[R-sig-eco] hierarchical partitioning: type of R-squared

[Howe, Eric (MNR)]

Good day Clement, and R users,
I've used the hier.part package.  I think that conceptually, if the form of relationship with the dependent variable differs among independent variables, hier.part won't provide unbiased results.  Different samples from the same population should yield the same estimates of the relative contribution of different independent variables to (explained) variation in the dependent variable (Chevan and Sutherland 1991). If the form of the relationships between independent and the dependent variables differ, then you'd get different results from different samples, e.g. if one sample included more values of the dependent variable from one end of the possible range (?).  Maybe someone can confirm or refute this? Or explain it better?

Since I use this package, I'd like to clear up something I noticed in Clement's message: I thought that when using "R-squ" as the goodness of fit measures, unadjusted values were used. That seemed consistent with Pearson's correlation coefficients. Can anyone confirm?

Thanks,
Eric Howe


-----Original Message-----
From: r-sig-ecology-bounces at r-project.org [mailto:r-sig-ecology-bounces at r-project.org] On Behalf Of Clément Tisseuil
Sent: October 14, 2009 3:16 AM
To: r-sig-ecology at r-project.org
Subject: [R-sig-eco] hierarchical partitioning: adaptation and interpretation

Dear R users,

In the hier.part package, hierarchical partitioning is built upon a GLM
(generalized linear model) framework to assess the independent and joint
effect from a set of predictors onto a single quantitative response
variable. In this context, the joint and independent effect from each factor
can be evaluated throughout the R² calculation (adjusted). My two questions
are:

1. Conceptually and from a statistical point of view, are there any problems
to adapt the philosophy of hierarchical partitioning to a GAM (generalized
additive model) framework when some quantitative predictors are supposed to
have a non-linear effect with the response variable?

2. Let's say that the total variance of a single continuous variable can be
explained by two qualitative factors (X1 and X2). I wonder if this total R²
value resulting from the hier.part analysis (total=joint+independent value),
and calculated individually for X1 and X2, can be discussed in terms of the
inter-group variance (i.e. something like the variance between the means of
each modalities of factors). If so, can the unexplained variation from the
analysis (1- total R²) be associated to the intra-group variance (e.g.
something like the variance within each modalities of factors)?
.
Thanks in advance for your help,

Clement

-- 
Clement Tisseuil - PhD student

Laboratoire  "Evolution et Diversité Biologique" (EDB)
UMR 5174 - Université Paul Sabatier CNRS
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31062 Toulouse Cedex 9 - France
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webpage: http://www.clement-tisseuil.eu

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