[R-sig-ME] magnitude of random effect vs significance: try 2
Mike Dunbar
mdu at ceh.ac.uk
Tue Sep 11 13:48:59 CEST 2007
I'm hoping I am getting close to the end of posting on this topic and associated topic "explaining lme variance component results".
Firstly many thanks again to John, Peter and Kevin for comments so far. I have discovered an error in the coding in one row, now corrected (thanks John) and am also much more informed as to how to ensure correct coding for nested model comparison (thanks Peter).
I'm also better informed as to the links between anova-based analyses and REML-based (thanks John), but still struggle with these anovas.
Two points I'd like to follow up on.
1.
Firstly Kevin's point that
"In my experience with biological data, factors that have levels that are widely (temporal/spatial) separated are often more variable than factors with levels that are closer together"
and linked to John's points
"Variances are not, for quantities that are differences multiples of chi-squared statistics, a good basis for inference."
and
"The estimate for s1^2 (MONTH} has a statistical error that is a compound of the errors in the ANOVA mean squares for both TIME and MONTH."
Generalising from anova mean squares principles, it makes sense that the variation for coarser-grain factors (i.e. less well replicated, more widely varying in time and or space) is likely to be higher by chance because confounded within it is some of the variation that ought to be in the finer level factors (whether the factors are specifed or unknown). In addition, the inevitable poorer replication at the coarse level reduces power. Now I can see how this follows analytically in the case of anova mean squares derived analysis, however I'd just like some advice that the same principles apply in REML-derived analyses.
If this reasoning is correct, then I have no trouble explaining the results from the attached analysis. In this case, to abbreviate the full table, we have.
Variance p-value (from LR test, removing single factor)
MONTH 0.639 0.1889
..
POLE 0.160 0.0496
...
Note that month is the coarser grain factor, and pole the finer. If there are any references as to why its the p-values from LR tests that matter and not the magnitude of the components (other than John Maindonald, pers. comm. which is OK of course) that would do me a massive favour. In my manuscript, I could of course illustrate with anova-derived workings now John has explained this, but I would prefer to just present the REML-based analyses.
2.
I'm still slightly muddled about the implications of including a random effect at the finest unreplicated level. Again I can understand that since there is no replication, the random effect at that level should be confounded with the residual. However, in practice, lme(r) still gives separate variances for the two components. How can this be? Is REML extracting some information that is not available in an anova-based analysis. In the analysis below, replication is obtained at the finest level by there being 2 levels of the height factor in many cases (but not all, its unbalanced), but since I know there is a consistent height effect, I add a fixed effect for this, are we back to square one and no fine-level replication. Again I would appreciate any advice and will try to bring this to a close now (honest!)
regards
Mike
# analysis: data are below
varcor.2h.insects.hf <- lme(log(insectdens+1) ~ HEIGHT, random=~1|MONTH/TIME/TRANSECT/POLE, data=temp4)
VarCorr(varcor.2h.insects.hf)
# variance for month: 0.639, time: 1.24, transect: 0.013, pole: 0.160, resid: 1.02
varcor.2h.insects.nomonth.hf <- lme(log(insectdens+1) ~ HEIGHT, random=~1|MONTHTIME/TRANSECT/POLE, data=invdens.bottommiddle) # P Dalgaard email
varcor.2h.insects.nopole.hf <- lme(log(insectdens+1) ~ HEIGHT, random=~1|MONTH/TIME/TRANSECT, data=invdens.bottommiddle)
anova(varcor.2h.insects.hf,varcor.2h.insects.nomonth.hf) # p=0.1889
anova(varcor.2h.insects.hf,varcor.2h.insects.nopole.hf) # p= 0.0496 (p is lower if ns month and transect terms removed)
# read in data first
temp4 <-
structure(list(MONTH = structure(as.integer(c(1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
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2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
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3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
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4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4)), .Label = c("4", "5", "6", "7"
), class = "factor"), TRANSECT = structure(as.integer(c(1, 1,
1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4,
4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3,
3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5,
1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4,
4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 2, 2,
2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5,
5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3,
3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1,
2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5,
5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3,
3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1,
1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5,
5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3,
3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1,
1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4,
4, 4, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3,
3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 1,
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4,
4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2,
3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5,
5, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4,
4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 2, 2, 2,
2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5,
5, 5, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4,
4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5)), .Label = c("1", "2",
"3", "4", "5"), class = "factor"), POLE = structure(as.integer(c(1,
1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11,
12, 12, 13, 13, 14, 14, 15, 16, 17, 17, 18, 18, 1, 2, 2, 3, 4,
4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13,
13, 14, 14, 15, 16, 17, 17, 18, 18, 1, 1, 2, 2, 3, 4, 4, 5, 5,
6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14,
15, 16, 17, 17, 18, 18, 1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7,
8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 16, 17,
17, 18, 18, 1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9,
10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 16, 17, 17, 18, 18,
1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11,
12, 12, 13, 13, 14, 14, 15, 16, 17, 17, 18, 18, 1, 2, 2, 3, 4,
4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13,
13, 14, 14, 15, 16, 17, 17, 18, 18, 1, 1, 2, 2, 3, 4, 4, 5, 5,
6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 13, 13, 14, 14, 15, 16,
17, 17, 18, 18, 1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8,
9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 16, 17, 17,
18, 18, 1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10,
10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 16, 17, 17, 18, 18, 1,
1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11,
12, 12, 13, 13, 14, 14, 15, 16, 17, 17, 18, 18, 1, 1, 2, 2, 3,
4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13,
13, 14, 14, 15, 16, 17, 17, 18, 18, 1, 2, 2, 3, 4, 4, 5, 5, 6,
6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14,
15, 16, 17, 17, 18, 18, 1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8,
8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 16, 17,
17, 18, 18, 1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10,
10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 16, 17, 17, 18, 18, 1,
2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11,
12, 12, 13, 13, 14, 14, 15, 16, 17, 17, 18, 18)), .Label = c("11",
"12", "13", "14", "23", "24", "31", "32", "33", "34", "41", "42",
"43", "44", "51", "52", "53", "54"), class = "factor"), TIME = structure(as.integer(c(1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4)), .Label = c("1", "2",
"3", "4"), class = "factor"), HEIGHT = structure(as.integer(c(1,
2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1,
2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2,
1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1,
2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1,
2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1,
2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1,
1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2,
1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1,
2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2,
1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1,
2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2,
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1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1,
2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2,
1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2)), .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), MONTHTIME = structure(as.integer(c(1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
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14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
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11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 15,
15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,
16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,
16)), .Label = c("4.1", "5.1", "6.1", "7.1", "4.2", "5.2", "6.2",
"7.2", "4.3", "5.3", "6.3", "7.3", "4.4", "5.4", "6.4", "7.4"
), class = "factor")), .Names = c("MONTH", "TRANSECT", "POLE",
"TIME", "HEIGHT", "insectdens", "MONTHTIME"), row.names = c("1",
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"812", "814", "815"), class = "data.frame")
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