Abstract
Logistic regression model is widely used in ecology and in the analysis of social economic systems, because of its good adaptability. In order to improve the measurement accuracy of logistic model, this paper proposes a new method. A compound grey-logistic model is developed to carry out the grey transformation of the original data. Practice shows that the grey transformation data has better simulation accuracy; at the same time, grey transformation can reduce the observation noise of the original data. Mean absolute percentage error index has been used to evaluate the accuracy of prediction model, and information entropy can be used to evaluate the change of information entropy of forecasting data. In this paper, three cases are used to verify the applicability of grey-logistic model. From the perspective of the type of original data, the three cases represent three different data conditions: sufficient data, insufficient data, and fragmentary data. The cases represent different related fields: market share data, economic growth data, and R&D output data. The results show that the proposed grey-logistic method can effectively carry out the population growth analysis.
Highlights
If a social economic system is regarded as an ecosystem, the species in the social economic system can be regarded as the population in the ecosystem
E logistic growth function was first proposed by the Belgian scholar Verhulst in 1838 [1]. He used the logistic function to construct a growth curve, and after that, the curve had been used to conduct demographic research until the end of the nineteenth century. e British statistician Cox proposed the logistic regression model in 1958 [2]. is model’s advantage in not making too many requirements in terms of normality, homogeneity of variance, etc., and the interpretability of coefficients has enabled logistic regression models to have been extensively adopted in many fields such as medicine and social surveys. e logistic regression model has been widely used for many years in the past
Rough the analysis of actual cases, the accuracy of greylogistic model is compared with that of the grey model, logistic model, AR model, and Autoregression Moving Average (ARMA) model. e empirical results indicate that the numerical aspects of the grey transformation effect of the composite grey-Logistic model’s mean absolute percentage error (MAPE) values are highly accurate. e results of entropy analysis show that the grey-logistic model can keep the information of the original data better
Summary
Grey system theory establishes a set of theories and methods to solve the related problems of incomplete information system, which has great development potential in practical applications. e grey system theory is a new theory that takes the grey system as the research object and uses a specific method to describe and control the grey system. Erefore, grey Lotka–Volterra model was applied to analyze the relationship in economic and social ecosystems [29]. As one of the methods to improve the accuracy of grey prediction model, data transformation technology is effective, and it provides a new angle for the establishment of grey prediction model. Data transformation technology is effective when used as a way to improve the prediction model. Grey system theory has its own research objects, the characteristics of which are “poor information” and “small samples,” while the research objects of other theoretical methods are not necessarily characteristic of "poor information” and “small samples.” erefore, in the study of combined forecasting models, a combination point must be found
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