Regression analysis in the presence of multicollinearity in brain substructures

在这项研究中，我们进行了广泛的模拟研究，以比较各种回归方法，以获得存在高度多重共线性的回归参数。共线程度的一个衡量标准是方差影响因子(VIF)。VIF值大于10表示高度碰撞。基于模拟，我们发现，在存在中等到较高的碰撞时，岭回归和套索对多重共线性和产量估计不那么敏感，具有较小的均方根误差(RMSE)。另一方面，通常的降维方法，即PCR法和PLSR法，会产生有偏的估计。仿真结果表明，LASSO和岭回归是分析共线性较高的脑成像数据的两种合适的方法。

In this research, we conducted extensive simulation studies to compare various regression methods to obtain regression parameters in the presence of high multicollinearity. One measure of the degree of collinearity is the variance inflaction factor (VIF). A VIF value greater than 10 is an indication of high colliearity. Based on the simulation, we found that, in the presence of moderate to higher colliearity, the ridge regression and LASSO are less sensitive to multicollinearity and yield estimates with smaller root mean square error (RMSE). On the other hand, the usual dimension reduction method, i.e., PCR and PLSR, yielded biased estimates. This simulation suggested that LASSO and ridge regression are two appropriate methods for analyzing brain imaging data with high collinearity.