Nonlinear Regression Model Of Generalized S-Curve And Its Applications In Bibliometrics

Nonlinear Regression Models (NRM) play a central part in modern statistical methods. These models have been one kind of most heavily-used methods first in abroad since recent twenty years. By comparison, Nonlinear Regression Analysis (NRA) based on the classical Linear Regression Analysis (LRA) can be put to use in dealing with the nonlinear relations between variables that can not be solved by linear regression method even under the simple linear transformation on variables and parameters for its unsatisfying goodness of fit. It has been proved that Nonlinear Regression Analysis is a powerful method in proceeding nonlinear problems with the aid of computer and some statistical software (SAS, SPSS); however, the good fitting result can not be gained every time for the complexities itself and the assumption of random disturbances errors of model. The selections of expectation function and the parameter initial value are two main factors contributing to this. These are two kinds of difficult problems in Nonlinear Regression Analysis for their complexities and flexibilities in proceeding by hand without normal method to abide by. In fact, it's a important factor for getting a rapid convergence criterion and a satisfying goodness of fit to select a fitting expectation function and an idea parameter initial value.This paper discusses and researches the Nonlinear Regression Model of Generalized S-Curve on the set of observations in the shape of S. It gives out a more widely used expectation function S-Curve on account of some famous S-Curve functions exited. Some general estimating methods of parameter initial value are obtained in detail. As an important application and test of the model, a Nonlinear Regression Model in bibliometrics are made out successfully with the help of computer and the statistical software SAS.In chapter 1, This paper gives out a brief introduction to Nonlinear Regression Analysis, staring with the basic concepts, general methods and the graph of assembly-line, then describes the general principle of selection of fitting expectation function and idea parameter initial value for Nonlinear Regression Model, up to somedifficult problems to be solved in the future.Chapter 2 presents the expression of generalized S-Curve function based on some kinds ordinary S-Curve functions widely used in the past in many branches of sciences such as Logistic Curve, Gompertz Curve, Bertalanffy Curve and Richards Curve and so on. It draws out the fundamental property representative formula of generalized S-Curve function. On account of the flexible relative increment rate of Richards Curve and the adaptive initial value of Gompertz Curve, the generalized S-Curve function can be concluded by solving the initial value problem and should be chosen as the expectation function in Nonlinear Regression Analysis first for its generalized properties of S-Curve.Chapter 3 contains the standard procedure for Nonlinear Regression Analysis on the set of observations of the national publishing organizations number from year 1971 to 2000 including the six general estimating methods of parameter initial value and the concrete number for this kind of S-Curve. By the aid of the SAS program, it shows that the Nonlinear Regression Model is a more idea model than the other S-Curve models about this set of observations.Chapter 4 is devoted to the applications of Nonlinear Regression Model in bibliometrics. This chapter analyses the advantages and the disadvantages of the increment of scientific document models existed already for many years, It points out that comprehensive model given in 1988 can not be put to use in the case of asymmetric increment. So a new Nonlinear Regression Model of Generalized S-Curve is made to fit and predict the increment of document instead of it by changing the Generalized S-Curve for the Logistic Curve in the last chapter.The Generalized S-Curve and general estimating methods of parameter initial value on S-Curve presented in this paper can solves two relative difficult problems in S-C...