Regularized Poisson regressions predict regional innovation output

Regional innovation output is influenced by many factors such as macroeconomic environments, residents consumption, fixed asset investment, foreign trade, fiscal revenue and expenditure, education, and research and development (R&D) input. Correctly predicting regional innovation output is an important subject in the economic field. In this paper, we propose four regularized Poisson regressions to forecast regional innovation output for 31 provinces in China. Firstly, we screen out 20 important factors and combine with four penalties: ridge penalty , least absolute shrinkage and selection operator penalty (LASSO), smoothly clipped absolute deviation penalty (SCAD), and minimax concave penalty (MCP) to construct four regularized Poisson regressions. Secondly, we introduce the cyclic coordinate descent (CCD) algorithm and the training set to complete variable selection and obtain the least squares weighted iterative estimators and make model selection by introducing three criterions to compare goodness of fit to different models. Finally, we apply the testing set and the learned regressions to exhibit the prediction performances and found that SCAD/MCP regularized Poisson regression predicts better than /LASSO regularized Poisson regression in terms of root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). In particular, MCP regularized Poisson regression outperforms the other three regularized Poisson regressions in predicting the number of granted patents in the three regions.