Using Penalized Poisson Regressions To Explore Low Fertility In The Population

Since the 1970s,the US and other western developed countries have taken the lead in entering low-fertility countries.Now China is also facing such this problem,its fertility rate has been declining for decades and has fallen to around 1.3 as of 2021,which means that China will face a serious problem of population ageing and depopulation.Therefore,this paper used four kinds of penalized Poisson regression and three kinds of penalized Poisson regression to respectively explore the variability of influencing factors for fertility desire between China and the US,hoping to provide some research ideas for China to get rid of low-fertility country.To explore influencing factors for low fertility desire in China,this paper selected a sample of 1956 cases from the China General Social Survey(CGSS).The expected children number of Chinese residents was used as the response variable to describe the fertility desire of Chinese residents,and 40 indicators such as age,education level,individual income and perception of retirement were used as predictor variables to construct four models:LASSO penalized Poisson regression,Ridge penalized Poisson regression,SCAD penalized Poisson regression and MCP penalized Poisson regression.Firstly,75%of the dataset was used to construct the four penalized Poisson regressions,an R~2/AIC/BIC were selected to compare the goodness of fit for the four penalized Poisson regressions.The remaining 25%of the dataset was used as the test set,combining the trained Poisson regressions were used to predict the expected children number and compare the prediction performance.The results showed that the MCP penalized Poisson regression had the best goodness of fit and predictive performance,with the MSE/MAPE/MAE of the three predictive indicators being 0.9182,0.5398,and 0.2655.Therefore,the MCP penalized Poisson regression can effectively predict the expected children number.Through variable selection using MCP penalized Poisson regression,it was found that such as age,education level,living area,subjective well-being,and family property have a significant impact on the low fertility desire in China,while leisure activities,personal happiness scores,and family investment have a limited impact.To explore influencing factors for low fertility desire in the US,a sample of 1194cases from the General Social Survey(GSS)was selected.The expected children number of the US residents was considered as the response variable to describe the fertility desire of American residents,and 13 group variables,including ethnicity,relevant national policy attitudes,and economic status were selected as predictor variables.The datasets was divided into training and testing sets at a ratio of 3:1.Group LASSO penalized Poisson regression,group SCAD penalized Poisson regression,and group MCP penalized Poisson regression were implemented on the training set.The optimal threshold was selected through 10-fold cross validation,and the group coordinate descent algorithm can simultaneously accomplish factor selections and parameter estimations.Comparing the goodness of fit and prediction performance for three group penalized Poisson regressions with four penalized Poisson regressions,it was observed that the three group models significantly outperformed the four penalized Poisson regressions,with the mean squared error(MSE),mean absolute percentage error(MAPE),and mean absolute error(MAE)for the three predictive indicators respectively being 0.8523,0.2342,and 0.5838.The variable selection of the group MCP penalized Poisson regression indicated that ethnicity,family size,age,and religious beliefs were the most important influencing factors for the low fertility desire in the US.This article applied four penalized Poisson regression models to explore the influencing factors for low fertility desire in China.The results indicated that the group MCP penalized Poisson regression was effective in selecting important variables and predicting the expected children for Chinese residents.Similarly,three group penalized Poisson regressions and four penalized Poisson regressions were applied to explore influencing factors for low fertility desire in US.The results showed that the three group models had significantly better goodness of fit and prediction performance than the four penalized Poisson regressions.In particular,the group MCP penalized Poisson regression was the most effective in group variable selections and prediction performance.By comparing the differences of influencing factors for low fertility desire between China and the US,it was found that age,economic status,culture,and policy were the main differences in low fertility desire.