The Effect Analysis Of Model Conditions In Linear Model

Linear model is a kind of statistical model and have a long history and wide applications. The inference results interpretation is an important aspect in model statistical inference. In this paper, the updates of parameter estimation which come from the changes of model components are explored. And it is benefit to result interpretation. On the base of effect analysis of model components, we emphasis the use of additional information introduced by unknown linear parameter. Furthermore, linear inequality restriction of linear parameter is discussed, and the difference between additional information and pure restriction in inference procedure and strategy is clarified. In addition, the estimation of new parameter introduced by the second-stage model in two-stage linear model is studied. And two estimate procedures in this situation are compared.In this paper, linear zero function (LZF) of linear model and projection operator of linear space are main tools, and covariate adjustment main way. The conclusions are get that: additional information in the form of linear equality maintain estimator unbiased and decrease the variance of estimator; additional information in the form of inequality, nonlinear equality and contradicting equality decrease the variance of estimator, but bring bias to it. And in the estimation problem in two-stage linear model, the equivalence between two-stage estimator and least square estimator is proved. The two-stage procedure is robust to model structure and give insight into the estimation results. An example of general linear growth curve model is cited to explain the application of two-stage procedure.