In the current estimation of a GLM model, the correlation structure of regressors is not used as the basis on which to lean strong predictive dimensions. Looking for linear combinations of regressors that merely maxim...
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In the current estimation of a GLM model, the correlation structure of regressors is not used as the basis on which to lean strong predictive dimensions. Looking for linear combinations of regressors that merely maximize the likelihood of the GLM has two major consequences: (1) collinearity of regressors is a factor of estimation instability, and (2) as predictive dimensions may lean on noise, both predictive and explanatory powers of the model are jeopardized. For a single dependent variable, attempts have been made to adapt PLS regression, which solves this problem in the classical linear Model, to GLM estimation. In this paper, we first discuss the methods thus developed, and then propose a technique, supervised component generalized linear regression (SCGLR), that combines PLS regression with GLM estimation in the multivariate context. SCGLR is tested on both simulated and real data. (C) 2013 Elsevier Inc. All rights reserved.
In event-history analysis with many possibly collinear regressors, Cox's proportional hazard model, like all generalizedlinear models, can fail to be identified. Dimension-reduction and regularization are therefo...
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In event-history analysis with many possibly collinear regressors, Cox's proportional hazard model, like all generalizedlinear models, can fail to be identified. Dimension-reduction and regularization are therefore needed. Penalty-based methods such as the ridge and the least absolute shrinkage and selection operator (LASSO) provide a regularized linear predictor, but fail to highlight the predictive structures. This is the gap filled by the supervised-component Cox regression (SCCoxR). Its principle is to compute a sequence of orthogonal explanatory components, which both rely on the strong correlation structures of regressors and optimize the goodness-of-fit of the model. One of its parameters tunes the balance between component strength and goodness of fit, thus bridging the gap between classical Cox regression with Cox regression on principal components. A second parameter allows the focus on subsets of highly correlated explanatory variables. A third parameter tunes the regularization of the model coefficients, leading to more robust estimates. Simulations show how to tune the parameters. The method is applied to the case study of polygamy in Dakar, Senegal.
When multiple correlated predictors are considered jointly in regression modeling, estimated coefficients may assume counterintuitive and theoretically uninterpretable values. We survey several statistical methods tha...
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When multiple correlated predictors are considered jointly in regression modeling, estimated coefficients may assume counterintuitive and theoretically uninterpretable values. We survey several statistical methods that implement strategies for the analysis of collinear data: regression with regularization (the elastic net), supervised component generalized linear regression, and random forests. Methods are illustrated for a data set with a wide range of predictors for segment duration in a German speech corpus. Results broadly converge, but each method has its own strengths and weaknesses. Jointly, they provide the analyst with somewhat different but complementary perspectives on the structure of collinear data. (C) 2018 The Authors. Published by Elsevier Ltd.
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