[R-sig-ME] R-sig-mixed-models Digest, Vol 9, Issue 19
Iasonas Lamprianou
lamprianou at yahoo.com
Fri Sep 14 11:50:34 CEST 2007
Dear friends, this is a question that has to do with both stats and lmer. I hope somebody could respond.
I gave a probabilities test to around 300 Year 6 and Year 7 pupils in England. I also gave the same test to their teachers (14 teachers). The test for the teachers consists of two parts, only 8 of the teachers completed the second part, so only 8 teachedrs and 230 pupils are in the analysis. I also gave the test to other 100 (approximately teachers), so I know where those 14 teachers stand compared to the other 100 teachers that completed the test. I am using the ability of the teachers on the two parts of the test as predictors of the ability of the pupils. This is the model:
ab2 <- lmer(PupilAbility ~ 1+TeacherAbilityPart_A * TeacherAbilityPArt_B +(1|TEACHER),mix,method="ML")
So, I have teachers as second level (random) and the performance of each teacher on each part of the test as predictor. Can lmer fit this model reliably in the sense that there are only eight teachers on the second level? Is it right to use second level variables (teacher's variables) as fixed effetcts where there are 230 rows/pupils and 8 teahcers (around 25 pupils per teacher - is there enough variance)?
Thanks for the response
P.S.These are the results
Linear mixed-effects model fit by maximum likelihood
Formula: ZPROBABI ~ 1 + ZPCABT * ZABILC + (1 | TEACHER)
Data: mix
AIC BIC logLik MLdeviance REMLdeviance
701 718.4 -345.5 691 695.5
Random effects:
Groups Name Variance Std.Dev.
TEACHER 0.28153 0.53059
Residual 0.98756 0.99376
number of obs: 238, groups: TEACHER, 9
Fixed effects:
Estimate Std. Error t value
(Intercept) -0.05188 0.29532 -0.1757
ZPCABT 0.41414 0.24732 1.6745
ZABILC 0.08206 0.24415 0.3361
ZPCABT:ZABILC -0.23751 0.34840 -0.6817
Correlation of Fixed Effects:
(Intr) ZPCABT ZABILC
ZPCABT 0.472
ZABILC -0.635 -0.520
ZPCABT:ZABI -0.675 -0.227 0.593
By the way, is anyone out there coming from Greece or Cyprus?
Dr. Iasonas Lamprianou
Department of Education
The University of Manchester
Oxford Road, Manchester M13 9PL, UK
Tel. 0044 161 275 3485
iasonas.lamprianou at manchester.ac.uk
----- Original Message ----
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Sent: Thursday, 13 September, 2007 7:00:05 PM
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Today's Topics:
1. Re: explaining lme variance component results (David Afshartous)
----------------------------------------------------------------------
Message: 1
Date: Thu, 13 Sep 2007 12:05:56 -0400
From: David Afshartous <dafshartous at med.miami.edu>
Subject: Re: [R-sig-ME] explaining lme variance component results
To: John Maindonald <john.maindonald at anu.edu.au>, Mike Dunbar
<mdu at ceh.ac.uk>
Cc: r-sig-mixed-models at r-project.org
Message-ID: <C30ED824.11B6%dafshartous at med.miami.edu>
Content-Type: text/plain; charset="US-ASCII"
All,
I don't have the initial e-mails from this thread and when I searched the
mail archives for "explaining lme variance component results" it doesn't
come up. Do the SIGs need to be searched differently then r-help?
Thanks,
David
On 9/6/07 5:07 AM, "John Maindonald" <john.maindonald at anu.edu.au> wrote:
> While I was out of contact with the list for a couple of days, I put the
> following together. It is for the data that Mike gave initially, so
> that
> it assumes no replicates within POLE. The mean square for
> MONTH:TIME:TRANSECT:POLE is the Residual.
>
> The variance component for TRANSECT is effectively zero. For
> purposes of exposition, it can be set to zero.
>
> The terms formula MONTH/TIME then suffices. lme() gives the numbers of
> groups as:
>
> Number of Observations: 286
> Number of Groups:
> MONTH TIME %in% MONTH
> 4 16
>
> Observe that the design is then very nearly a complete balanced design:
>
>> with(temp, table(MONTH,TIME))
> TIME
> MONTH 1 2 3 4
> 4 18 17 18 18
> 5 18 18 18 17
> 6 18 18 18 18
> 7 18 18 18 18
>
> Observe that
> 286/16=17.875
> less than 18 because two of the TIME:MONTH combinations have
> only 17 values. The harmonic mean, which is 17.87, seems however
> preferable.
>
> If the design were balanced, with replicates at
> MONTH/TIME/POLE level equal to n1=4/n2=4/n3=17.87
> then the mean squares would estimate, respectively
>
> 4 x 17.87 s1^2 + 17.87 s2^2 + s3^2 = 4 x 17.87 (s1^2 + s2^2 /4 +
> s3^2 / (4*17.87)
> 17.87 s2^2 + s3^2 = 17.87 ( s2^2 + s3^2 / 17.87)
> s3^2
>
> In the first two cases, a second version of the formula is given
> that makes (to me, at least) better intuitive sense.
>
> We have
> Variance Anova DF No. of repeats
> Component mean square per 'parent'
> MONTH 0.75287 74.10751 3 4
> TIME 1.07395 20.52433 12 4
> Residual 1.20354 1.20356 270 17.87 (harmonic mean)
>
> Observe that the residual mean square estimates the residual variance.
> The TIME variance component is calculated pretty much as
> (20.52433 - 1.20356)/17.87 = 1.0813, which does not quite agree
> with the ML estimate (nor should it; equating mean squares to expected
> mean squares is not the same as REML!)).
>
> The statistical error is affected both by the statistical error in
> the TIME
> anova mean square, and by the statistical error in the Residual mean
> square. The variance formula that is given below for MONTH can be
> readily adapted for this case also.
>
> The MONTH variance component is calculated pretty much as: (74.10751 -
> 20.52433)/(4*17.87) = 0.7497 Again the agreement with the REML
> estimate is, quite properly, not perfect.
>
> 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. The variances of the two anova mean squares (both sample
> values of chi-squared statistics, under the usual assumptions) add,
> while the quantities themselves are subtracted. The SE (sqrt of
> variance), for the estimate s1^2 of sig1^2, is
>
> sqrt( (n2 * n3 * sig1^2 + n3 * sig2^2 + sig3^2)^2 / nu1
> + (n3 * sig2^2 + sig3^2)^2 / nu2 ) / (n2*n3)
>
> [The n's are the numbers of repeats. The nu's are degrees of freedom.]
>
> Variances are not, for quantities that are differences multiples of
> chi-squared statistics, a good basis for inference. (Here I am tempted
> to make rude comments about over-reliance on variances in much
> sample survey work!). The variance calculations may however be useful
> in giving an idea of the relative contributions of the different
> sources of
> statistical noise.
>
> I'd expect, though I have not gone through the arithmetic in detail,
> that the estimate for SE[s1^2] will increase, if we allow for the
> possibility that the TRANSECT component of variance, even though
> estimated as zero, may actually be greater than zero.
>
> 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 5 Sep 2007, at 4:54 AM, Mike Dunbar wrote:
>
>> 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,
>> 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, 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,
>> 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, 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, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 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, 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, 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, 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, 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, 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, 2L, 1L, 1L, 1L, 2L, 1L, 2L,
>> 1L, 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, 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, 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, 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), .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",
>> "TRANSECT", "POLE", "TIME", "HEIGHT", "insectdens"), class =
>> "data.frame", row.names = c(1L,
>> 2L, 4L, 5L, 7L, 9L, 10L, 13L, 14L, 16L, 17L, 19L, 20L, 22L, 23L,
>> 25L, 26L, 28L, 29L, 31L, 32L, 34L, 35L, 37L, 38L, 40L, 41L, 43L,
>> 44L, 46L, 47L, 49L, 50L, 53L, 55L, 56L, 58L, 60L, 61L, 64L, 65L,
>> 67L, 68L, 70L, 71L, 73L, 74L, 76L, 77L, 79L, 80L, 82L, 83L, 85L,
>> 86L, 88L, 89L, 91L, 92L, 94L, 95L, 97L, 98L, 100L, 101L, 103L,
>> 104L, 106L, 107L, 109L, 111L, 112L, 115L, 116L, 118L, 119L, 121L,
>> 122L, 124L, 125L, 127L, 128L, 130L, 131L, 133L, 134L, 136L, 137L,
>> 139L, 140L, 142L, 143L, 145L, 146L, 148L, 149L, 151L, 152L, 154L,
>> 155L, 157L, 158L, 160L, 162L, 163L, 166L, 167L, 169L, 170L, 172L,
>> 173L, 175L, 176L, 178L, 179L, 181L, 182L, 184L, 185L, 187L, 188L,
>> 190L, 191L, 193L, 194L, 196L, 197L, 199L, 200L, 202L, 203L, 205L,
>> 206L, 208L, 209L, 211L, 213L, 214L, 217L, 218L, 220L, 221L, 223L,
>> 224L, 226L, 227L, 229L, 230L, 232L, 233L, 235L, 236L, 238L, 239L,
>> 241L, 242L, 244L, 245L, 247L, 248L, 250L, 251L, 253L, 254L, 256L,
>> 259L, 260L, 262L, 264L, 265L, 268L, 269L, 271L, 272L, 274L, 275L,
>> 277L, 278L, 280L, 281L, 283L, 284L, 286L, 287L, 289L, 290L, 292L,
>> 293L, 295L, 296L, 298L, 299L, 301L, 302L, 304L, 305L, 307L, 310L,
>> 311L, 313L, 315L, 316L, 319L, 320L, 322L, 323L, 325L, 326L, 328L,
>> 329L, 331L, 332L, 334L, 335L, 337L, 338L, 340L, 341L, 343L, 344L,
>> 346L, 347L, 349L, 350L, 352L, 353L, 355L, 356L, 358L, 359L, 361L,
>> 362L, 364L, 366L, 367L, 370L, 371L, 373L, 374L, 376L, 377L, 379L,
>> 380L, 382L, 383L, 385L, 386L, 388L, 389L, 394L, 395L, 397L, 398L,
>> 400L, 401L, 403L, 404L, 406L, 407L, 409L, 410L, 412L, 413L, 415L,
>> 417L, 418L, 421L, 422L, 424L, 425L, 427L, 428L, 430L, 431L, 433L,
>> 434L, 436L, 437L, 439L, 440L, 442L, 443L, 445L, 446L, 448L, 449L,
>> 451L, 452L, 454L, 455L, 457L, 458L, 460L, 461L, 463L, 464L, 466L,
>> 468L, 469L, 472L, 473L, 475L, 476L, 478L, 479L, 481L, 482L, 484L,
>> 485L, 487L, 488L, 490L, 491L, 493L, 494L, 496L, 497L, 499L, 500L,
>> 502L, 503L, 505L, 506L, 508L, 509L, 511L, 512L, 514L, 515L, 517L,
>> 519L, 520L, 523L, 524L, 526L, 527L, 529L, 530L, 532L, 533L, 535L,
>> 536L, 538L, 539L, 541L, 542L, 544L, 545L, 547L, 548L, 550L, 551L,
>> 553L, 554L, 556L, 557L, 559L, 560L, 562L, 563L, 565L, 566L, 568L,
>> 570L, 571L, 574L, 575L, 577L, 578L, 580L, 581L, 583L, 584L, 586L,
>> 587L, 589L, 590L, 592L, 593L, 595L, 596L, 598L, 599L, 601L, 602L,
>> 604L, 605L, 607L, 608L, 610L, 611L, 613L, 616L, 617L, 619L, 621L,
>> 622L, 625L, 626L, 628L, 629L, 631L, 632L, 634L, 635L, 637L, 638L,
>> 640L, 641L, 643L, 644L, 646L, 647L, 649L, 650L, 652L, 653L, 655L,
>> 656L, 658L, 659L, 661L, 662L, 664L, 667L, 668L, 670L, 672L, 673L,
>> 676L, 677L, 679L, 680L, 682L, 683L, 685L, 686L, 688L, 689L, 691L,
>> 692L, 694L, 695L, 697L, 698L, 700L, 701L, 703L, 704L, 706L, 707L,
>> 709L, 710L, 712L, 713L, 715L, 718L, 719L, 721L, 723L, 724L, 727L,
>> 728L, 730L, 731L, 733L, 734L, 736L, 737L, 739L, 740L, 742L, 743L,
>> 745L, 746L, 748L, 749L, 751L, 752L, 754L, 755L, 757L, 758L, 760L,
>> 761L, 763L, 764L, 766L, 769L, 770L, 772L, 774L, 775L, 778L, 779L,
>> 781L, 782L, 784L, 785L, 787L, 788L, 790L, 791L, 793L, 794L, 796L,
>> 797L, 799L, 800L, 802L, 803L, 805L, 806L, 808L, 809L, 811L, 812L,
>> 814L, 815L))
>>
>>
>> --
>> This message (and any attachments) is for the recipient on...{{dropped}}
>
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End of R-sig-mixed-models Digest, Vol 9, Issue 19
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