Modelling with multiple explanatory variables

Modelling with multiple explanatory variables.

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...

Integer Valued AR Processes with Explanatory Variables

Integer valued AR (INAR) processes are perfectly suited for modelling count data. We consider the inclusion of explanatory variables into the INAR model to extend the applicability of INAR models and give an alternative to Poisson regression models. An efficient MCMC algorithm is constructed to analyze the model and incorporates both explanatory variable and order selection. The methodology is ...

Linear regression with compositional explanatory variables

Compositional explanatory variables should not be directly used in a linear regression model because any inference statistic can become misleading. While various approaches for this problem were proposed, here an approach based on the isometric logratio (ilr) transformation is used. It turns out that the resulting model is easy to handle, and that parameter estimation can be done like in usual ...

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...