The Application Of Multilevel Count Model For Complex Sampling Survey Data

In medical multistage complex sampling survey researches, hierarchically structured data is fairly common. In order to solve the within-group dependence, multilevel models have been proposed and are prevalent recently. In the first chapter of the article, the difference between a multilevel linear model and a general linear model accounts for the composite residual structure, which is level-2 error ( u 0 j, u1 j) and level-1 error ( ei j) contained in the multilevel linear model. When processing hierarchically structured data, the multilevel model considers hierarchy of the residuals, which are assigned to corresponding data hierarchy levels. Through estimating level-1 error and using explanatory variables to explain residual variances, the multilevel model can get effective parameter estimation values, pure level-1 error, and composite residual structure. Refer to Jichuan Wang's study, the modeling process of multilevel models is following the five steps: running the empty model→adding level-2 explanatory variables into the empty model→adding level-1 explanatory variables into the empty model→testing level 1 random slopes→testing cross-level interactions.The second chapter of the article describes parameter estimation and hypothesis testing methods of the multilevel Poisson model(ML_Poisson), the multilevel negative binomial model(ML_NB), the multilevel zero-inflated Poisson model(ML_ZIP), and the multilevel zero-inflated negative binomial model(ML_ZINB). The ML_Poisson and ML_NB models are general multilevel count models. When data includes a large number of zeros, the multilevel zero-inflated count model are appropriate. The multilevel zero-inflated count model includes two parts, which represent two processes of extra zeros, so we can get little estimation errors and correct parameter estimation values. A simulation study of the ML_Poisson,ZIP and ML_ZIP models is carried out in this chapter. The parameter estimation values of ML_Poisson and ZIP are biased. Whatever the number of level-1 i or level-2 j is, the parameter estimation values of the multilevel zero-inflated count model are near the real values. The simulation study indicates that the multilevel zero-inflated count model is much more appropriate for clustered extra-zero count data than the ML_Poisson or ZIP.The third chapter of the article analyzes influenced factors of hospital visits in two weeks and the number of joints pain. Two examples are hierarchical, and individuals are nested in villages or families. We applied a series of multilevel count models to these examples. Vuong's tests of the second example indicate that the multilevel zero-inflated count models fit the data better than multilevel general count models. The data has over-dispersion phenomenon, so the ML_ZINB fits the data best.The form of a multilevel model is various, because the number of random slopes or levels isn't fixed. In two parts of multilevel zero-inflated models, explanatory variables can be different and random effect can be correlative. In a word, modeling a clustered count data should base on the research purposes and model principles.