Cage of covariance in calibration modeling: Regressing multiple and strongly correlated response variables onto a low rank subspace of explanatory variables

Modelling with multiple explanatory variables.

Sparse Modeling of Categorial Explanatory Variables

Shrinking methods in regression analysis are usually designed for metric predictors. If independent variables are categorial some modifications are necessary. In this article two L1-penalty based methods for factor selection and clustering of categories are presented and investigated. The first approach is designed for nominal scale levels, the second one for ordinal predictors. All methods are...

Dimension Reduction of the Explanatory Variables in Multiple Linear Regression

In classical multiple linear regression analysis problems will occur if the regressors are either multicollinear or if the number of regressors is larger than the number of observations. In this note a new method is introduced which constructs orthogonal predictor variables in a way to have a maximal correlation with the dependent variable. The predictor variables are linear combinations of the...

Forward selection of explanatory variables.

This paper proposes a new way of using forward selection of explanatory variables in regression or canonical redundancy analysis. The classical forward selection method presents two problems: a highly inflated Type I error and an overestimation of the amount of explained variance. Correcting these problems will greatly improve the performance of this very useful method in ecological modeling. T...

The effects of measurement error in response variables and tests of association of explanatory variables in change models.

Biomedical studies often measure variables with error. Examples in the literature include investigation of the association between the change in some outcome variable (blood pressure, cholesterol level etc.) and a set of explanatory variables (age, smoking status etc.). Typically, one fits linear regression models to investigate such associations. With the outcome variable measured with error, ...