On Feb 12, 2012, at 7:39 AM, Evagelopoulos Thanasis wrote:
Could you please help me on the following ANCOVA issue?
This is a part of my dataset:
sampling dist h
1 wi 200 0.8687212
2 wi 200 0.8812909
3 wi 200 0.8267464
4 wi 0 0.8554508
5 wi 0 0.9506721
6 wi 0 0.8112781
7 wi 400 0.8687212
8 wi 400 0.8414646
9 wi 400 0.7601675
10 wi 900 0.6577048
11 wi 900 0.6098403
12 wi 900 0.5574382
13 sp 200 0.9149264
14 sp 200 0.9149264
15 sp 200 0.9248187
16 sp 0 0.9974016
17 sp 0 0.9997114
18 sp 0 0.8812909
...
h is the dependent variable, distance the covariate and sampling the
factor.
the slopes for h~distance linear regressions are significantly
different from 0 for all samplings
In order to compare the regression slopes for each sampling, i did
an ANCOVA with the ancova() function of the HH package:
mod<-ancova(h~sampling*dist,data)
There was a significant interaction term:
Barely. A borderline interaction may be of trivial importance when
interpreted in the context of a model which has much stronger "main
effects". Just using the anova table will hide the magnitude of the
interaction effects. Was this an effect that was predicted by theory
or even one which has interpretation in an experimental setting that
leads to actionable conclusions?
Analysis of Variance Table
Response: h
Df Sum Sq Mean Sq F value Pr(>F)
sampling 3 0.22822 0.07607 13.7476 2.624e-06 ***
dist 1 0.51291 0.51291 92.6908 5.703e-12 ***
sampling:dist 3 0.05112 0.01704 3.0792 0.03822 *
Residuals 40 0.22134 0.00553
Because there exist significantly different regression slopes, I did
a post hoc test with glht() to find out between which samplings:
summary(glht(mod, linfct=mcp(sampling="Tukey")))
The results seem to say that there are no significantly different
slopes for any of the pair-wise comparisons of factor levels:
Simultaneous Tests for General Linear Hypotheses
Multiple Comparisons of Means: Tukey Contrasts
Fit: aov(formula = h ~ sampling * dist, data = data)
Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
sp - au == 0 0.06696 0.04562 1.468 0.457
su - au == 0 -0.02238 0.04562 -0.491 0.961
wi - au == 0 0.01203 0.04562 0.264 0.994
su - sp == 0 -0.08934 0.04562 -1.958 0.204
wi - sp == 0 -0.05493 0.04562 -1.204 0.624
wi - su == 0 0.03441 0.04562 0.754 0.875
(Adjusted p values reported -- single-step method)
Warning message:
In mcp2matrix(model, linfct = linfct) :
covariate interactions found -- default contrast might be
inappropriate
My questions are:
- Did I make a mistake somewhere? (I probably did!)
(I did a search for prior questions of this sort (post-hoc testing in
models with interactions) and found many fewer than I would have
expected and many that I found had no answers offered, which I found
surprising.)
You called the multiple comparisons function without specifying the
"level" at which the multiple comparisons should be conducted and the
function warned you that it might not be returning the results you
expect under such conditions. I've looked at multcomp::glht's help
page and it wasn't immediately evident to me how one would request
comparisons just among the second-order interactions. It appears there
are both matrix and "symbolic" options, but the exact syntax for
specifying the symbolic options is not to my reading well described.
The description in the help page texts seems at odds within the
example on the same page.
A vignette is cited on the help page. Looking through the vignette,
"Simultaneous Inference in General Parametric Models", I see that
there is an example of the application of `glht` to an interaction
model (section 6.3). It uses the matrix formulation but unfortunately
does not include the code used to create the "K" matrix for that
model. I tried using the code offered earlier in the vignette for that
purpose but it doesn't agree with the offered K matrix in that
section. So ...
K <- read.table( text="(Icpt) s<10 s10-20 s>20 gMale s<10:gMale
s10-20:gMale s>20:gMale
None:Female 1 0 0 0 0 0 0 0
<10:Female 1 1 0 0 0 0 0 0
10-20:Female 1 0 1 0 0 0 0 0
>20:Female 1 0 0 1 0 0 0 0
None:Male 1 0 0 0 1 0 0 0
<10:Male 1 1 0 0 1 1 0 0
10-20:Male 1 0 1 0 1 0 1 0
>20:Male 1 0 0 1 1 0 0 1 ", header=TRUE, check.names=FALSE)
K <- as.matrix(K)
(And then I get the same output as in the vignette. Unfortunately the
mechanical process of constructing that matrix did not leave me with
the theoretical understanding of how it was created.
##-----------
Another option might be to simply use TukeyHSD specifying the second
argument as "sampling:dist". When used with the example on TukeyHSD on
this model I get what seem to me to be interpretable results:
fm2 <- aov(breaks ~ wool * tension, data = warpbreaks)
TukeyHSD(fm2, "wool:tension")
It appears that all of the nominally significant comparisons involve
the "A" wool type and "L" tension, so an industrially meaningful
response would be to tighten up the loom tension only when using type
"A". That was not a conclusion that would ahve been possible to arrive
at using just a simple model of:
breaks ~ wool + tension
I'm hoping that some of the real statisticians will comment on these
ideas. I'm just a suburban physician with hopes of learning as I get
older.
- Could I do pairwise ANCOVAs and thus have just two factor levels
(=two regression slopes) to compare each time?
What does the warning message "covariate interactions found --
default contrast might be inappropriate" mean?
Thank you!
Athanasios Evagelopoulos
David Winsemius, MD
West Hartford, CT
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
