基于偏最小二乘回归的养老床位数预测研究

Prediction of Nursing Beds Based on Partial Least Squares Method

摘要: 构建和完善社会养老保障体系是应对人口老龄化的重要战略手段，是关乎民生的重大工程。养老床位是重要的养老资源，精准预测养老床位数具有重要意义。首先，文章选取国内生产总值、人均卫生费用、社区服务机构数、老年人抚养比等与养老床位数相关的15个指标。其次，根据留一交叉验证法，选取4个主成分，建立偏最小二乘回归模型以预测我国养老床位总数，并对回归系数和回归方程进行显著性检验。最后，以总的均方百分比误差(RMSPE)和平均绝对百分比误差(MAPE)作为模型评价指标，将偏最小二乘回归和逐步回归模型进行对比。结果表明：与养老床位数规模显著相关的指标为：社区服务机构数、离退人员参加养老保险人数、医疗保险基金支出、城镇职工基本养老保险累计结余、城镇居民人均可支配收入、城镇居民人均可支配收入等；偏最小二乘回归在预测养老床位数方面比逐步回归具有更好的预测效果。

Abstract: Building and improving the social security system for the elderly are an important strategic means to deal with the aging of the population, and it is a major project related to people’s livelihood. Pension beds are an important resource for the elderly, and accurate prediction of the number of beds for the elderly is of great significance. First, the article selects 15 indicators related to the number of elderly care beds, such as GDP, per capita health expenditure, number of community service agencies, and elderly dependency ratio. Secondly, according to the leave-one-out cross-validation method, four principal components are selected, a partial least squares regression model is established to predict the total number of quasi-care beds in my country, and the regression coefficient and regression equation are tested for significance. Finally, the total mean square percentage error (RMSPE) and average absolute percentage error (MAPE) are used as model evaluation indicators to compare partial least squares regression and stepwise regression models. The results show that the indicators that are significantly related to the scale of pension beds are: number of community service agencies, number of retired persons participating in pension insurance, medical insurance fund expenditure, accumulated balance of basic pension insurance for urban employees, per capita disposable income of urban residents, per capita urban residents, disposable income, etc. Partial least squares regression has a better predictive effect than stepwise regression in predicting the number of retirement beds.