Sağlam Kısmi En Küçük Kareler Regresyonu

Abstract

Partial Least Squares Regression (PLSR) method is a Latent Variables (LVs) regression method. Therefore, in this method, firstly, a set of unrelated LVs is predicted and then, the relationship of these LVs with dependent variable is modeled. The most popular algorithms used in literature for obtaining PLSR model are NIPALS and SIMPLS algorithms. NIPALS algorithm called PLS1, when it is used for one dependent variable and called PLS2, when it is used for multiple Y variables. However, classic Least Squares (LS) steps are used in NIPALS algorithm for obtaining loadings, components and regression coefficients and SIMPLS algorithm depends on the covariance matrix between independent and dependent variables and LS regression. Therefore, if there are outliers in the data set, the results obtained with both of the these two algorithms are affected. Hence, the robust PLSR methods, which are the robust versions of PLS1, PLS2 and SIMPLS algorithms, suggested in literature.