A Performance Assessment of Model Selection Criteria When the Number of Objects Is Much Larger than the Number of Variables in PLSR

Partial Least Squares Regression (PLSR) is a method for constructing predictive models when the variables are many and highly collinear. Its goal is to predict a set of response variables from a set of predictor variables. This prediction is achieved by extracting a set of orthogonal factors called latent variables from the predictor variables. This study investigated the performances of model selection criteria in selecting the true number of latent variables from PLSR models for data sets that have various observations and variable numbers. Their performances have been compared in terms of the simulation study and 5-fold cross validation. This simulation has been performed for different numbers of predictor variables and different numbers of observation units to compare the performance of two types of Multivariate Akaike Information criterion and three types of Wold’s R criterion in finding the number of true latent variables. The simulation results show that all criteria achieved the true number of latent variables for a small-sized design matrix. It was noticed that when the observation numbers were increased, PLSR worked with a larger number of latent variables, except for some cases. Wold’S R_2 and Wold’S R_3 found less numbers as the number of latent variables.