunshine, humidity and air pressure.According to the hierachical characteristics of meteorological data, this paper put forward the way of hierarchical regression model considering both meteorological factors and group effects. Firstly we properly selected factors by collinearity diagnostics from the property of monthly rainfall, and set up a dummy variable according to the seasonal effects corresponding to every month; After that, we can build hierachical linear model (HLM2) for longitudinal data grouped by month with seasonal effects. Then compare and improve the model according to some optimization principles (proportion reduction in variance, coefficients’significance, convergence rate, residual comparisons etc) to explain fixed effects and random effects properly and make a illustration of group effects in the way of "scatter-regression-coefficient" comparation. Finally evaluate relative fitting in the view of residuals.After comparing rainfall in different regions, it suggests that we should take the geographical effects as high-level effects. First, select two representative regions’ meteorological data by cluster analysis. In dealing with the data structure of "seasonal-geographical" interaction effects, we convert it into a "month-season-geographic" fully nested structure, then do modeling by theories of hierachical linear model (HLM3). At last, make comparations and improvements similar to HLM2. It shows that variabilities and "seasonal-regional" group effects of monthly rainfall can be well explained by variables in each level (meteorological factors, seasonal effects, geographic effects). Also, some guiding significance conclusions for precipitation are drew out.

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