Maximum Likelihood Regression on Relevant Components
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1992 · Volume 54 · Issue 2
DOI: 10.1111/j.2517-6161.1992.tb01902.x
Abstract
Most regression methods for multicollinear data are only based on assumptions about the conditional distribution of the dependent variable, given the explanatory variables. Here we propose a new prediction method taking a joint multinomial distribution for all the variables as the starting point. A hypothesis is formulated stating that only a fixed small number of components constructed from the explanatory variables is relevant for prediction, and maximum-likelihood-type estimates of the parameters in the model are developed under this hypothesis.
Keywords
akaike criterion, collinearity, likelihood ratio test, multiple regression, prediction, principal components, relevant components from explanatory variables
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