Abstract
Among many statistical methods for linear models with the multicollinearity problem, partial least squares regression (PLSR) has become, in recent years, increasingly popular and, very often, the best choice. However, while dealing with the predicting problem from automobile market, we noticed that the results from PLSR appear unstable though it is still the best among some standard statistical methods. This unstable feature is likely due to the impact of the information contained in explanatory variables that is irrelevant to the response variable. Based on the algorithm of PLSR, this paper introduces a new method, modified partial least squares regression (MPLSR), to emphasize the impact of the relevant information of explanatory variables on the response variable. With the MPLSR method, satisfactory predicting results are obtained in the above practical problem. The performance of MPLSR, PLSR and some standard statistical methods are compared by a set of Monte Carlo experiments. This paper shows that the MPLSR is the most stable and accurate method, especially when the ratio of the number of observation and the number of explanatory variables is low.
Highlights
In automobile market, the auction price of two-year-in-service vehicle is an important indicator of that vehicle’s market value, which is of great interest to manufacturers, dealers, financial institutions and consumers
When the four methods (PLSR, RR, principal components regression (PCR) and variable subset selection method (VSS)) are used to predict the auction price referred in the first paragraph, the algorithms of partial least squares regression (PLSR) and RR reach better results compared to the very large average relative errors from using VSS and PCR, their performances on five different vehicle lines are unstable, and unsatisfactory, despite the fact that the five vehicle lines have very similar position in automobile market. While studying this practical question, we discovered the reason behind the unstable performance of PLSR and developed the more stable modified partial lease square regression (MPLSR), a modification of PLSR
modified partial least squares regression (MPLSR) method has been introduced when the explanatory matrix X includes much information irrelevant to the response variable Y. It is an algebraic algorithm based on the result of the PLSR method
Summary
The auction price of two-year-in-service vehicle is an important indicator of that vehicle’s market value, which is of great interest to manufacturers, dealers, financial institutions and consumers. When linear model is used to predict the auction price, multicollinearity arises. Multicollinearity often exists when the number of explanatory variables is large compared to the number of observations, and it causes difficulty estimating parameters. The variable subset selection method (VSS) is used to avoid the multicollinearity caused by too many variables, and the stepwise version is used here. The ridge regression (RR) was suggested by Hoerl and Kennard (1970) as a
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