[R-sig-ME] magnitude of random effect vs significance: try 2
John Maindonald
john.maindonald at anu.edu.au
Wed Sep 12 01:08:51 CEST 2007
I'll take your points in reverse order
1. You might like to compare the following, using the kiwishade data
frame from the DAAG package
VarCorr(lme(yield ~ shade, random=~1|block/shade/plot,
data=kiwishade)) ## The units are plots
VarCorr(lme(yield ~ shade, random=~1|block/shade, data=kiwishade))
The first one splits the block:shade component of variance between
block:shade and block:shade:plot This is just wrong. The alleged
block:shade:plot component has nothing to do with plots. It is some
deep mystery in the internal workings of lme() that it splits the
block:shade component of variance in this strange way rather than
throwing an error or recognizing that block:shade:plot is just
another name for the residual, and that it should act accordingly.
Doug may be able to throw light on this.
2. "Variances are not a good basis for inference". Variances are
readily interpretable when the distributions are normal. In other
circumstances, they are more problematic, and care is necessary.
That is all I was saying.
John.
John Maindonald email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473 fax : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
John Maindonald email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473 fax : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
On 11 Sep 2007, at 9:48 PM, Mike Dunbar wrote:
>
> 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,
> 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,
> 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, 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, 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, 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, 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, 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, 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, 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,
> 1, 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, 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, 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)), .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,
> 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 9,
> 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
> 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 13, 13, 13, 13, 13, 13, 13,
> 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
> 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 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, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
> 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 10, 10, 10, 10,
> 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
> 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 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, 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,
> 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
> 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 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, 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",
> "2", "4", "5", "7", "9", "10", "13", "14", "16", "17", "19",
> "20", "22", "23", "25", "26", "28", "29", "31", "32", "34", "35",
> "37", "38", "40", "41", "43", "44", "46", "47", "49", "50", "53",
> "55", "56", "58", "60", "61", "64", "65", "67", "68", "70", "71",
> "73", "74", "76", "77", "79", "80", "82", "83", "85", "86", "88",
> "89", "91", "92", "94", "95", "97", "98", "100", "101", "103",
> "104", "106", "107", "109", "111", "112", "115", "116", "118",
> "119", "121", "122", "124", "125", "127", "128", "130", "131",
> "133", "134", "136", "137", "139", "140", "142", "143", "145",
> "146", "148", "149", "151", "152", "154", "155", "157", "158",
> "160", "162", "163", "166", "167", "169", "170", "172", "173",
> "175", "176", "178", "179", "181", "182", "184", "185", "187",
> "188", "190", "191", "193", "194", "196", "197", "199", "200",
> "202", "203", "205", "206", "208", "209", "211", "213", "214",
> "217", "218", "220", "221", "223", "224", "226", "227", "229",
> "230", "232", "233", "235", "236", "238", "239", "241", "242",
> "244", "245", "247", "248", "250", "251", "253", "254", "256",
> "259", "260", "262", "264", "265", "268", "269", "271", "272",
> "274", "275", "277", "278", "280", "281", "283", "284", "286",
> "287", "289", "290", "292", "293", "295", "296", "298", "299",
> "301", "302", "304", "305", "307", "310", "311", "313", "315",
> "316", "319", "320", "322", "323", "325", "326", "328", "329",
> "331", "332", "334", "335", "337", "338", "340", "341", "343",
> "344", "346", "347", "349", "350", "352", "353", "355", "356",
> "358", "359", "361", "362", "364", "366", "367", "370", "371",
> "373", "374", "376", "377", "379", "380", "382", "383", "385",
> "386", "388", "389", "394", "395", "397", "398", "400", "401",
> "403", "404", "406", "407", "409", "410", "412", "413", "415",
> "417", "418", "421", "422", "424", "425", "427", "428", "430",
> "431", "433", "434", "436", "437", "439", "440", "442", "443",
> "445", "446", "448", "449", "451", "452", "454", "455", "457",
> "458", "460", "461", "463", "464", "466", "468", "469", "472",
> "473", "475", "476", "478", "479", "481", "482", "484", "485",
> "487", "488", "490", "491", "493", "494", "496", "497", "499",
> "500", "502", "503", "505", "506", "508", "509", "511", "512",
> "514", "515", "517", "519", "520", "523", "524", "526", "527",
> "529", "530", "532", "533", "535", "536", "538", "539", "541",
> "542", "544", "545", "547", "548", "550", "551", "553", "554",
> "556", "557", "559", "560", "562", "563", "565", "566", "568",
> "570", "571", "574", "575", "577", "578", "580", "581", "583",
> "584", "586", "587", "589", "590", "592", "593", "595", "596",
> "598", "599", "601", "602", "604", "605", "607", "608", "610",
> "611", "613", "616", "617", "619", "621", "622", "625", "626",
> "628", "629", "631", "632", "634", "635", "637", "638", "640",
> "641", "643", "644", "646", "647", "649", "650", "652", "653",
> "655", "656", "658", "659", "661", "662", "664", "667", "668",
> "670", "672", "673", "676", "677", "679", "680", "682", "683",
> "685", "686", "688", "689", "691", "692", "694", "695", "697",
> "698", "700", "701", "703", "704", "706", "707", "709", "710",
> "712", "713", "715", "718", "719", "721", "723", "724", "727",
> "728", "730", "731", "733", "734", "736", "737", "739", "740",
> "742", "743", "745", "746", "748", "749", "751", "752", "754",
> "755", "757", "758", "760", "761", "763", "764", "766", "769",
> "770", "772", "774", "775", "778", "779", "781", "782", "784",
> "785", "787", "788", "790", "791", "793", "794", "796", "797",
> "799", "800", "802", "803", "805", "806", "808", "809", "811",
> "812", "814", "815"), class = "data.frame")
>
>
>
> --
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