[R-sig-ME] interpretation of range value from lme model with exponential correlation structure
Kevin Wright
kw.stat at gmail.com
Thu Nov 20 17:49:37 CET 2014
I have an example in the agridat package you might find useful. First
the code and then a bit of interpretation.
require(agridat)
dat <- harris.wateruse
dat <- subset(dat, day!=268)
# Rescale day for nicer output, and convergence issues, add quadratic term
dat <- transform(dat, ti=day/100)
dat <- transform(dat, ti2=ti*ti)
require(nlme)
m3l <- lme(water ~ 0 + age:species + age:species:ti + age:species:ti2,
data=dat, na.action=na.omit,
random = list(tree=pdDiag(~1+ti)),
cor = corExp(form=~ day|tree),
)
print(m3l)
Linear mixed-effects model fit by REML
Data: dat
Log-restricted-likelihood: -497.8969
Fixed: water ~ 0 + age:species + age:species:ti + age:species:ti2
ageA1:speciesS1 ageA2:speciesS1 ageA1:speciesS2 ageA2:speciesS2
-14.569534 -12.305968 -6.749603 -11.362943
ageA1:speciesS1:ti ageA2:speciesS1:ti ageA1:speciesS2:ti ageA2:speciesS2:ti
14.408342 13.538021 7.920372 12.837023
ageA1:speciesS1:ti2 ageA2:speciesS1:ti2 ageA1:speciesS2:ti2 ageA2:speciesS2:ti2
-2.980521 -2.856673 -1.844861 -2.940303
Random effects:
Formula: ~1 + ti | tree
Structure: Diagonal
(Intercept) ti Residual
StdDev: 0.3935732 0.1668882 0.4000106
Correlation Structure: Exponential spatial correlation
Formula: ~day | tree
Parameter estimate(s):
range
4.721752
Number of Observations: 953
Number of Groups: 40
This example comes from a book by Schabenberger & Pierce. See:
http://books.google.com/books?id=c2Rr_J7geGQC&pg=PA518#v=onepage&q&f=false
They say "since the measurement times are coded in days, this estimate
of phi=4.721752 implies that water usage exhibits temporal correlation
over 3*phi = 14.16 days."
They did not justify this...it looks like a rule-of-thumb. Note that
exp(-14.16/4.7217) = .05.
Kevin
On Wed, Nov 19, 2014 at 10:53 PM, Janee Wilkinson
<janeemwilkinson at gmail.com> wrote:
> Hi there,
>
> I am fitting a model using the lme function with an exponential correlation
> structure, e.g.
> lme(y~fixed1+fixed2, random =~1|subject,
> cor=corExp(form=~distance|subject,nugget=TRUE))
>
> How do I interpret the range value?
>
> In a paper I described the range as the distance at which observations are
> uncorrelated but a reviewer has said this is incorrect and that the range
> specifies the rate at which the correlation tends to zero.
>
> I thought that the usual interpretation of the range was that observations
> separated by less than the range are spatially autocorrelated, whereas
> observations further apart than the range are not.
>
> >From the help file for corExp, letting d denote the range and n denote the
> nugget effect, the correlation between two observations a distance r apart
> is (1-n)*exp(-r/d). So when the distance=range, the correlation will be
> (1-n)*exp(-1), which will not be zero.
>
> Any help would be much appreciated.
>
> Thanks,
>
> Janee.
>
> [[alternative HTML version deleted]]
>
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--
Kevin Wright
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