Hi everyone,
I am trying to piece together the current best-practices for
"phylogenetic ANOVA" with multi-state predictors.
In my dataset, my four-level factor is non-random with respect to
phylogeny. That is, if I know which higher level clade an species
belongs to, I can predict with pretty good success which factor level
it will be in. My understanding is that this situation likely
overinflates my degrees of freedom and makes traditional F-tests
inappropriate. I came across this paper (Garland et al 1993.
Phylogenetic Analysis of Covariance by Computer Simulation. Systematic
Biology 42:265 -292.) where the authors empirically recalculate
critical values for F-ratios using computer simulations, tree
topology, and a model of character evolution.
I also have found that I can use PGLS (with ape and nlme) and specify
my model like this.
gls(myVar~myFactor,corr=corPagel(val=1,phy=myTree,fixed=F),data=myDF)
As I understand it, gls() is doing a multiple generalized LS
regression with as many dummy variables as there are factor levels.
Is this a correct characterization? Does this sidestep the degrees of
freedom problem discussed by Garland et al.? Can anybody point me to
references discussing the mechanics of this process and why this is an
appropriate thing to do?
Finally, I get a negative value for estimated lambda. Any ideas on
what that means?
Thanks to everyone for any advice/references/.
Andrew Barr
PhD Student
University of Texas at Austin
####results from my model
Generalized least squares fit by REML
Model: LIWI ~ Hab
Data: aggast
AIC BIC logLik
-65.61627 -56.28418 38.80814
Correlation Structure: corPagel
Formula: ~1
Parameter estimate(s):
lambda
-0.1480891
Coefficients:
Value Std.Error t-value p-value
(Intercept) 1.4492742 0.01876415 77.23635 0.0000
HabH -0.0224975 0.03149986 -0.71421 0.4798
HabL -0.0668761 0.03066232 -2.18105 0.0360
HabO -0.1630386 0.02567505 -6.35008 0.0000
Correlation:
(Intr) HabH HabL
HabH -0.686
HabL -0.794 0.485
HabO -0.936 0.594 0.542
Standardized residuals:
Min Q1 Med Q3 Max
-2.17865325 -0.60297897 -0.09760938 0.41995284 2.91201671
Residual standard error: 0.06913702
Degrees of freedom: 39 total; 35 residual
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