1980-2020年間美國首次公開發行的證券，在發行第一天的收盤價相對於發行價格的平均上漲幅度為18.4%。傳統文獻研究IPO折價時多著重於尋找解釋變數，而未以預測為主要目的，並且文獻中多以線性模型為假設。但影響IPO折價的因素很多，彼此也可能以不同形式影響IPO折價，線性的假設未必能提供模型最好的預測能力。近來也有研究使用機器學習方法，發現機器學習模型能夠很好地預測IPO折價。故本研究將針對線性與非線性的變數挑選方式與函數形式對模型預測能力的影響進行探討。
在函數形式方面，研究使用多元線性迴歸與非線性的多層感知器模型做比較，變數的挑選方法則是用線性假設下的加權平均最小平方法以及沒有線性假設的隨機森林特徵重要程度這兩種方法來比較。研究發現加權平均最小平方法所找出的變數較適用於多元線性迴歸模型，而利用隨機森林特徵重要程度所找出之變數較適用於多層感知器模型，但此兩種組合在IPO折價的預測能力並無顯著差異。

IPO underpricing has existed for a long time. The average IPO underpricing is 18.4% in the US stock market in 1980-2020. Conventional IPO studies focused on the explanatory power of the variables often used linear regression as the selected model. However, there may be variables having non-linear explanatory power. Studies show that machine learning methods provide good predictive power in IPO underpricing. This paper analyses the predictive power of linear and non-linear methods in IPO underpricing.
Weighted-average least squares (WALS) and multiple linear regression are used to evaluate the performance of linear methods, while random forest feature importance and multilayer perception (MLP) are used to assess the performance of non-linear methods. Results show that when multiple linear regression is selected as the model, WALS is a more appropriate variables selection method than random forest feature importance. Besides, random forest feature importance is a more suitable variables selection method for MLP. However, the two combinations show no statistically significant difference in the predictive power of IPO underpricing.

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