lm-utils {MPSEM}

Linear Modelling Utility Functions

Description

Utility functions to build linear models using Phylogenetic Eigenvector Maps among their explanatory variables.

Usage

lmforwardsequentialAICc(y, x, object)

lmforwardsequentialsidak(y, x, object, alpha = 0.05)

Arguments

y

A response variable.

x

Descriptors to be used as auxiliary traits.

object

A PEM-class object.

alpha

The threshold above which to stop adding variables.

Details

Function lmforwardsequentialsidak, performs a forward stepwise selection of the PEM eigenvectors until the familywise test of significance of the new variable to be included exceeds the threshold alpha. The familiwise type I error probability is obtained using the Holm-Sidak correction of the testwise probabilities, thereby correcting for type I error rate inflation due to multiple testing. lmforwardsequentialAICc carries out forward stepwise selection of the eigenvectors as long as the candidate model features a lower sample-size-corrected Akaike information criterion than the previous model. The final model should be regarded as overfit from the Neyman-Pearson (i.e. frequentist) point of view, but it is the model that minimizes information loss from the standpoint of information theory.

Value

An lm-class object.

Functions

• lmforwardsequentialAICc: Forward stepwise variable addition using the sample-size-corrected Akaike Information Criterion.

• lmforwardsequentialsidak: Forward stepwise variable addition using a Sidak multiple testing corrected alpha error threshold as the stopping criterion.

Author(s)

Guillaume Guenard, with contribution from Pierre Legendre Maintainer: Guillaume Guenard <[e-mail]>

References

Burnham, K. P. & Anderson, D. R. 2002. Model selection and multimodel inference: a practical information-theoretic approach, 2nd ed. Springer-Verlag. xxvi + 488 pp.

Holm, S. 1979. A simple sequentially rejective multiple test procedure. Scand. J. Statist. 6: 65-70.

Sidak, Z. 1967. Rectangular confidence regions for means of multivariate normal distributions. J. Am. Stat. Ass. 62, 626-633.