基于GBDT模型的贵州省GDP空间化研究

Spatial Analysis of Guizhou Province’s GDP Based on the GBDT Model

摘要: 传统的GDP统计数据仅能反映地区经济发展的总体水平，而GDP空间化可以反映出经济活动的空间特征。本文以贵州省为研究对象，用2000~2022年的长时间序列多源数据集作为模型训练数据，选用传统多元线性回归模型(MLR)与5种机器学习模型：DT、RF、AdaBoost、XGBoost和GBDT模型进行对比分析，结果表明：机器学习模型拟合结果精度和交叉验证精度均优于传统多元线性回归模型，表明在GDP与多元变量之间存在复杂关系时，线性回归模型往往具有局限性，机器学习模型通过不断地迭代计算，能够更好地处理非线性关系，从而提高模型的预测性能。其中以GBDT模型误差最小(拟合结果R²为0.90、MAE和RMSE分别为51.25亿元和76.32亿元；交叉验证R²为0.98、MAE和RMSE分别为0.04亿元和0.13亿元)，相较于其他模型，该模型表现出最佳的拟合能力，模型的稳定性最高。贵州省经济空间分布特征主要是以城市为中心的经济发展圈层结构，结合现状分析了成因并提出了规划、建设及财政等方面建议。

Abstract: Traditional GDP statistics only reflect the overall level of regional economic development, while spatialization of GDP can unveil the spatial characteristics of economic activities. This paper takes Guizhou Province as the research object, utilizing a long-term time series multi-source dataset from 2000 to 2022 as the model training data. It compares the traditional multiple linear regression model (MLR) with five machine learning models: DT, RF, AdaBoost, XGBoost, and GBDT models. The results indicate that machine learning models exhibit superior fitting accuracy and cross-validation precision compared to the traditional multiple linear regression model. This suggests that linear regression models often have limitations when dealing with complex relationships between GDP and multiple variables. Machine learning models, through iterative computation, can better handle nonlinear relationships, thereby enhancing the predictive performance of the model. Among these, the GBDT model demonstrates the smallest error (with a fitting result R² of 0.90, MAE and RMSE of 51.25 billion yuan and 76.32 billion yuan respectively; cross-validation R² of 0.98, MAE and RMSE of 0.04 billion yuan and 0.13 billion yuan respectively), exhibiting the best fitting capability and highest stability compared to other models. The spatial distribution characteristics of Guizhou Province’s economy primarily manifest as an urban-centric economic development concentric structure. Combining current analysis, this paper elucidates the causes and proposes suggestions in terms of planning, construction, and finance.