Parameter Estimation And Applied Research Of Multilevel Linear Model

In biology, medicine, sociology, economics, and so on, longitudinal data is a hot topic in recent years. Its most prominent characteristic is that it can infer the reasonable relationship between variables. With the development of research, longitudinal data pay more attention to both the overall average trend and individual differences development, while it only consider of the overall average trend at the early years. So a new model is needed. In view of layer, layer longitudinal data of multi-sample, then use multilevel linear model to do some research. Firstly, in the situation that the covariance matrix is known and singular, prove that fixed effects and random effects’linear combination of multilevel linear model is the best linear unbiased estimation. In addition, when the covariance matrix is unknown, comprehensively analyze six different variance estimation methods. Secondly, for finite population, we study the unique minimax predictor of multilevel linear model’s linear predictable variable. Finally, by using multilevel linear model, we analyze the influence that scientific research funds utilization ratio and proportion of scientific researchers of every province exercises on GDP. Results show that the former can advance GDP’s development, but the latter is not significant. And the final model’s forecast is satisfactory.