[R-sig-ME] explaining lme variance component results
Mike Dunbar
mdu at ceh.ac.uk
Tue Sep 4 20:54:38 CEST 2007
Thanks to all, a couple more comments following up on Kevin's comments below, and also ones sent to me directly.
I have plotted the data in many different ways, having spent several years (yes!) trying to work out a suitable analysis for these data. The aim of this particular analysis is to try to keep things as simple as possible, I'm aware in particular that there are differences between the behaviour of the factors across the months (so one option is a month by month analysis - which I have done but it was vetoed by co-workers for this paper so long as there's a simple interpretation as well), and also that time is generally the most important factor overall (this is already documented by others - the data are of drifting macroinvertebrates in rivers in case anyones interested).
The structure of the nesting is designed to mirror our expected view of the correlations in the data based on spatial/temporal proximity, a bit as Kevin describes below: so four times were measured across a day and the experiment repeated across four months, and for each of the 16 occasions, we have five transects, within those four poles each, and not described previously, 1-3 measures at different heights on the poles.
Regarding the zero values: yes the normality is an assumption, I hope to do better once this initial analysis is over. What I hoped to show is despite this, and despite the assumptions of the variance components analysis, there is evidence of an effect of TRANSECT and / or POLE, once MONTH and TIME are accounted for.
What is very pertinent (thanks John) is the fact that in the data as described, there is no replication within the lowest stratum, POLE. There was one seeming replicate, but that must be an error. This may well be the source of the problem that the POLE variance component was large but not significant.
I had thought that despite the lack of replication within POLE that it would still be possible to estimate a variance component for POLE separately from the residual. The very wooly reasoning being that the POLE component represents consistency in drift density between POLEs across TRANSECT, TIME and MONTH, and residual represents lack of consistency.
If my reasoning above is flawed, I really don't want to ditch the POLE component, as its fairly central to the analysis, and I could bring in HEIGHT to give replication within POLE (previous data is for one height only). I'd prefer to do this as a fixed effect and I've posted below some example data/code: can anyone comment if this is valid?
Regarding the issue of magnitude of variance component/random effect vs significance, I wonder if there is more too it than that, certainly in this case we know that TIME is more important than MONTH, despite being nested, but more critically, I can show some data where the magnitude of the component doesn't seem to relate to its significance. I'll post this in a separate mail to avoid confusion, once again any comments are welcome. This gives me a real headache explaining my results to my co-workers, let alone reviewers. I ought to add that there could easily still be mistakes where, as one regarding a non-replicate
has already been identified.
All the best again - hope this is interesting to others struggling with similar issues??
Mike
varcor.2h.insects.hf <- lme(log(insectdens+1) ~ HEIGHT, random=~1|MONTH/TIME/TRANSECT/POLE, data=temp2)
# introduce HEIGHT as a fixed effect, there are two heights per pole for some poles: hence unbalanced
VarCorr(varcor.2h.insects.hf)
# variances: MONTH - 0.639, TIME: 1.248, TRANSECT: 0.013, POLE: 0.160, Residual: 1.016
varcor.2h.insects.nospat.hf <- lme(log(insectdens+1) ~ HEIGHT, random=~1|MONTH/TIME, data=temp2)
anova(varcor.2h.insects.hf,varcor.2h.insects.nospat.hf)
# two spatial factors together marginally signficant: p=0.06, but test likely conservative
# simulation approach for null distribution (Faraway) probably too difficult at this depth of nesting
intervals(varcor.2h.insects.hf)
# again some evidence for significance of TRANSECT, but POLE lower bound close to 0.
# delete transect term and just compare models with and without pole term
varcor.2h.insects.pole.hf <- lme(log(insectdens+1) ~ HEIGHT, random=~1|MONTH/TIME/POLE, data=temp2)
# test pole factor on its own. This is possible as pole is coded as a combination of transect and pole within transect
anova(varcor.2h.insects.pole.hf,varcor.2h.insects.nospat.hf)
# p=0.019. This would be great if analysis is valid
# read in data: this time with one or two heights per pole
temp2 <-
structure(list(MONTH = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L
), .Label = c("4", "5", "6", "7"), class = "factor"), TRANSECT = structure(c(1L,
1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L,
1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L,
5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L,
5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L,
5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L,
5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L,
5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L,
5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L,
5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L,
5L, 5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L,
5L, 5L, 5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
5L, 5L, 5L, 5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
5L, 5L, 5L, 5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
5L, 5L, 5L, 5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
5L, 5L, 5L, 5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
5L, 5L, 5L, 5L, 5L, 5L), .Label = c("1", "2", "3", "4", "5"), class = "factor"),
POLE = structure(c(1L, 1L, 2L, 2L, 3L, 4L, 4L, 5L, 5L, 6L,
6L, 7L, 7L, 8L, 8L, 9L, 9L, 10L, 10L, 11L, 11L, 12L, 12L,
13L, 13L, 14L, 14L, 15L, 16L, 17L, 17L, 18L, 18L, 1L, 2L,
2L, 3L, 4L, 4L, 5L, 5L, 5L, 6L, 7L, 7L, 8L, 8L, 9L, 9L, 10L,
10L, 11L, 11L, 12L, 12L, 13L, 13L, 14L, 14L, 15L, 16L, 17L,
17L, 18L, 18L, 1L, 1L, 2L, 2L, 3L, 4L, 4L, 5L, 5L, 6L, 6L,
7L, 7L, 8L, 8L, 9L, 9L, 10L, 10L, 11L, 11L, 12L, 12L, 13L,
13L, 14L, 14L, 15L, 16L, 17L, 17L, 18L, 18L, 1L, 1L, 2L,
2L, 3L, 4L, 4L, 5L, 5L, 6L, 6L, 7L, 7L, 8L, 8L, 9L, 9L, 10L,
10L, 11L, 11L, 12L, 12L, 13L, 13L, 14L, 14L, 15L, 16L, 17L,
17L, 18L, 18L, 1L, 1L, 2L, 2L, 3L, 4L, 4L, 5L, 5L, 6L, 6L,
7L, 7L, 8L, 8L, 9L, 9L, 10L, 10L, 11L, 11L, 12L, 12L, 13L,
13L, 14L, 14L, 15L, 16L, 17L, 17L, 18L, 18L, 1L, 2L, 2L,
3L, 4L, 4L, 5L, 5L, 6L, 6L, 7L, 7L, 8L, 8L, 9L, 9L, 10L,
10L, 11L, 11L, 12L, 12L, 13L, 13L, 14L, 14L, 15L, 16L, 17L,
17L, 18L, 18L, 1L, 2L, 2L, 3L, 4L, 4L, 5L, 5L, 6L, 6L, 7L,
7L, 8L, 8L, 9L, 9L, 10L, 10L, 11L, 11L, 12L, 12L, 13L, 13L,
14L, 14L, 15L, 16L, 17L, 17L, 18L, 18L, 1L, 1L, 2L, 2L, 3L,
4L, 4L, 5L, 5L, 6L, 6L, 7L, 7L, 8L, 8L, 9L, 9L, 10L, 10L,
11L, 11L, 13L, 13L, 14L, 14L, 15L, 16L, 17L, 17L, 18L, 18L,
1L, 1L, 2L, 2L, 3L, 4L, 4L, 5L, 5L, 6L, 6L, 7L, 7L, 8L, 8L,
9L, 9L, 10L, 10L, 11L, 11L, 12L, 12L, 13L, 13L, 14L, 14L,
15L, 16L, 17L, 17L, 18L, 18L, 1L, 1L, 2L, 2L, 3L, 4L, 4L,
5L, 5L, 6L, 6L, 7L, 7L, 8L, 8L, 9L, 9L, 10L, 10L, 11L, 11L,
12L, 12L, 13L, 13L, 14L, 14L, 15L, 16L, 17L, 17L, 18L, 18L,
1L, 1L, 2L, 2L, 3L, 4L, 4L, 5L, 5L, 6L, 6L, 7L, 7L, 8L, 8L,
9L, 9L, 10L, 10L, 11L, 11L, 12L, 12L, 13L, 13L, 14L, 14L,
15L, 16L, 17L, 17L, 18L, 18L, 1L, 1L, 2L, 2L, 3L, 4L, 4L,
5L, 5L, 6L, 6L, 7L, 7L, 8L, 8L, 9L, 9L, 10L, 10L, 11L, 11L,
12L, 12L, 13L, 13L, 14L, 14L, 15L, 16L, 17L, 17L, 18L, 18L,
1L, 2L, 2L, 3L, 4L, 4L, 5L, 5L, 6L, 6L, 7L, 7L, 8L, 8L, 9L,
9L, 10L, 10L, 11L, 11L, 12L, 12L, 13L, 13L, 14L, 14L, 15L,
16L, 17L, 17L, 18L, 18L, 1L, 2L, 2L, 3L, 4L, 4L, 5L, 5L,
6L, 6L, 7L, 7L, 8L, 8L, 9L, 9L, 10L, 10L, 11L, 11L, 12L,
12L, 13L, 13L, 14L, 14L, 15L, 16L, 17L, 17L, 18L, 18L, 1L,
2L, 2L, 3L, 4L, 4L, 5L, 5L, 6L, 6L, 7L, 7L, 8L, 8L, 9L, 9L,
10L, 10L, 11L, 11L, 12L, 12L, 13L, 13L, 14L, 14L, 15L, 16L,
17L, 17L, 18L, 18L, 1L, 2L, 2L, 3L, 4L, 4L, 5L, 5L, 6L, 6L,
7L, 7L, 8L, 8L, 9L, 9L, 10L, 10L, 11L, 11L, 12L, 12L, 13L,
13L, 14L, 14L, 15L, 16L, 17L, 17L, 18L, 18L), .Label = c("11",
"12", "13", "14", "23", "24", "31", "32", "33", "34", "41",
"42", "43", "44", "51", "52", "53", "54"), class = "factor"),
TIME = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
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2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L), .Label = c("1",
"2", "3", "4"), class = "factor"), HEIGHT = structure(c(1L,
2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L,
2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L,
1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L,
2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L,
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1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L), .Label = c("1", "2", "3"
), class = "factor"), insectdens = c(0, 0, 63.64, 11.99,
14.57, 22.5, 15.53, 0, 20.49, 107.6, 0, 87.16, 19.82, 22.24,
18.28, 51.92, 33.87, 42.1, 59.01, 0, 47.32, 15.78, 12.46,
43.02, 12.23, 9.98, 27.75, 7.47, 38.92, 11.78, 11.18, 0,
0, 120.6, 44.61, 24.02, 45.9, 26.78, 14.56, 80.2, 62.34,
37.4, 32.44, 17.58, 47.52, 8.94, 26.01, 54.7, 9.19, 141.89,
29.36, 10.39, 48.88, 14.6, 20.46, 158.34, 20.5, 9.52, 18.82,
14.36, 47.94, 12.26, 45.76, 31.44, 53.82, 104.37, 112, 74.4,
59.88, 73.38, 94.36, 73.78, 120.26, 305, 48.12, 129.45, 264.87,
53.88, 129.36, 87.9, 107.03, 57.33, 145.53, 90.48, 95.2,
110, 116.55, 110.44, 492, 50.7, 140.4, 68.16, 111.28, 104.8,
59.76, 75, 91.92, 68.4, 12.92, 19.94, 22.6, 17.38, 53.6,
102.6, 10.45, 151.92, 30.3, 0, 0, 0, 39.18, 34.96, 16.38,
21.38, 18.32, 60.4, 35.48, 16.9, 0, 24.96, 56.28, 263.76,
38.24, 37.12, 9.26, 30.76, 26.24, 25.88, 46.48, 7.2, 21.09,
48.87, 0, 28.1, 10.09, 44.28, 67.26, 0, 0, 29.72, 50.49,
63.92, 0, 0, 0, 18.28, 10.82, 7.5, 27.06, 21.48, 9.09, 21.94,
13.56, 10.4, 13.25, 46.6, 31.74, 8.57, 11.98, 12.08, 30.55,
12.46, 31.16, 27.27, 16.35, 78.15, 100.8, 13.54, 80.44, 69.35,
104.55, 83.6, 37.32, 0, 107.7, 91.55, 21.52, 50.76, 22.28,
17, 55.6, 52.85, 40.72, 15.76, 15.12, 41.08, 25.44, 10.79,
87.36, 19.58, 19.94, 78.32, 13.04, 39.54, 40.55, 74.08, 14.37,
34.68, 31.68, 69.4, 62.28, 13.13, 117.96, 41.02, 18.27, 72.66,
34.74, 30.2, 69.86, 17.4, 100.89, 16.72, 95.7, 43.92, 0,
27.6, 129.6, 73.64, 147.4, 107.82, 92.16, 46.9, 76.1, 52.78,
52.32, 60.57, 46.7, 48.65, 49.41, 0, 54.8, 30.18, 59.2, 0,
12.52, 0, 0, 15.89, 90.39, 35.42, 26.64, 8.54, 17.46, 52.98,
7.88, 48.81, 12.68, 49.85, 32.67, 64.6, 41.2, 20.2, 8.47,
80.29, 38.52, 17.28, 35.94, 41.55, 9.4, 237.25, 0, 38.88,
24.56, 25.69, 0, 15.42, 0, 0, 0, 0, 467.64, 25.82, 36, 11.64,
112.05, 31.54, 42.08, 0, 26.86, 79.74, 0, 27.18, 17.48, 0,
34.95, 14.45, 43.88, 33.76, 23.24, 32.2, 16.29, 72.84, 189.99,
436.05, 365.6, 259.98, 329.29, 228, 158.4, 140.91, 448.95,
433.84, 47.11, 228.9, 193.13, 130.3, 335.73, 609.9, 202.54,
371.88, 332, 360.36, 219.56, 338.91, 329.94, 139.15, 262.34,
285.9, 357.76, 253.68, 353.35, 839.16, 368, 717.42, 840.18,
2081.2, 900.15, 1052.03, 705.12, 1276.65, 512.25, 838.88,
614.46, 734.58, 479.52, 286.38, 3020.4, 750.6, 885.96, 796.8,
932.49, 824.67, 1476.09, 716.76, 576.46, 528.58, 568.8, 568.8,
712.53, 1168.86, 1864.56, 997.26, 792.05, 1807.52, 899.25,
939.03, 1487.7, 1121.12, 166.5, 84.96, 78.7, 31.98, 169.2,
99.35, 124.2, 176.85, 116.88, 104.6, 45.43, 0, 82.44, 193.05,
53.5, 204.49, 135.72, 201.9, 129.76, 49.71, 50.5, 93.06,
239.98, 75.72, 221.54, 207.79, 218.24, 73.26, 96.4, 227.63,
155.4, 141.7, 280.63, 98.25, 58.4, 16.6, 30.84, 141.72, 0,
277.16, 313.82, 534.19, 104.74, 508.04, 67.62, 68.44, 119.7,
215.37, 26.92, 0, 63.24, 48.68, 11.62, 81.36, 142.5, 65.07,
28.06, 133.5, 126.54, 70.28, 79.62, 107.73, 36.16, 30.14,
31.76, 407.76, 422.24, 274.24, 317.7, 241.5, 190.3, 644.49,
162.17, 1104.24, 324.78, 268.24, 214.2, 449.25, 363.22, 475.57,
197.12, 311.63, 154.28, 461.3, 352.52, 247.69, 382.65, 395.25,
270.63, 399.84, 338.4, 529.48, 440.82, 394.56, 270.48, 322,
441.22, 353.5, 452.4, 414.96, 699.72, 89.04, 173.7, 347.6,
10150.24, 563.67, 353.94, 456.88, 117.92, 513, 245.48, 440.37,
372.36, 398.86, 334.35, 428, 410.13, 398.06, 674.87, 438.75,
226.16, 367.9, 416.8, 501.48, 522.6, 616.11, 421.2, 309.96,
423.09, 232.08, 198.06, 48.66, 109.59, 49.59, 58.05, 152.08,
0, 617.83, 64.66, 372.75, 32.07, 66.81, 112.24, 68.28, 83.64,
157.48, 145.2, 46.24, 143, 99.18, 117.5, 158.05, 61.1, 91.68,
67.5, 112.62, 98.21, 117.54, 58.92, 77.3, 0)), .Names = c("MONTH",
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