Application Study On Methods Between Direct Observation Regression And Indirect Observation Regression

As one of important and effective data processing methods, nonlinearregression analysis has been widely used in related fields such as surveying andmapping, environtology, economics, biomedizinische, earthquake predictionand speech signal processing. Most of the commonly used nonlinear regressionmodels can be converted into linear regression models to estimate parameter byappropriate mathematical transformation. Such models can be called linearizedmodels. However, some nonlinear regression models can not be converted intolinear regression models by the way of mathematical transformation. Suchmodels can be called nonlinearized models. Scholars at home and abroad haveperformed a large number of studies and presented a variety of nonlinearregression methods.The basic computing method for linearized model is converting nonlinearmodels to linear models by appropriate mathematical transformation, thencalculating regression coefficients by Least Squares. There are two regressionmethods to convert nonlinear models into linear models. One is taking indirectobservation, namely the function of direct observation, as dependent variable after linearization, which is commonly used method, and we call it indirectobservation regression (IOR). While the other is taking direct observation asdependent variable after linearization, and we call it direct observationregression (DOR).This paper has proposed direct observation regression method of nonlinearregression models, and has given direct observation regression models of9relatively common unitary nonlinear regression models (exponential function,power exponent function, normal distribution function, growth function,hyperbolic function, growth curve function, composite curve function, S-shapedcurve function, and Logistic curve function). In addition, exponential function,power exponent function, normal distribution function, growth function, andhyperbolic function are taken as examples, and simulation experiments are usedto compare the differences between DOR and traditional IOR, and thendetermining the more effective relatively regression method applied to linearprocessing of unitary nonlinear regression models.The study of this paper shows that IOR and DOR have the same forms infunction model and regression equation. However, their linearizationapproaches are different, and the differences between linearization approacheslead to the differences between the results of both regression methods. Theresults of simulation experiments demonstrate that when the numericaldifferences among observations are smaller, the results of IOR are equivalent tothose of DOR. When the numerical differences among observations are larger, the results of DOR are better than those of IOR. Regardless of the numericaldifferences among observations are smaller or larger, DOR has preferableregression results. So, DOR is more practical and effective.