Multi-level Interception Normal Regression Model Approach

In medical fields, many kinds of data have a hierarchical,nested,or clustered structure. For example, animal and human studies of inheritance deal with a natural hierarchy where offspring are grouped within families. Otherwise, data created by clinical trials carried out in several randomly chosen centers or groups of individuals. An important inner character of such data is that the observed values between individuals are not independent, that is, the individuals in the same unit of the same level are similar and relevant. Because of this, if analyzed by traditional statistics methods, it will lead to biased parameter estimates and an increase in typeⅠerror rates, even false results far away from the fact.The multilevel model has become popular for the analysis of data that have a hierarchical or clustered structure. By using the multilevel analysis, it not only obtains statistically efficient and unbiased estimates of regression coefficients and provides correct standard errors,confidence intervals and significance tests; but also allows the use of covariates measured at any levels of a hierarchy in a model, so that clusters all information and receives correct results.This paper is related to the multilevel normal regression model. It makes the critical assumption that the dependent variables either follow or can be transformed to follow a normal distribution. In fact, violation of the normality assumption can occur in many instances. Such as, in medical fields, because measure is limited, the data are censored at some threshold value, although the latent dependent variable is continuous. In such case, the dependent variable values in a certain range are replaced by the threshold value so that the dependent variable follow a mixed distribution concluding a continuous distribution and a discrete distribution, that is, a censored distribution. If we still use multilevel normal regression model to analyze it, it will lead to biased parameter estimates, even false results.In order to resolve this problem, it is necessary to modify the multilevel normal regression model. Here, this paper presents such a model, called"multilevel censored normal regression model", the combination of the multilevel normal regression model and the censored normal regression model. By the simulation study, we compare and contrast the performances of the multilevel censored normal regression model and the multilevel normal regression model in the cases that observed values are censored; we also compare the results of the multilevel censored normal regression model in different simulation settings that we considered, that is, different the...