Researches On Multivariable Analysis Methods In Non-optimal Data

Multivariable data analysis methods, including linear regression models, logistic models and discriminant models were widely used in medical researches. Their theories were compact and their good properties were very attractive provided the datum used to generate the postulated model being optimal. In medical researches, the optimality of observed data about the postulated model was unknown in many cases. If data was non- optimal, statistical inferences drawn from the built model would be perturbated and lost their theoretical meaning and lead to erroneous conclusions. In this paper, a group of multivariable data analysis methods were present. They are more robust than ordinary methods which, without lost generality, can be considered as special cases of these new methods correspondingly.Three robust biased estimates of multiple regression coefficients were proposed in this paper. Robust estimate and biased estimate of regression coefficients are two kinds of regression model fitting methods for non-optimal data. They can overcome the negative influences of outliers and multicollinearity respectively. Simulation shows that robust methods be ineffective as multicollinearity existed and biased methods be breakdown when outliers presented. Then robust methds and biased methods cann't be used to fit regression models when outliers and multicollinearity coexisted in observational data. In order to fit regression model in non-optimal data which included outliers and multicollinearity. biased estimates and M-estimate of linear regression coefficients were combined together mathematically. Finally, we obtained three robust biased model fitting methods which were called as robust principal component estimate, robust ridge estimate and robust root-root estimate respectively. The comparison simulations show that new methods uniformly better than ordinary LS estimate, M-estimate and biased methods. Robust principal estimate is practical, but other two new methods are not convenient in application since there isn't a possible technique to determine the optimal k value until now. The existence of the optimal k value is obvious following the simulations, however, this paper provided a platform for further theoretical studies in this field.