Hi Tom,
In an OLS regression, the residuals from both regressions (varA ~ varB
and varB ~ varA) are different but their distributions are (more or
less) symmetric. So, because the residuals are independent (ie, their
covariance is null), the residual standard error will be the same (or
very close in practice).
In GLS, the residuals are not independent, so this difference in the
distribution of the residuals affects the estimation of the residual
standard errors (because we need to estimate the covaraince of the
residuals), and consequently the associated tests.
Best,
Emmanuel
Le 11/07/2013 11:03, Tom Schoenemann a écrit :
Hi all,
I ran a PGLS with two variables, call them VarA and VarB, using a phylogenetic
tree and corPagel. When I try to predict VarA from VarB, I get a significant
coefficient for VarB. However, if I invert this and try to predict VarB from
VarA, I do NOT get a significant coefficient for VarA. Shouldn't these be both
significant, or both insignificant (the actual outputs and calls are pasted
below)?
If I do a simple lm for these, I get the same significance level for the
coefficients either way (i.e., lm(VarA ~ VarB) vs. lm(VarB ~ VarA), though the
values of the coefficients of course differ.
Can someone help me understand why the PGLS would not necessarily be symmetric
in this same way?
Thanks,
-Tom
outTree_group_by_brain_LambdaEst_redo1 <- gls(log_group_size_data ~
log_brain_weight_data, correlation = bm.t.100species_lamEst_redo1,data =
DF.brain.repertoire.group, method= "ML")
summary(outTree_group_by_brain_LambdaEst_redo1)
Generalized least squares fit by maximum likelihood
Model: log_group_size_data ~ log_brain_weight_data
Data: DF.brain.repertoire.group
AIC BIC logLik
89.45152 99.8722 -40.72576
Correlation Structure: corPagel
Formula: ~1
Parameter estimate(s):
lambda
0.7522738
Coefficients:
Value Std.Error t-value p-value
(Intercept) -0.0077276 0.2628264 -0.029402 0.9766
log_brain_weight_data 0.4636859 0.1355499 3.420778 0.0009
Correlation:
(Intr)
log_brain_weight_data -0.637
Standardized residuals:
Min Q1 Med Q3 Max
-1.7225003 -0.1696079 0.5753531 1.0705308 3.0685637
Residual standard error: 0.5250319
Degrees of freedom: 100 total; 98 residual
Here is the inverse:
outTree_brain_by_group_LambdaEst_redo1 <- gls(log_brain_weight_data ~
log_group_size_data, correlation = bm.t.100species_lamEst_redo1,data =
DF.brain.repertoire.group, method= "ML")
summary(outTree_brain_by_group_LambdaEst_redo1)
Generalized least squares fit by maximum likelihood
Model: log_brain_weight_data ~ log_group_size_data
Data: DF.brain.repertoire.group
AIC BIC logLik
-39.45804 -29.03736 23.72902
Correlation Structure: corPagel
Formula: ~1
Parameter estimate(s):
lambda
1.010277
Coefficients:
Value Std.Error t-value p-value
(Intercept) 1.2244133 0.20948634 5.844836 0.0000
log_group_size_data -0.0234525 0.03723828 -0.629796 0.5303
Correlation:
(Intr)
log_group_size_data -0.095
Standardized residuals:
Min Q1 Med Q3 Max
-2.0682836 -0.3859688 1.1515176 1.5908565 3.1163377
Residual standard error: 0.4830596
Degrees of freedom: 100 total; 98 residual
_________________________________________________
P. Thomas Schoenemann
Associate Professor
Department of Anthropology
Cognitive Science Program
Indiana University
Bloomington, IN 47405
Phone: 812-855-8800
E-mail: t...@indiana.edu
Open Research Scan Archive (ORSA) Co-Director
Consulting Scholar
Museum of Archaeology and Anthropology
University of Pennsylvania
http://www.indiana.edu/~brainevo
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