[R] Naming a random effect in lmer

Douglas Bates bates at stat.wisc.edu
Sun May 24 16:37:50 CEST 2009


Hi Bill,

I'm about to take a look at this.  If I understand the issue, very
long expressions for what I call the "grouping factor" of a random
effects term (the expressions on the right hand side of the vertical
bar) are encountering problems with deparse.  I should have realized
that, any time one uses deparse, disaster looms.

I can tell you the reason that the collection of random-effects terms
is being named is partly for the printed form and partly so that terms
with the same grouping factor can be associated.

I guess my simplistic solution to the problem would be to precompute
these sums and give them names, if it is the sum like

Z2 + Z3 + Z4 + Z5 + Z6 + Z7 + Z8 + Z9

that is important, why not evaluate the sum

testGroupSamp <- within(testGroupSamp, Z29 <- Z2 + Z3 + Z4 + Z5 + Z6 +
Z7 + Z8 + Z9)

and use Z29 as the grouping factor.

Even the use of variables with names like Z1, Z2, ... and the use of
expressions like paste("Z", 2:9, sep = "") is not idiomatic R/S code.
It's an SPSS/SASism.  (You know I never realized before how close the
word "SASism", meaning a construction that is natural in SAS, is to
"Sadism".)  Why not create a matrix Z and evaluate these sums as
matrix/vector products?


Zs2<- paste("Z",2:9,sep="")


On Fri, May 22, 2009 at 5:30 PM, William Dunlap <wdunlap at tibco.com> wrote:
>> -----Original Message-----
>> From: r-help-bounces at r-project.org
>> [mailto:r-help-bounces at r-project.org] On Behalf Of spencerg
>> Sent: Friday, May 22, 2009 3:01 PM
>> To: Leigh Ann Starcevich
>> Cc: r-help at r-project.org
>> Subject: Re: [R] Naming a random effect in lmer
>>
>> [ ... elided statistical advice ... ]
>> If you and your advisor still feel that what you are doing
>> makes sense,
>> I suggest you first get the source code via "svn checkout
>> svn://svn.r-forge.r-project.org/svnroot/lme4" (or by downloading
>> "lme4_0.999375-30.tar.gz" from
>> "http://cran.fhcrc.org/web/packages/lme4/index.html"), then
>> walk through
>> the code line by line using the "debug" function (or "browser" or the
>> "debug" package). From this, you will likely see either (a)
>> how you can
>> do what you want differently to achieve the same result or (b) how to
>> modify the code so it does what you want.
>
> The coding error is right in the error message:
>  Error in names(bars) <- unlist(lapply(bars, function(x)
> deparse(x[[3]])))
> and I suspect that traceback() would tell you that came from a call
> to lmerFactorList.
>
> That code implicitly assumes that deparse() will produce a scalar
> character
> vector, but it doesn't if the input expression is complicated enough.
> Changing the
>    deparse(x[[3]])
> to
>    deparse(x[[3]])[1]
> or
>    paste(collapse=" ", deparse(x[[3]])[1])
> would fix it.  The first truncates the name and the second my make a
> very
> long name.
>
> There is at least one other use of that idiom in the lme4 code and your
> dataset and analysis may require that all of them be fixed.
>
>>
>>
>> Hope this helps.
>> Spencer
>>
>>
>> Leigh Ann Starcevich wrote:
>> > Here is a test data set and code. I am including the data set after
>> > the code and discussion to make reading easier. Apologies
>> for the size
>> > of the data set, but my problem occurs when there are a lot of Z
>> > variables. Thanks for your time.
>> >
>> > # Enter data below
>> >
>> > # Sample code
>> > library(lme4)
>> > mb<- length(unique(testsamp$WYear))
>> >
>> > # Create the formula for the set of identically distributed random
>> > effects
>> > Zs<- paste("Z",2:(mb-1)),sep="")
>> > Trendformula <-as.formula(paste("LogY ~ WYear +
>> (1+WYear|Site) + (1|",
>> > randommodel=paste(paste(Zs,collapse="+"), ")")))
>> >
>> > fittest<-lmer(Trendformula, data = testsamp)
>> > summary(fittest)
>> >
>> > # Here I get an error because the name of the random effect is too
>> > long to print
>> > # in the random effects output (I think).
>> > # The error message is: Error in names(bars) <- unlist(lapply(bars,
>> > function(x)
>> > # deparse(x[[3]]))) : 'names' attribute [3] must be the
>> same length as
>> > the vector [2]
>> >
>> > # However, when fewer Z variables are used in the random portion of
>> > the model,
>> > # there is no error.
>> > # Using only Z2 + ... + Z9 for the random intercept
>> >
>> > Zs2<- paste("Z",2:9,sep="")
>> > Trendformula2 <-as.formula(paste("LogY ~ WYear + (1+WYear|Site) +
>> > (1|", randommodel=paste(paste(Zs2,collapse="+"), ")")))
>> > fittest2<-lmer(Trendformula2, data = testsamp)
>> > summary(fittest2)
>> >
>> >
>> > # Is there a way to either name the set of iid random effects
>> > something else or
>> > # to define a random variable that could be used in the
>> model to create a
>> > # random intercept?
>> >
>> > # I have had some success in lme, but it would be helpful for my
>> > simulation if I
>> > # could conduct this analysis with lmer. My model in lme is
>> not correctly
>> > # estimating one of the variance components (random Site intercept).
>> > # I am using:
>> >
>> > detach(package:lme4)
>> > library(nlme)
>> > random.model.lme
>> >
>> <-as.formula(paste("~-1+",paste(paste("Z",2:(mb-1),sep=""),col
>> lapse="+")))
>> >
>> >
>> > n<-dim(testsamp)[1]
>> > testsampgroup <- rep(1,n)
>> > testsamp.lme <-cbind(testsamp,testsampgroup)
>> > testgroupSamp<- groupedData(LogY ~ WYearCen|testsampgroup,
>> inner= ~Site,
>> > data= data.frame(testsamp.lme))
>> >
>> > fittest3<-lme(LogY ~ WYearCen, random=
>> > pdBlocked(list(pdIdent(~-1+WYearCen:as.factor(Site)),
>> > pdIdent(~-1+as.factor(Site)), pdIdent(random.model.lme))),data=
>> > testgroupSamp)
>> > summary(fittest3)
>> > VarCorr(fittest3)
>> >
>> >
>> > # Data
>> >
>> > testsamp <-
>> > structure(list(Year = c(2008, 2008, 2008, 2008, 2008, 2008, 2008,
>> > 2009, 2009, 2009, 2009, 2009, 2009, 2009, 2010, 2010, 2010, 2010,
>> > 2010, 2010, 2010, 2011, 2011, 2011, 2011, 2011, 2011, 2011, 2012,
>> > 2012, 2012, 2012, 2012, 2012, 2012, 2013, 2013, 2013, 2013, 2013,
>> > 2013, 2013, 2014, 2014, 2014, 2014, 2014, 2014, 2014, 2015, 2015,
>> > 2015, 2015, 2015, 2015, 2015, 2016, 2016, 2016, 2016, 2016, 2016,
>> > 2016, 2017, 2017, 2017, 2017, 2017, 2017, 2017, 2018, 2018, 2018,
>> > 2018, 2018, 2018, 2018, 2019, 2019, 2019, 2019, 2019, 2019, 2019,
>> > 2020, 2020, 2020, 2020, 2020, 2020, 2020, 2021, 2021, 2021, 2021,
>> > 2021, 2021, 2021, 2022, 2022, 2022, 2022, 2022, 2022, 2022),
>> > WYear = c(0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2,
>> > 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4,
>> > 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7,
>> > 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10,
>> > 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12,
>> > 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14,
>> > 14, 14), Site = c(4, 18, 26, 40, 67, 75, 94, 4, 18, 26, 40,
>> > 67, 75, 94, 4, 18, 26, 40, 67, 75, 94, 4, 18, 26, 40, 67,
>> > 75, 94, 4, 18, 26, 40, 67, 75, 94, 4, 18, 26, 40, 67, 75,
>> > 94, 4, 18, 26, 40, 67, 75, 94, 4, 18, 26, 40, 67, 75, 94,
>> > 4, 18, 26, 40, 67, 75, 94, 4, 18, 26, 40, 67, 75, 94, 4,
>> > 18, 26, 40, 67, 75, 94, 4, 18, 26, 40, 67, 75, 94, 4, 18,
>> > 26, 40, 67, 75, 94, 4, 18, 26, 40, 67, 75, 94, 4, 18, 26,
>> > 40, 67, 75, 94), LogY = c(0.848648866298552, 0.809143925760456,
>> > 0.734173952725014, 1.46749967704437, 0.716106254860468,
>> > 0.843871512951468,
>> > 1.09120092433378, 0.800893809796851, 0.996674977596997,
>> > 0.917613604481207,
>> > 1.71928772722884, 0.797853604855215, 0.922298691760041,
>> > 0.964654422529188,
>> > 0.782903180421921, 1.13457969553106, 1.21628917384868,
>> 2.03084776647495,
>> > 0.872954085910578, 1.02192794559856, 0.746307251774509,
>> > 0.439812203188778,
>> > 1.11164109549224, 1.18414357836729, 2.00157711459358,
>> 0.66577753155877,
>> > 0.856374433428581, 0.343862060001402, 0.278505653147057,
>> > 1.20632152691478, 1.32289150679746, 2.19814430598707,
>> 0.538363941164496,
>> > 0.820038163290321, 0.070054765524828, 0.0479738684639024,
>> > 1.29137364087568, 1.52436357249377, 2.32150525025777,
>> 0.595507040392793,
>> > 0.851417610550757, -0.115908144193410, 0.0118306018140099,
>> > 1.39448009350962, 1.71677754106603, 2.59146662837284,
>> 0.595750060671620,
>> > 0.855387479311679, -0.430729785591898, 0.0178423104900579,
>> > 1.60964246000316, 1.99184029256509, 2.86865842252168,
>> 0.695124899993409,
>> > 0.96175860396451, -0.600991172113926, -0.174420349224615,
>> > 1.73794158380868, 2.06718359946362, 3.04502112974038,
>> 0.730730638403177,
>> > 0.961110819398807, -0.856693722990918, -0.549458074126028,
>> > 1.52302453916110, 2.05923417821491, 2.95885487422314,
>> 0.302432275785407,
>> > 0.718537282886428, -1.41807557701934, -0.474811468779057,
>> > 1.88486023048201, 2.47921637905194, 3.31076232685622,
>> 0.600331824659821,
>> > 0.997014319132077, -1.36760375228162, -0.491828047247449,
>> > 2.09353379020743, 2.74721582678157, 3.58818112810645,
>> 0.65742631492698,
>> > 1.06027358323846, -1.58298244571648, -0.934472752299038,
>> > 1.83456803880667, 2.62936515021684, 3.56971226362308,
>> 0.389323036788794,
>> > 0.748060984171013, -2.13928096660883, -1.26100797232926,
>> > 1.83430218924218, 2.65380472944419, 3.62529901196750,
>> 0.271765247781891,
>> > 0.639379726021376, -2.50138714617066, -1.36434864536697,
>> > 1.95417376162485, 2.84537426171405, 3.76029816545047,
>> 0.171262422338166,
>> > 0.63595411426061, -2.72648123827278), Y = c(2.33648781083889,
>> > 2.24598443402562, 2.08375999711081, 4.33837423214822,
>> 2.04644932501053,
>> > 2.32535220351989, 2.97784809630864, 2.22753102803039,
>> 2.70925849019601,
>> > 2.50330936997246, 5.5805521729813, 2.22076916113014,
>> 2.51506510968675,
>> > 2.62388074570782, 2.18781467519546, 3.10986617752641,
>> 3.37464176115807,
>> > 7.62054406285807, 2.39397241834575, 2.77854648986394,
>> 2.10919688492552,
>> > 1.55241565242538, 3.03934215461328, 3.26788693363161,
>> 7.40071868133414,
>> > 1.94600301201132, 2.35460841009671, 1.41038407371191,
>> 1.32115407405314,
>> > 3.34117160999488, 3.75426116973332, 9.0082813655785,
>> 1.71320166935217,
>> > 2.27058648893032, 1.07256691933604, 1.04914323924183,
>> 3.63778012876121,
>> > 4.59222002395514, 10.1910027761430, 1.81395045797806,
>> 2.34296591199978,
>> > 0.89055702237416, 1.01190086017652, 4.03287730840125,
>> 5.56656151506009,
>> > 13.3493357676049, 1.81439133829339, 2.35228566604212,
>> 0.650034535742804,
>> > 1.01800243542715, 5.00102284245171, 7.32900887997844,
>> 17.6133726381587,
>> > 2.00395935282089, 2.61629345414488, 0.548267938797843,
>> 0.839943753736141,
>> > 5.68562798048777, 7.90253504257589, 21.0104751440743,
>> 2.07659729526341,
>> > 2.61459920843830, 0.424563488824068, 0.577262559146385,
>> 4.58607500338397,
>> > 7.83996349588931, 19.2758857986172, 1.35314603256567,
>> 2.05143035272921,
>> > 0.242179624775457, 0.622002312266844, 6.58543393476032,
>> 11.9319106582846,
>> > 27.4060098478603, 1.82272352466727, 2.71017801013783,
>> 0.254716592899401,
>> > 0.611507507191544, 8.11353609874542, 15.5991406590765,
>> 36.1682306843681,
>> > 1.92981919064962, 2.8871607600197, 0.20536170381795,
>> 0.392792910103641,
>> > 6.26242843503692, 13.8649649375266, 35.5063752059022,
>> 1.47598127057995,
>> > 2.11289909722918, 0.117739471204143, 0.283368255138982,
>> 6.26076379244682,
>> > 14.2079935097071, 37.5359451785784, 1.31227890476568,
>> 1.89530490631499,
>> > 0.0819712136688162, 0.2555470735606, 7.0580849532232,
>> 17.2079977586343,
>> > 42.961233624846, 1.18680215155599, 1.88882343537745,
>> 0.065449185044807
>> > ), Z2 = c(0.47227027821606, 0.47227027821606, 0.47227027821606,
>> > 0.47227027821606, 0.47227027821606, 0.47227027821606,
>> 0.47227027821606,
>> > 0.269868730409177, 0.269868730409177, 0.269868730409177,
>> > 0.269868730409177, 0.269868730409177, 0.269868730409177,
>> > 0.269868730409177, 0.0986058822648916, 0.0986058822648916,
>> > 0.0986058822648916, 0.0986058822648916, 0.0986058822648916,
>> > 0.0986058822648916, 0.0986058822648916, -0.0415182662167964,
>> > -0.0415182662167964, -0.0415182662167964, -0.0415182662167964,
>> > -0.0415182662167964, -0.0415182662167964, -0.0415182662167964,
>> > -0.150503715035887, -0.150503715035887, -0.150503715035887,
>> > -0.150503715035887, -0.150503715035887, -0.150503715035887,
>> > -0.150503715035887, -0.228350464192381, -0.228350464192381,
>> > -0.228350464192381, -0.228350464192381, -0.228350464192381,
>> > -0.228350464192381, -0.228350464192381, -0.275058513686277,
>> > -0.275058513686277, -0.275058513686277, -0.275058513686277,
>> > -0.275058513686277, -0.275058513686277, -0.275058513686277,
>> > -0.290627863517575, -0.290627863517575, -0.290627863517575,
>> > -0.290627863517575, -0.290627863517575, -0.290627863517575,
>> > -0.290627863517575, -0.275058513686277, -0.275058513686277,
>> > -0.275058513686277, -0.275058513686277, -0.275058513686277,
>> > -0.275058513686277, -0.275058513686277, -0.228350464192381,
>> > -0.228350464192381, -0.228350464192381, -0.228350464192381,
>> > -0.228350464192381, -0.228350464192381, -0.228350464192381,
>> > -0.150503715035887, -0.150503715035887, -0.150503715035887,
>> > -0.150503715035887, -0.150503715035887, -0.150503715035887,
>> > -0.150503715035887, -0.0415182662167965, -0.0415182662167965,
>> > -0.0415182662167965, -0.0415182662167965, -0.0415182662167965,
>> > -0.0415182662167965, -0.0415182662167965, 0.0986058822648916,
>> > 0.0986058822648916, 0.0986058822648916, 0.0986058822648916,
>> > 0.0986058822648916, 0.0986058822648916, 0.0986058822648916,
>> > 0.269868730409177, 0.269868730409177, 0.269868730409177,
>> > 0.269868730409177, 0.269868730409177, 0.269868730409177,
>> > 0.269868730409177, 0.47227027821606, 0.47227027821606,
>> 0.47227027821606,
>> > 0.47227027821606, 0.47227027821606, 0.47227027821606,
>> 0.47227027821606
>> > ), Z3 = c(-0.456256435177108, -0.456256435177108,
>> -0.456256435177108,
>> > -0.456256435177108, -0.456256435177108, -0.456256435177108,
>> > -0.456256435177108, -0.0651794907395872, -0.0651794907395872,
>> > -0.0651794907395872, -0.0651794907395872, -0.0651794907395872,
>> > -0.0651794907395872, -0.0651794907395872, 0.175483244298888,
>> > 0.175483244298888, 0.175483244298888, 0.175483244298888,
>> > 0.175483244298888, 0.175483244298888, 0.175483244298888,
>> > 0.290800804838157, 0.290800804838157, 0.290800804838157,
>> > 0.290800804838157, 0.290800804838157, 0.290800804838157,
>> > 0.290800804838157, 0.305842225778062, 0.305842225778062,
>> > 0.305842225778062, 0.305842225778062, 0.305842225778062,
>> > 0.305842225778062, 0.305842225778062, 0.245676542018443,
>> > 0.245676542018443, 0.245676542018443, 0.245676542018443,
>> > 0.245676542018443, 0.245676542018443, 0.245676542018443,
>> > 0.135372788459142, 0.135372788459142, 0.135372788459142,
>> > 0.135372788459142, 0.135372788459142, 0.135372788459142,
>> > 0.135372788459142, 4.80758108354045e-17, 4.80758108354045e-17,
>> > 4.80758108354045e-17, 4.80758108354045e-17, 4.80758108354045e-17,
>> > 4.80758108354045e-17, 4.80758108354045e-17, -0.135372788459142,
>> > -0.135372788459142, -0.135372788459142, -0.135372788459142,
>> > -0.135372788459142, -0.135372788459142, -0.135372788459142,
>> > -0.245676542018443, -0.245676542018443, -0.245676542018443,
>> > -0.245676542018443, -0.245676542018443, -0.245676542018443,
>> > -0.245676542018443, -0.305842225778062, -0.305842225778062,
>> > -0.305842225778062, -0.305842225778062, -0.305842225778062,
>> > -0.305842225778062, -0.305842225778062, -0.290800804838157,
>> > -0.290800804838157, -0.290800804838157, -0.290800804838157,
>> > -0.290800804838157, -0.290800804838157, -0.290800804838157,
>> > -0.175483244298888, -0.175483244298888, -0.175483244298888,
>> > -0.175483244298888, -0.175483244298888, -0.175483244298888,
>> > -0.175483244298888, 0.0651794907395869, 0.0651794907395869,
>> > 0.0651794907395869, 0.0651794907395869, 0.0651794907395869,
>> > 0.0651794907395869, 0.0651794907395869, 0.456256435177108,
>> > 0.456256435177108, 0.456256435177108, 0.456256435177108,
>> > 0.456256435177108, 0.456256435177108, 0.456256435177108),
>> > Z4 = c(0.393641410895141, 0.393641410895141, 0.393641410895141,
>> > 0.393641410895141, 0.393641410895141, 0.393641410895141,
>> > 0.393641410895141, -0.168703461812203, -0.168703461812203,
>> > -0.168703461812203, -0.168703461812203, -0.168703461812203,
>> > -0.168703461812203, -0.168703461812203, -0.341732653414463,
>> > -0.341732653414463, -0.341732653414463, -0.341732653414463,
>> > -0.341732653414463, -0.341732653414463, -0.341732653414463,
>> > -0.276846706563615, -0.276846706563615, -0.276846706563615,
>> > -0.276846706563615, -0.276846706563615, -0.276846706563615,
>> > -0.276846706563615, -0.0979187925203697, -0.0979187925203697,
>> > -0.0979187925203697, -0.0979187925203697, -0.0979187925203697,
>> > -0.0979187925203697, -0.0979187925203697, 0.0987052888458345,
>> > 0.0987052888458345, 0.0987052888458345, 0.0987052888458345,
>> > 0.0987052888458345, 0.0987052888458345, 0.0987052888458345,
>> > 0.244207109056825, 0.244207109056825, 0.244207109056825,
>> > 0.244207109056825, 0.244207109056825, 0.244207109056825,
>> > 0.244207109056825, 0.297295611025701, 0.297295611025701,
>> > 0.297295611025701, 0.297295611025701, 0.297295611025701,
>> > 0.297295611025701, 0.297295611025701, 0.244207109056826,
>> > 0.244207109056826, 0.244207109056826, 0.244207109056826,
>> > 0.244207109056826, 0.244207109056826, 0.244207109056826,
>> > 0.0987052888458344, 0.0987052888458344, 0.0987052888458344,
>> > 0.0987052888458344, 0.0987052888458344, 0.0987052888458344,
>> > 0.0987052888458344, -0.0979187925203697, -0.0979187925203697,
>> > -0.0979187925203697, -0.0979187925203697, -0.0979187925203697,
>> > -0.0979187925203697, -0.0979187925203697, -0.276846706563615,
>> > -0.276846706563615, -0.276846706563615, -0.276846706563615,
>> > -0.276846706563615, -0.276846706563615, -0.276846706563615,
>> > -0.341732653414463, -0.341732653414463, -0.341732653414463,
>> > -0.341732653414463, -0.341732653414463, -0.341732653414463,
>> > -0.341732653414463, -0.168703461812203, -0.168703461812203,
>> > -0.168703461812203, -0.168703461812203, -0.168703461812203,
>> > -0.168703461812203, -0.168703461812203, 0.393641410895141,
>> > 0.393641410895141, 0.393641410895141, 0.393641410895141,
>> > 0.393641410895141, 0.393641410895141, 0.393641410895141),
>> > Z5 = c(-0.307723646230283, -0.307723646230283, -0.307723646230283,
>> > -0.307723646230283, -0.307723646230283, -0.307723646230283,
>> > -0.307723646230283, 0.351684167120324, 0.351684167120324,
>> > 0.351684167120324, 0.351684167120324, 0.351684167120324,
>> > 0.351684167120324, 0.351684167120324, 0.300960489170276,
>> > 0.300960489170276, 0.300960489170276, 0.300960489170276,
>> > 0.300960489170276, 0.300960489170276, 0.300960489170276,
>> > 0.0135263141200131, 0.0135263141200131, 0.0135263141200131,
>> > 0.0135263141200131, 0.0135263141200131, 0.0135263141200131,
>> > 0.0135263141200131, -0.230869588730213, -0.230869588730213,
>> > -0.230869588730213, -0.230869588730213, -0.230869588730213,
>> > -0.230869588730213, -0.230869588730213, -0.307416230000283,
>> > -0.307416230000283, -0.307416230000283, -0.307416230000283,
>> > -0.307416230000283, -0.307416230000283, -0.307416230000283,
>> > -0.207505955250191, -0.207505955250191, -0.207505955250191,
>> > -0.207505955250191, -0.207505955250191, -0.207505955250191,
>> > -0.207505955250191, 2.73029795708800e-17, 2.73029795708800e-17,
>> > 2.73029795708800e-17, 2.73029795708800e-17, 2.73029795708800e-17,
>> > 2.73029795708800e-17, 2.73029795708800e-17, 0.207505955250191,
>> > 0.207505955250191, 0.207505955250191, 0.207505955250191,
>> > 0.207505955250191, 0.207505955250191, 0.207505955250191,
>> > 0.307416230000283, 0.307416230000283, 0.307416230000283,
>> > 0.307416230000283, 0.307416230000283, 0.307416230000283,
>> > 0.307416230000283, 0.230869588730212, 0.230869588730212,
>> > 0.230869588730212, 0.230869588730212, 0.230869588730212,
>> > 0.230869588730212, 0.230869588730212, -0.0135263141200123,
>> > -0.0135263141200123, -0.0135263141200123, -0.0135263141200123,
>> > -0.0135263141200123, -0.0135263141200123, -0.0135263141200123,
>> > -0.300960489170277, -0.300960489170277, -0.300960489170277,
>> > -0.300960489170277, -0.300960489170277, -0.300960489170277,
>> > -0.300960489170277, -0.351684167120323, -0.351684167120323,
>> > -0.351684167120323, -0.351684167120323, -0.351684167120323,
>> > -0.351684167120323, -0.351684167120323, 0.307723646230283,
>> > 0.307723646230283, 0.307723646230283, 0.307723646230283,
>> > 0.307723646230283, 0.307723646230283, 0.307723646230283),
>> > Z6 = c(0.219001863703187, 0.219001863703187, 0.219001863703187,
>> > 0.219001863703187, 0.219001863703187, 0.219001863703187,
>> > 0.219001863703187, -0.438003727406375, -0.438003727406375,
>> > -0.438003727406375, -0.438003727406375, -0.438003727406375,
>> > -0.438003727406375, -0.438003727406375, -0.084231486039687,
>> > -0.084231486039687, -0.084231486039687, -0.084231486039687,
>> > -0.084231486039687, -0.084231486039687, -0.084231486039687,
>> > 0.269540755326999, 0.269540755326999, 0.269540755326999,
>> > 0.269540755326999, 0.269540755326999, 0.269540755326999,
>> > 0.269540755326999, 0.301701868178519, 0.301701868178519,
>> > 0.301701868178519, 0.301701868178519, 0.301701868178519,
>> > 0.301701868178519, 0.301701868178519, 0.076574078217897,
>> > 0.076574078217897, 0.076574078217897, 0.076574078217897,
>> > 0.076574078217897, 0.076574078217897, 0.076574078217897,
>> > -0.191435195544744, -0.191435195544744, -0.191435195544744,
>> > -0.191435195544744, -0.191435195544744, -0.191435195544744,
>> > -0.191435195544744, -0.306296312871592, -0.306296312871592,
>> > -0.306296312871592, -0.306296312871592, -0.306296312871592,
>> > -0.306296312871592, -0.306296312871592, -0.191435195544745,
>> > -0.191435195544745, -0.191435195544745, -0.191435195544745,
>> > -0.191435195544745, -0.191435195544745, -0.191435195544745,
>> > 0.0765740782178983, 0.0765740782178983, 0.0765740782178983,
>> > 0.0765740782178983, 0.0765740782178983, 0.0765740782178983,
>> > 0.0765740782178983, 0.301701868178517, 0.301701868178517,
>> > 0.301701868178517, 0.301701868178517, 0.301701868178517,
>> > 0.301701868178517, 0.301701868178517, 0.269540755327,
>> 0.269540755327,
>> > 0.269540755327, 0.269540755327, 0.269540755327, 0.269540755327,
>> > 0.269540755327, -0.0842314860396875, -0.0842314860396875,
>> > -0.0842314860396875, -0.0842314860396875, -0.0842314860396875,
>> > -0.0842314860396875, -0.0842314860396875, -0.438003727406375,
>> > -0.438003727406375, -0.438003727406375, -0.438003727406375,
>> > -0.438003727406375, -0.438003727406375, -0.438003727406375,
>> > 0.219001863703188, 0.219001863703188, 0.219001863703188,
>> > 0.219001863703188, 0.219001863703188, 0.219001863703188,
>> > 0.219001863703188), Z7 = c(-0.141858517577507, -0.141858517577507,
>> > -0.141858517577507, -0.141858517577507, -0.141858517577507,
>> > -0.141858517577507, -0.141858517577507, 0.42557555273252,
>> > 0.42557555273252, 0.42557555273252, 0.42557555273252,
>> 0.42557555273252,
>> > 0.42557555273252, 0.42557555273252, -0.185507292216737,
>> > -0.185507292216737,
>> > -0.185507292216737, -0.185507292216737, -0.185507292216737,
>> > -0.185507292216737, -0.185507292216737, -0.338278003454058,
>> > -0.338278003454058, -0.338278003454058, -0.338278003454058,
>> > -0.338278003454058, -0.338278003454058, -0.338278003454058,
>> > -0.0327365809794237, -0.0327365809794237, -0.0327365809794237,
>> > -0.0327365809794237, -0.0327365809794237, -0.0327365809794237,
>> > -0.0327365809794237, 0.272804841495205, 0.272804841495205,
>> > 0.272804841495205, 0.272804841495205, 0.272804841495205,
>> > 0.272804841495205, 0.272804841495205, 0.272804841495207,
>> > 0.272804841495207, 0.272804841495207, 0.272804841495207,
>> > 0.272804841495207, 0.272804841495207, 0.272804841495207,
>> > 4.25663509926017e-16, 4.25663509926017e-16, 4.25663509926017e-16,
>> > 4.25663509926017e-16, 4.25663509926017e-16, 4.25663509926017e-16,
>> > 4.25663509926017e-16, -0.272804841495207, -0.272804841495207,
>> > -0.272804841495207, -0.272804841495207, -0.272804841495207,
>> > -0.272804841495207, -0.272804841495207, -0.272804841495206,
>> > -0.272804841495206, -0.272804841495206, -0.272804841495206,
>> > -0.272804841495206, -0.272804841495206, -0.272804841495206,
>> > 0.0327365809794244, 0.0327365809794244, 0.0327365809794244,
>> > 0.0327365809794244, 0.0327365809794244, 0.0327365809794244,
>> > 0.0327365809794244, 0.338278003454055, 0.338278003454055,
>> > 0.338278003454055, 0.338278003454055, 0.338278003454055,
>> > 0.338278003454055, 0.338278003454055, 0.185507292216741,
>> > 0.185507292216741, 0.185507292216741, 0.185507292216741,
>> > 0.185507292216741, 0.185507292216741, 0.185507292216741,
>> > -0.425575552732522, -0.425575552732522, -0.425575552732522,
>> > -0.425575552732522, -0.425575552732522, -0.425575552732522,
>> > -0.425575552732522, 0.141858517577507, 0.141858517577507,
>> > 0.141858517577507, 0.141858517577507, 0.141858517577507,
>> > 0.141858517577507, 0.141858517577507), Z8 = c(0.083314261738317,
>> > 0.083314261738317, 0.083314261738317, 0.083314261738317,
>> > 0.083314261738317, 0.083314261738317, 0.083314261738317,
>> > -0.345159084344455, -0.345159084344455, -0.345159084344455,
>> > -0.345159084344455, -0.345159084344455, -0.345159084344455,
>> > -0.345159084344455, 0.379949655180232, 0.379949655180232,
>> > 0.379949655180232, 0.379949655180232, 0.379949655180232,
>> > 0.379949655180232, 0.379949655180232, 0.143739990032049,
>> > 0.143739990032049, 0.143739990032049, 0.143739990032049,
>> > 0.143739990032049, 0.143739990032049, 0.143739990032049,
>> > -0.284733356050736, -0.284733356050736, -0.284733356050736,
>> > -0.284733356050736, -0.284733356050736, -0.284733356050736,
>> > -0.284733356050736, -0.251773867890516, -0.251773867890516,
>> > -0.251773867890516, -0.251773867890516, -0.251773867890516,
>> > -0.251773867890516, -0.251773867890516, 0.114442667222960,
>> > 0.114442667222960, 0.114442667222960, 0.114442667222960,
>> > 0.114442667222960, 0.114442667222960, 0.114442667222960,
>> > 0.320439468224296, 0.320439468224296, 0.320439468224296,
>> > 0.320439468224296, 0.320439468224296, 0.320439468224296,
>> > 0.320439468224296, 0.114442667222965, 0.114442667222965,
>> > 0.114442667222965, 0.114442667222965, 0.114442667222965,
>> > 0.114442667222965, 0.114442667222965, -0.251773867890520,
>> > -0.251773867890520, -0.251773867890520, -0.251773867890520,
>> > -0.251773867890520, -0.251773867890520, -0.251773867890520,
>> > -0.284733356050731, -0.284733356050731, -0.284733356050731,
>> > -0.284733356050731, -0.284733356050731, -0.284733356050731,
>> > -0.284733356050731, 0.143739990032042, 0.143739990032042,
>> > 0.143739990032042, 0.143739990032042, 0.143739990032042,
>> > 0.143739990032042, 0.143739990032042, 0.379949655180234,
>> > 0.379949655180234, 0.379949655180234, 0.379949655180234,
>> > 0.379949655180234, 0.379949655180234, 0.379949655180234,
>> > -0.345159084344455, -0.345159084344455, -0.345159084344455,
>> > -0.345159084344455, -0.345159084344455, -0.345159084344455,
>> > -0.345159084344455, 0.0833142617383167, 0.0833142617383167,
>> > 0.0833142617383167, 0.0833142617383167, 0.0833142617383167,
>> > 0.0833142617383167, 0.0833142617383167), Z9 = c(-0.0440394305225472,
>> > -0.0440394305225472, -0.0440394305225472, -0.0440394305225472,
>> > -0.0440394305225472, -0.0440394305225472, -0.0440394305225472,
>> > 0.239071194265257, 0.239071194265257, 0.239071194265257,
>> > 0.239071194265257, 0.239071194265257, 0.239071194265257,
>> > 0.239071194265257, -0.436038757151818, -0.436038757151818,
>> > -0.436038757151818, -0.436038757151818, -0.436038757151818,
>> > -0.436038757151818, -0.436038757151818, 0.16647872637096,
>> > 0.16647872637096, 0.16647872637096, 0.16647872637096,
>> 0.16647872637096,
>> > 0.16647872637096, 0.16647872637096, 0.318922908948979,
>> 0.318922908948979,
>> > 0.318922908948979, 0.318922908948979, 0.318922908948979,
>> > 0.318922908948979, 0.318922908948979, -0.120987446490507,
>> > -0.120987446490507, -0.120987446490507, -0.120987446490507,
>> > -0.120987446490507, -0.120987446490507, -0.120987446490507,
>> > -0.326666105524386, -0.326666105524386, -0.326666105524386,
>> > -0.326666105524386, -0.326666105524386, -0.326666105524386,
>> > -0.326666105524386, 1.6560876488147e-15, 1.6560876488147e-15,
>> > 1.6560876488147e-15, 1.6560876488147e-15, 1.6560876488147e-15,
>> > 1.6560876488147e-15, 1.6560876488147e-15, 0.326666105524385,
>> > 0.326666105524385, 0.326666105524385, 0.326666105524385,
>> > 0.326666105524385, 0.326666105524385, 0.326666105524385,
>> > 0.120987446490508, 0.120987446490508, 0.120987446490508,
>> > 0.120987446490508, 0.120987446490508, 0.120987446490508,
>> > 0.120987446490508, -0.318922908948989, -0.318922908948989,
>> > -0.318922908948989, -0.318922908948989, -0.318922908948989,
>> > -0.318922908948989, -0.318922908948989, -0.166478726370943,
>> > -0.166478726370943, -0.166478726370943, -0.166478726370943,
>> > -0.166478726370943, -0.166478726370943, -0.166478726370943,
>> > 0.436038757151805, 0.436038757151805, 0.436038757151805,
>> > 0.436038757151805, 0.436038757151805, 0.436038757151805,
>> > 0.436038757151805, -0.239071194265252, -0.239071194265252,
>> > -0.239071194265252, -0.239071194265252, -0.239071194265252,
>> > -0.239071194265252, -0.239071194265252, 0.0440394305225465,
>> > 0.0440394305225465, 0.0440394305225465, 0.0440394305225465,
>> > 0.0440394305225465, 0.0440394305225465, 0.0440394305225465
>> > ), Z10 = c(0.0207056819701757, 0.0207056819701757,
>> 0.0207056819701757,
>> > 0.0207056819701757, 0.0207056819701757, 0.0207056819701757,
>> > 0.0207056819701757, -0.141981819224062, -0.141981819224062,
>> > -0.141981819224062, -0.141981819224062, -0.141981819224062,
>> > -0.141981819224062, -0.141981819224062, 0.371109530696229,
>> > 0.371109530696229, 0.371109530696229, 0.371109530696229,
>> > 0.371109530696229, 0.371109530696229, 0.371109530696229,
>> > -0.392270282599825, -0.392270282599825, -0.392270282599825,
>> > -0.392270282599825, -0.392270282599825, -0.392270282599825,
>> > -0.392270282599825, -0.0361780597061064, -0.0361780597061064,
>> > -0.0361780597061064, -0.0361780597061064, -0.0361780597061064,
>> > -0.0361780597061064, -0.0361780597061064, 0.356774827793781,
>> > 0.356774827793781, 0.356774827793781, 0.356774827793781,
>> > 0.356774827793781, 0.356774827793781, 0.356774827793781,
>> > -0.0061434441010547, -0.0061434441010547, -0.0061434441010547,
>> > -0.0061434441010547, -0.0061434441010547, -0.0061434441010547,
>> > -0.0061434441010547, -0.344032869658285, -0.344032869658285,
>> > -0.344032869658285, -0.344032869658285, -0.344032869658285,
>> > -0.344032869658285, -0.344032869658285, -0.00614344410104096,
>> > -0.00614344410104096, -0.00614344410104096, -0.00614344410104096,
>> > -0.00614344410104096, -0.00614344410104096, -0.00614344410104096,
>> > 0.356774827793798, 0.356774827793798, 0.356774827793798,
>> > 0.356774827793798, 0.356774827793798, 0.356774827793798,
>> > 0.356774827793798, -0.0361780597061478, -0.0361780597061478,
>> > -0.0361780597061478, -0.0361780597061478, -0.0361780597061478,
>> > -0.0361780597061478, -0.0361780597061478, -0.392270282599797,
>> > -0.392270282599797, -0.392270282599797, -0.392270282599797,
>> > -0.392270282599797, -0.392270282599797, -0.392270282599797,
>> > 0.371109530696221, 0.371109530696221, 0.371109530696221,
>> > 0.371109530696221, 0.371109530696221, 0.371109530696221,
>> > 0.371109530696221, -0.141981819224062, -0.141981819224062,
>> > -0.141981819224062, -0.141981819224062, -0.141981819224062,
>> > -0.141981819224062, -0.141981819224062, 0.0207056819701758,
>> > 0.0207056819701758, 0.0207056819701758, 0.0207056819701758,
>> > 0.0207056819701758, 0.0207056819701758, 0.0207056819701758
>> > ), Z11 = c(-0.00849937774690609, -0.00849937774690609,
>> > -0.00849937774690609,
>> > -0.00849937774690609, -0.00849937774690609, -0.00849937774690609,
>> > -0.00849937774690609, 0.0716376124382085, 0.0716376124382085,
>> > 0.0716376124382085, 0.0716376124382085, 0.0716376124382085,
>> > 0.0716376124382085, 0.0716376124382085, -0.248910348302249,
>> > -0.248910348302249, -0.248910348302249, -0.248910348302249,
>> > -0.248910348302249, -0.248910348302249, -0.248910348302249,
>> > 0.43225406827121, 0.43225406827121, 0.43225406827121,
>> 0.43225406827121,
>> > 0.43225406827121, 0.43225406827121, 0.43225406827121,
>> -0.307191795709549,
>> > -0.307191795709549, -0.307191795709549, -0.307191795709549,
>> > -0.307191795709549, -0.307191795709549, -0.307191795709549,
>> > -0.146917815339487, -0.146917815339487, -0.146917815339487,
>> > -0.146917815339487, -0.146917815339487, -0.146917815339487,
>> > -0.146917815339487, 0.360616455833108, 0.360616455833108,
>> > 0.360616455833108, 0.360616455833108, 0.360616455833108,
>> > 0.360616455833108, 0.360616455833108, 2.37442501121216e-14,
>> > 2.37442501121216e-14, 2.37442501121216e-14, 2.37442501121216e-14,
>> > 2.37442501121216e-14, 2.37442501121216e-14, 2.37442501121216e-14,
>> > -0.360616455833123, -0.360616455833123, -0.360616455833123,
>> > -0.360616455833123, -0.360616455833123, -0.360616455833123,
>> > -0.360616455833123, 0.146917815339424, 0.146917815339424,
>> > 0.146917815339424, 0.146917815339424, 0.146917815339424,
>> > 0.146917815339424, 0.146917815339424, 0.307191795709669,
>> > 0.307191795709669, 0.307191795709669, 0.307191795709669,
>> > 0.307191795709669, 0.307191795709669, 0.307191795709669,
>> > -0.432254068271316, -0.432254068271316, -0.432254068271316,
>> > -0.432254068271316, -0.432254068271316, -0.432254068271316,
>> > -0.432254068271316, 0.248910348302301, 0.248910348302301,
>> > 0.248910348302301, 0.248910348302301, 0.248910348302301,
>> > 0.248910348302301, 0.248910348302301, -0.0716376124382226,
>> > -0.0716376124382226, -0.0716376124382226, -0.0716376124382226,
>> > -0.0716376124382226, -0.0716376124382226, -0.0716376124382226,
>> > 0.00849937774690764, 0.00849937774690764, 0.00849937774690764,
>> > 0.00849937774690764, 0.00849937774690764, 0.00849937774690764,
>> > 0.00849937774690764), Z12 = c(0.00295373795124409,
>> 0.00295373795124409,
>> > 0.00295373795124409, 0.00295373795124409, 0.00295373795124409,
>> > 0.00295373795124409, 0.00295373795124409, -0.0299593420769036,
>> > -0.0299593420769036, -0.0299593420769036, -0.0299593420769036,
>> > -0.0299593420769036, -0.0299593420769036, -0.0299593420769036,
>> > 0.132074282677049, 0.132074282677049, 0.132074282677049,
>> > 0.132074282677049, 0.132074282677049, 0.132074282677049,
>> > 0.132074282677049, -0.323223324378965, -0.323223324378965,
>> > -0.323223324378965, -0.323223324378965, -0.323223324378965,
>> > -0.323223324378965, -0.323223324378965, 0.450234056282428,
>> > 0.450234056282428, 0.450234056282428, 0.450234056282428,
>> > 0.450234056282428, 0.450234056282428, 0.450234056282428,
>> > -0.27385370433672, -0.27385370433672, -0.27385370433672,
>> > -0.27385370433672, -0.27385370433672, -0.27385370433672,
>> > -0.27385370433672, -0.15317241090017, -0.15317241090017,
>> > -0.15317241090017, -0.15317241090017, -0.15317241090017,
>> > -0.15317241090017, -0.15317241090017, 0.389893409563986,
>> > 0.389893409563986, 0.389893409563986, 0.389893409563986,
>> > 0.389893409563986, 0.389893409563986, 0.389893409563986,
>> > -0.153172410899934, -0.153172410899934, -0.153172410899934,
>> > -0.153172410899934, -0.153172410899934, -0.153172410899934,
>> > -0.153172410899934, -0.273853704336934, -0.273853704336934,
>> > -0.273853704336934, -0.273853704336934, -0.273853704336934,
>> > -0.273853704336934, -0.273853704336934, 0.450234056282481,
>> > 0.450234056282481, 0.450234056282481, 0.450234056282481,
>> > 0.450234056282481, 0.450234056282481, 0.450234056282481,
>> > -0.323223324378928, -0.323223324378928, -0.323223324378928,
>> > -0.323223324378928, -0.323223324378928, -0.323223324378928,
>> > -0.323223324378928, 0.132074282677017, 0.132074282677017,
>> > 0.132074282677017, 0.132074282677017, 0.132074282677017,
>> > 0.132074282677017, 0.132074282677017, -0.0299593420768935,
>> > -0.0299593420768935, -0.0299593420768935, -0.0299593420768935,
>> > -0.0299593420768935, -0.0299593420768935, -0.0299593420768935,
>> > 0.00295373795124293, 0.00295373795124293, 0.00295373795124293,
>> > 0.00295373795124293, 0.00295373795124293, 0.00295373795124293,
>> > 0.00295373795124293), Z13 = c(-0.000820388989417742,
>> > -0.000820388989417742,
>> > -0.000820388989417742, -0.000820388989417742, -0.000820388989417742,
>> > -0.000820388989417742, -0.000820388989417742, 0.00984466787301128,
>> > 0.00984466787301128, 0.00984466787301128, 0.00984466787301128,
>> > 0.00984466787301128, 0.00984466787301128, 0.00984466787301128,
>> > -0.0533252843121323, -0.0533252843121323, -0.0533252843121323,
>> > -0.0533252843121323, -0.0533252843121323, -0.0533252843121323,
>> > -0.0533252843121323, 0.170640909798784, 0.170640909798784,
>> > 0.170640909798784, 0.170640909798784, 0.170640909798784,
>> > 0.170640909798784, 0.170640909798784, -0.351946876459913,
>> > -0.351946876459913, -0.351946876459913, -0.351946876459913,
>> > -0.351946876459913, -0.351946876459913, -0.351946876459913,
>> > 0.469262501946444, 0.469262501946444, 0.469262501946444,
>> > 0.469262501946444, 0.469262501946444, 0.469262501946444,
>> > 0.469262501946444, -0.351946876459763, -0.351946876459763,
>> > -0.351946876459763, -0.351946876459763, -0.351946876459763,
>> > -0.351946876459763, -0.351946876459763, 1.30897668096353e-14,
>> > 1.30897668096353e-14, 1.30897668096353e-14, 1.30897668096353e-14,
>> > 1.30897668096353e-14, 1.30897668096353e-14, 1.30897668096353e-14,
>> > 0.351946876459646, 0.351946876459646, 0.351946876459646,
>> > 0.351946876459646, 0.351946876459646, 0.351946876459646,
>> > 0.351946876459646, -0.469262501946203, -0.469262501946203,
>> > -0.469262501946203, -0.469262501946203, -0.469262501946203,
>> > -0.469262501946203, -0.469262501946203, 0.351946876459683,
>> > 0.351946876459683, 0.351946876459683, 0.351946876459683,
>> > 0.351946876459683, 0.351946876459683, 0.351946876459683,
>> > -0.170640909798657, -0.170640909798657, -0.170640909798657,
>> > -0.170640909798657, -0.170640909798657, -0.170640909798657,
>> > -0.170640909798657, 0.0533252843120879, 0.0533252843120879,
>> > 0.0533252843120879, 0.0533252843120879, 0.0533252843120879,
>> > 0.0533252843120879, 0.0533252843120879, -0.009844667873002,
>> > -0.009844667873002, -0.009844667873002, -0.009844667873002,
>> > -0.009844667873002, -0.009844667873002, -0.009844667873002,
>> > 0.000820388989416903, 0.000820388989416903, 0.000820388989416903,
>> > 0.000820388989416903, 0.000820388989416903, 0.000820388989416903,
>> > 0.000820388989416903), Z14 = c(0.000157883934625923,
>> > 0.000157883934625923,
>> > 0.000157883934625923, 0.000157883934625923, 0.000157883934625923,
>> > 0.000157883934625923, 0.000157883934625923, -0.00221037508476475,
>> > -0.00221037508476475, -0.00221037508476475, -0.00221037508476475,
>> > -0.00221037508476475, -0.00221037508476475, -0.00221037508476475,
>> > 0.0143674380509829, 0.0143674380509829, 0.0143674380509829,
>> > 0.0143674380509829, 0.0143674380509829, 0.0143674380509829,
>> > 0.0143674380509829, -0.0574697522039801, -0.0574697522039801,
>> > -0.0574697522039801, -0.0574697522039801, -0.0574697522039801,
>> > -0.0574697522039801, -0.0574697522039801, 0.158041818561072,
>> > 0.158041818561072, 0.158041818561072, 0.158041818561072,
>> > 0.158041818561072, 0.158041818561072, 0.158041818561072,
>> > -0.316083637122359, -0.316083637122359, -0.316083637122359,
>> > -0.316083637122359, -0.316083637122359, -0.316083637122359,
>> > -0.316083637122359, 0.474125455683776, 0.474125455683776,
>> > 0.474125455683776, 0.474125455683776, 0.474125455683776,
>> > 0.474125455683776, 0.474125455683776, -0.541857663638757,
>> > -0.541857663638757, -0.541857663638757, -0.541857663638757,
>> > -0.541857663638757, -0.541857663638757, -0.541857663638757,
>> > 0.474125455683927, 0.474125455683927, 0.474125455683927,
>> > 0.474125455683927, 0.474125455683927, 0.474125455683927,
>> > 0.474125455683927, -0.316083637122536, -0.316083637122536,
>> > -0.316083637122536, -0.316083637122536, -0.316083637122536,
>> > -0.316083637122536, -0.316083637122536, 0.158041818561182,
>> > 0.158041818561182, 0.158041818561182, 0.158041818561182,
>> > 0.158041818561182, 0.158041818561182, 0.158041818561182,
>> > -0.0574697522040225, -0.0574697522040225, -0.0574697522040225,
>> > -0.0574697522040225, -0.0574697522040225, -0.0574697522040225,
>> > -0.0574697522040225, 0.0143674380509932, 0.0143674380509932,
>> > 0.0143674380509932, 0.0143674380509932, 0.0143674380509932,
>> > 0.0143674380509932, 0.0143674380509932, -0.00221037508476627,
>> > -0.00221037508476627, -0.00221037508476627, -0.00221037508476627,
>> > -0.00221037508476627, -0.00221037508476627, -0.00221037508476627,
>> > 0.00015788393462604, 0.00015788393462604, 0.00015788393462604,
>> > 0.00015788393462604, 0.00015788393462604, 0.00015788393462604,
>> > 0.00015788393462604), WYearCen = c(-7, -7, -7, -7, -7, -7,
>> > -7, -6, -6, -6, -6, -6, -6, -6, -5, -5, -5, -5, -5, -5, -5,
>> > -4, -4, -4, -4, -4, -4, -4, -3, -3, -3, -3, -3, -3, -3, -2,
>> > -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, 0, 0,
>> > 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2,
>> > 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5,
>> > 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7)), .Names = c("Year",
>> > "WYear", "Site", "LogY", "Y", "Z2", "Z3", "Z4", "Z5", "Z6", "Z7",
>> > "Z8", "Z9", "Z10", "Z11", "Z12", "Z13", "Z14", "WYearCen"),
>> row.names
>> > = c(4L,
>> > 18L, 26L, 40L, 67L, 75L, 94L, 104L, 118L, 126L, 140L, 167L, 175L,
>> > 194L, 204L, 218L, 226L, 240L, 267L, 275L, 294L, 304L, 318L, 326L,
>> > 340L, 367L, 375L, 394L, 404L, 418L, 426L, 440L, 467L, 475L, 494L,
>> > 504L, 518L, 526L, 540L, 567L, 575L, 594L, 604L, 618L, 626L, 640L,
>> > 667L, 675L, 694L, 704L, 718L, 726L, 740L, 767L, 775L, 794L, 804L,
>> > 818L, 826L, 840L, 867L, 875L, 894L, 904L, 918L, 926L, 940L, 967L,
>> > 975L, 994L, 1004L, 1018L, 1026L, 1040L, 1067L, 1075L, 1094L,
>> > 1104L, 1118L, 1126L, 1140L, 1167L, 1175L, 1194L, 1204L, 1218L,
>> > 1226L, 1240L, 1267L, 1275L, 1294L, 1304L, 1318L, 1326L, 1340L,
>> > 1367L, 1375L, 1394L, 1404L, 1418L, 1426L, 1440L, 1467L, 1475L,
>> > 1494L), class = "data.frame")
>> >
>> >
>> >
>> >
>> >
>> >
>> > At 11:17 AM 5/22/2009 -0700, spencerg wrote:
>> >> The first exaample on the "lmer" help page uses a formula
>> "Reaction ~
>> >> Days + (Days|Subject)". Here, "Subject" is the name of a column in
>> >> the data.frame "sleepstudy", with levels "308", "309", ... .
>> >>
>> >> Does this answer your question? If no, please provide commented,
>> >> minimal, self-contained, reproducible code, as requested in the
>> >> posting guide "http://www.R-project.org/posting-guide.html". Your
>> >> example is not "self-contained, reproducible".
>> >>
>> >> Hope this helps. Spencer
>> >>
>> >>
>> >> Leigh Ann Starcevich wrote:
>> >>> Dear guRus:
>> >>>
>> >>> I am using lmer for a mixed model that includes a random
>> intercept
>> >>> for a set of effects that have the same distribution, Normal(0,
>> >>> sig2b). This set of effects is of variable size, so I am using an
>> >>> as.formula statement to create the formula for lmer. For
>> example, if
>> >>> the set of random effects has dimension 8, then the lmer call is:
>> >>>
>> >>> Zs<- paste("Z",1:mb,sep="")
>> >>> Trendformula <-as.formula(paste("LogY ~ WYear + (1+WYear|Site) +
>> >>> (1|", paste(paste(Zs,collapse="+"), ")")))
>> >>> fit2.4a<-lmer(Trendformula, data = testsamp)
>> >>>
>> >>> which, for mb=8, expands to:
>> >>>
>> >>> fit1<-lmer(LogY ~ WYear + (1 | Site) + (1 | Year) + (1 |
>> Z1+ Z2 + Z3
>> >>> + Z4 + Z5 + Z6 + Z7 + Z8), data = testsamp)
>> >>>
>> >>>
>> >>> I have no problems with this. However, if the set of
>> random effects
>> >>> has a dimension of 30, then the lmer call is:
>> >>>
>> >>> fit2<-lmer(LogY ~ WYear + (1 | Site) + (1 | Year) + (1 |
>> Z1+Z2 + Z3
>> >>> + Z4 + Z5 + Z6 + Z7 + Z8 + Z9 + Z10 + Z11 + Z12 + Z13 +
>> Z14 + Z15 +
>> >>> Z16 + Z17 + Z18 + Z19 + Z20 + Z21 + Z22 + Z23 + Z24 + Z25 + Z26 +
>> >>> Z27 + Z28 + Z29+ Z30), data = testsamp)
>> >>>
>> >>> In this case, I get an error because the name "Z1+Z2 + Z3
>> + Z4 + Z5
>> >>> + Z6 + Z7 + Z8 + Z9 + Z10 + Z11 + Z12 + Z13 + Z14 + Z15 +
>> Z16 + Z17
>> >>> + Z18 + Z19 + Z20 + Z21 + Z22 + Z23 + Z24 + Z25 + Z26 +
>> Z27 + Z28 +
>> >>> Z29+ Z30" is too long to print in the output. Is there any way to
>> >>> name the random effect in lmer so that the shorter (and more
>> >>> descriptive) name may be used and the error avoided? Or
>> is there a
>> >>> way to combine these into a single variable prior to the lmer
>> >>> function call? In SAS, I am able to parameterize these as
>> a Toeplitz
>> >>> structure with bandwidth 1.
>> >>>
>> >>> Thanks for any help.
>> >>>
>> >>> Leigh Ann Starcevich
>> >>> Doctoral student
>> >>> Oregon State University
>> >>> Corvallis, Oregon
>> >>> [[alternative HTML version deleted]]
>> >>>
>> >>> ______________________________________________
>> >>> R-help at r-project.org mailing list
>> >>> https://stat.ethz.ch/mailman/listinfo/r-help
>> >>> PLEASE do read the posting guide
>> >>> http://www.R-project.org/posting-guide.html
>> >>> and provide commented, minimal, self-contained, reproducible code.
>> >>>
>> >>>
>> >>
>> >
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>



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