Tectonic Theory And Statistical Inference Dual Goal Logistic Regression Model

Single-objective Logistic regression model is typical of generalized linear mod-el, it is common statistic model when the response variable of model is Classifedvariable. It has been widely used in researching sociology, psychology, demog-raphy, economics and biological medicine and other domains because Logisticregression model doesn’t specially require normality of data, homogeneity ofvariance and the type of independent variable.At present, domestic and overseason researching for Logistic regression model mainly confned to single-objective L-ogistic regression model, multi-objective Logistic regression model about its theoryand application research is not deep,waiting for further study. Given all of that,this paper mainly studiesf statistical inference theory for double-objective Logisticregression model, the main content is divided into three parts: building double-objective Logistic regression, parameters estimation and goodness-of-ft test fordouble-objective Logistic regression.double-objective Logistic regression based on building thought of the single-objective Logistic regression model established. First of all, the use of verticaldensity representation (denoted as VDR) theory structure standard binary Lo-gistic distribution function. And then by binary Logistic distribution functiondirectly transform into double–objective Logistic regression model.It is difcult to fgure out double–objective Logistic regression model param-eters from the internal structure of model,the main reason is that the joint dis-tribution of the2-d classifcation dependent variable is unknown, frequently-usedmaximum likelihood estimate is failure. The estimate methods for this article areclassifed into three steps: frstly, set up based on the estimated parameters of thesame equivalent model---nonlinear model. Secondly, the use of nonlinear leastsquares estimation (denoted as NLSE) drawn about the double-objective Logisticregression model parameter estimation equation; Thirdly,based on the Newton-Raphson iteration algorithm to work out the double–objective Logistic regressionmodel parameter estimation. Finally, in a certain hypothesis conditions, discussthe large sample properties of model parameter estimation.The general idea of goodness-of-ft test for double-objective Logistic regres-sion model is to use likelihood ratio test method. The double-objective Logisticregression model parameter estimation in place of the frst order Taylor expansion,the model is transformed into linear model form. proceed to the next step, basedon likelihood ratio test method structure test statistics that tests goodness-of-ftfor double-objective Logistic regression model.