[R] lme, nlsList, nlsList.selfStart
Prof Brian Ripley
ripley at stats.ox.ac.uk
Fri Feb 17 19:25:59 CET 2006
This is a bug in nlsList.formula, where the author forgot that deparsing
can spread over multiple lines. Here is a patch:
--- nlsList.R (revision 2298)
+++ nlsList.R (working copy)
@@ -60,8 +60,9 @@
} else if (length(level) > 1) {
stop("Multiple levels not allowed")
}
- model <- eval(parse(text = paste(deparse(model[[2]]),
- deparse(getCovariateFormula(model)[[2]]), sep = "~")))
+ model <- eval(parse(text = paste(paste(deparse(model[[2]]), collapse=" "),
+ paste(deparse(getCovariateFormula(model)[[2]]), collapse=" "),
+ sep = "~")))
groups <- getGroups(data, form = grpForm, level = level)[drop = TRUE]
}
if (is.null(start) && is.null(attr(data, "parameters"))) {
which will probably not survive emailing but should show you what the
change is.
On Fri, 17 Feb 2006, Patrick Giraudoux wrote:
> Well, right, Dose was indeed in the global environment and not in the
> data.frame. Changing it with
>
> mydata2$Dose<-100 # the real dose at the beginning of the experiment
>
> improves the thing in a sense... but I face a new error:
>
> mymod3<-nlsList(Conc+1 ~ Dose * exp(lKe+lKa-lCl) *
> (exp(-exp(lKe)*Tps)-exp(-exp(lKa)*Tps)) /(exp(lKa)-exp(lKe)) | Organ,
> data=mydata2,
> start= c(lKe=-2.77, lKa=-1.41, lCl=-1.13)
> )
>
> Error in exp(-exp(lKa) * Conc + 1 ~ Tps) :
> Non-numeric argument to mathematical function
> Error in exp(-exp(lKa) * Conc + 1 ~ Tps) :
> Non-numeric argument to mathematical function
> Error in exp(-exp(lKa) * Conc + 1 ~ Tps) :
> Non-numeric argument to mathematical function
>
> I have checked the variables in the data.frame with:
>
>> sapply(mydata2,is.factor)
> Tps Conc Organ Dose
> FALSE FALSE TRUE FALSE
>> sapply(mydata2,is.character)
> Tps Conc Organ Dose
> FALSE FALSE FALSE FALSE
>
> So everything looks OK on this side...
>
> Furthermore, I have still this "old" error intact:
>
>> mymod4<-nlsList(SSfol,data=mydata2)
> Error in eval(expr, envir, enclos) : object "input" not found
> Error in eval(expr, envir, enclos) : object "input" not found
> Error in eval(expr, envir, enclos) : object "input" not found
>
>
> I am really sorry for calling help and boring everybody on this likely
> trivial issue (this looks like asking a community to participate to debogging
> line by line, a shame!!!), but I must admit that I am really lost...
>
> Thanks for your concern,
>
> Kind regards,
>
> Patrick
>
>
> Prof Brian Ripley a écrit :
>> We don't have Dose, and I think that is where the error lies. If Dose were
>> part of mydata2, this is likely to work, but otherwise it is Dose which has
>> the wrong length.
>>
>> ?nlsList says
>>
>> data: a data frame in which to interpret the variables named in
>> 'model'.
>>
>> and it means it: you must get all the variables from there.
>>
>>
>> On Fri, 17 Feb 2006, Patrick Giraudoux wrote:
>>
>>> Spencer,
>>>
>>> Thanks for the hint. I did not dare to bore people with the full data
>>> set and though that this kind of error may have been trivial and often
>>> encountered (so leading to a short answer), even though I did not see
>>> related messages on the r-help list. I already did the checks suggested
>>> before posting, and was aware of the possible confusion between 1 and l
>>> (actually the variable names were not given by myself).
>>>
>>> It seems that the trouble comes when the grouping variable "Organ" is
>>> used. The best (?) I can do is to dump the data.frame here below.
>>>
>>> With this example, one can get exactly the same errors:
>>>
>>> mymod2<-nls(Conc~Dose * exp(lKe+lKa-lCl) *
>>> (exp(-exp(lKe)*Tps)-exp(-exp(lKa)*Tps)) /(exp(lKa)-exp(lKe)),
>>> data=mydata2,
>>> start= c(lKe=-2.77, lKa=-1.41, lCl=-1.13)
>>> )
>>>
>>> ... works well!!!
>>>
>>> but we get then:
>>>
>>> mymod3<-nlsList(Conc~Dose * exp(lKe+lKa-lCl) *
>>> (exp(-exp(lKe)*Tps)-exp(-exp(lKa)*Tps)) /(exp(lKa)-exp(lKe)) | Organ,
>>> data=mydata2,
>>> start= c(lKe=-2.77, lKa=-1.41, lCl=-1.13)
>>> )
>>> Error in model.frame(formula, rownames, variables, varnames, extras,
>>> extranames, :
>>> variable lengths differ
>>> Error in model.frame(formula, rownames, variables, varnames, extras,
>>> extranames, :
>>> variable lengths differ
>>> Error in model.frame(formula, rownames, variables, varnames, extras,
>>> extranames, :
>>> variable lengths differ
>>>
>>>
>>> > mymod4<-nlsList(SSfol,data=mydata2)
>>> Error in eval(expr, envir, enclos) : object "input" not found
>>> Error in eval(expr, envir, enclos) : object "input" not found
>>> Error in eval(expr, envir, enclos) : object "input" not found
>>>
>>>
>>> Sorry and apologise for the inconvenience met,
>>>
>>> Kind regards,
>>>
>>> Patrick
>>>
>>>
>>>
>>> # data.frame just to copy and past into R
>>>
>>> "mydata2" <-
>>> structure(list(Tps = c(1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3,
>>> 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6,
>>> 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9,
>>> 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 14,
>>> 14, 14, 14, 14, 17, 17, 17, 17, 17, 20, 20, 20, 20, 25, 28, 29,
>>> 50, 50, 50, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136,
>>> 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4,
>>> 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7,
>>> 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10,
>>> 10, 10, 11, 11, 11, 11, 11, 11, 14, 14, 14, 14, 14, 17, 17, 17,
>>> 17, 17, 20, 20, 20, 20, 25, 28, 29, 50, 50, 50, 136, 136, 136,
>>> 136, 136, 136, 136, 136, 136, 136, 1, 1, 1, 1, 1, 1, 2, 2, 2,
>>> 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5,
>>> 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8,
>>> 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11,
>>> 11, 11, 14, 14, 14, 14, 14, 17, 17, 17, 17, 17, 20, 20, 20, 20,
>>> 25, 28, 29, 50, 50, 50, 136, 136, 136, 136, 136, 136, 136, 136,
>>> 136, 136), Conc = c(0, 0, 0, 0, 0, 0, 0, 0.807852503274902,
>>> 0.204371494701886,
>>> 0.579222129993907, 0.989062273721619, 0, 1.11728297897571,
>>> 1.41057428121324,
>>> 0.888883702851307, 1.259907624008, 1.45753269675829, 1.07077516747401,
>>> 0.843279379, 0, 0.763110069196737, 1.11297791434297, 1.10087763997637,
>>> 0.946929594501016, 1.33112168, 0.654041755, 0.694167499, 1.289548703,
>>> 1.117139864, 0.807196192, 0.720221376552025, 0.560082823, 0.476583438,
>>> 2.590855204, 0.51510972, 1.072946887, 0.537999938614396,
>>> 0.886684225905255,
>>> 0.630178116793598, 1.31534758842196, 1.33333958571746, 0.922032210748255,
>>> 0.429930193046174, 1.35881467717335, 0.790045927902363, 1.22484702570724,
>>> 0.808104508207897, 1.31185966817903, 1.51837686425553, 1.74105163638734,
>>> 1.80365598487402, 1.13240352674377, 1.50086243061644, 2.06355364280445,
>>> 0.439350890906039, 1.54692793444949, 1.78758216051046, 1.09043400023239,
>>> 0.811328376840514, 0.459192443530981, 0.695333473157298,
>>> 0.387995007681174,
>>> 0.784627063444921, 1.02282256375842, 0.382687104107726, 0.554290634950242,
>>> 0.130420456296453, 0.324194753224919, 0.31106140274139, 0.513473505828888,
>>> 0.878620320248701, 1.18404358659996, 0.136926837896477, 0, 0,
>>> 0.835588760032974, 0.558617235576616, 1.21002805866839, 0.769381068031404,
>>> 1.04514254228094, 0.373251847173678, 0.389005898972802, 0.183141006154896,
>>> 0.223596336820146, 0.315526423315647, 0.0930349732768131,
>>> 0.169959185212759,
>>> 0.161878841748425, 0, 0.0483041009105874, 0, 0, 0, 0.0777005553478052,
>>> 0, 0.153175826795441, 0.0428171049833677, 0, 0, 0, 0, 0, 0, 0,
>>> 0, 0, 0, 26.564295705327, 5.5893744508169, 7.22612934071834,
>>> 36.6563989567777, 0, 28.8967184437329, 28.4030370337251, 28.0886043901352,
>>> 26.1230935842208, 28.8895673910072, 42.6814210131968, 32.3555695551062,
>>> 0.76883326657205, 34.6159136622156, 38.329242204291, 56.4476583636484,
>>> 26.6249506083603, 31.3001451026823, 23.7339071829084, 23.3702284599355,
>>> 36.669903715038, 44.7377244306005, 31.2079335923023, 32.8613384312272,
>>> 29.4259634309146, 45.6112405959009, 48.1231689836687, 55.0037961570027,
>>> 32.9822316456421, 20.0382768189682, 26.0986380308655, 28.8915584506145,
>>> 28.7949023823068, 30.0278417498425, 58.8089779973569, 20.3602570111197,
>>> 29.6269605259023, 28.4404986724604, 30.2165182590977, 19.9204461889074,
>>> 31.1019196559556, 30.3847467747055, 36.8726911479995, 51.0618036275519,
>>> 23.5408013442579, 36.6948355347593, 27.4753860809429, 24.1341667099646,
>>> 27.5411488989643, 35.9021799354022, 19.7417897046158, 31.1403887303244,
>>> 46.1743622734049, 34.8235854891765, 22.1714704189293, 33.6805966894274,
>>> 35.2814908686112, 42.9767437212852, 38.1264997164547, 5.3651357974451,
>>> 42.8990434918385, 25.4908883698364, 25.99649502, 36.4958105490917,
>>> 40.8004126550705, 5.36867162116895, 0.00898476265269363, 0,
>>> 27.6810997945798,
>>> 28.7918300045713, 45.7577183830352, 35.9276318604787, 34.9717618087238,
>>> 29.620354272564, 24.6537513599869, 13.5363982464958, 25.8289073574818,
>>> 12.0090406245759, 4.753436805, 11.849214652228, 8.41410147611612,
>>> 0, 1.80855352862552, 1.1987530031681, 1.01148025243171, 0.495675369574172,
>>> 1.62701127228732, 0, 16.6288242287241, 1.23656061354912,
>>> 0.323708776035328,
>>> 0, 0.566916625204436, 0, 0, 0, 0, 0, 0, 0, 2.53578781871283,
>>> 3.50083667130797, 0, 0.98049572179098, 0, 3.57129673217304,
>>> 2.77298867949388,
>>> 2.12302645642669, 4.11923869203499, 4.69069462193674, 2.8698666062651,
>>> 2.05079837323067, 0.0602771574448942, 5.96454350250626, 2.26267114439802,
>>> 3.06911285674854, 2.04233129537404, 2.62181873844029, 1.51813653072598,
>>> 1.46193772981073, 2.69864635755833, 3.44016493913122, 2.50834832469627,
>>> 3.48170744166168, 1.00637581555435, 1.67065398473081, 4.18855363095027,
>>> 3.39649762611015, 1.72804613460423, 1.40053679329531, 2.37032387724109,
>>> 3.19332545080983, 2.49474373894248, 2.17800931288708, 2.7601484443213,
>>> 0.91266104095844, 1.93485048639199, 1.19692593420788, 1.79537330666258,
>>> 2.14020930767983, 3.0122526724942, 2.81112226980754, 3.54890724398174,
>>> 3.01022926452999, 2.38263226710738, 3.53569238341869, 3.47869329713911,
>>> 0.679333339820719, 2.4764260756438, 3.82615100065366, 2.20449890383871,
>>> 1.371303113329, 1.2427787019995, 1.73319133880954, 0.391268883238408,
>>> 1.73610193837913, 2.68494324646718, 1.77065393606844, 1.45079980147062,
>>> 0.763775702906329, 0.98566725668627, 0.37838763208699, 0.841811919286804,
>>> 1.46436462204795, 1.98409602726, 0.507005887891038, 0.465515668274195,
>>> 0, 1.873365675227, 1.69023864630648, 2.65530855919137, 2.34392199908302,
>>> 1.61917643594837, 1.05165934333345, 0.564642823436471, 0.121621029620328,
>>> 0.515007625737071, 0.524345809084086, 0.130898614090571,
>>> 0.332427740242623,
>>> 0.110214989555118, 0, 0.128642193589, 0.119407067173878,
>>> 0.128926224027295,
>>> 0.0622331866694357, 0.215645168287442, 0, 0.859343941945178,
>>> 0.0500810300696456, 0, 0, 0.0628746592609754), Organ =
>>> 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, 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, 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)), .Label = c("Carc", "TD", "Foie"), class = c("ordered",
>>> "factor"))), .Names = c("Tps", "Conc", "Organ"), row.names = c("1",
>>> "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13",
>>> "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24",
>>> "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35",
>>> "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46",
>>> "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57",
>>> "58", "59", "60", "61", "62", "63", "64", "65", "66", "67", "68",
>>> "69", "70", "71", "72", "73", "74", "75", "76", "77", "78", "79",
>>> "80", "81", "82", "83", "84", "85", "86", "87", "88", "89", "90",
>>> "91", "92", "93", "94", "95", "96", "97", "98", "99", "100",
>>> "101", "102", "103", "104", "105", "106", "107", "108", "109",
>>> "110", "111", "112", "113", "114", "115", "116", "117", "118",
>>> "119", "120", "121", "122", "123", "124", "125", "126", "127",
>>> "128", "129", "130", "131", "132", "133", "134", "135", "136",
>>> "137", "138", "139", "140", "141", "142", "143", "144", "145",
>>> "146", "147", "148", "149", "150", "151", "152", "153", "154",
>>> "155", "156", "157", "158", "159", "160", "161", "162", "163",
>>> "164", "165", "166", "167", "168", "169", "170", "171", "172",
>>> "173", "174", "175", "176", "177", "178", "179", "180", "181",
>>> "182", "183", "184", "185", "186", "187", "188", "189", "190",
>>> "191", "192", "193", "194", "195", "196", "197", "198", "199",
>>> "200", "201", "202", "203", "204", "205", "206", "207", "208",
>>> "209", "210", "211", "212", "213", "214", "215", "216", "217",
>>> "218", "219", "220", "221", "222", "223", "224", "225", "226",
>>> "227", "228", "229", "230", "231", "232", "233", "234", "235",
>>> "236", "237", "238", "239", "240", "241", "242", "243", "244",
>>> "245", "246", "247", "248", "249", "250", "251", "252", "253",
>>> "254", "255", "256", "257", "258", "259", "260", "261", "262",
>>> "263", "264", "265", "266", "267", "268", "269", "270", "271",
>>> "272", "273", "274", "275", "276", "277", "278", "279", "280",
>>> "281", "282", "283", "284", "285", "286", "287", "288", "289",
>>> "290", "291", "292", "293", "294", "295", "296", "297", "298",
>>> "299", "300"), class = c("nfnGroupedData", "nfGroupedData", "groupedData",
>>> "data.frame"), formula = quote(Conc ~ Tps | Organ), FUN = function (x)
>>> max(x, na.rm = TRUE), order.groups = TRUE)
>>>
>>>
>>>
>>>
>>> Spencer Graves a écrit :
>>>> Regarding the following:
>>>>
>>>>> mymod3<-nlsList(Conc~Dose * exp(lKe+lKa-lCl) *
>>>>> (exp(-exp(lKe)*Tps)-exp(-exp(lKa)*Tps)) /(exp(lKa)-exp(lKe)),
>>>>> data=mydata,
>>>>> start= c(lKe=-2.77, lKa=-1.41, lCl=-1.13)
>>>>> Error in model.frame(formula, rownames, variables, varnames, extras,
>>>>> extranames, :
>>>>> variable lengths differ
>>>>
>>>> This example is NOT self contained and is entirely too
>>>> complicated for me to try to replicate it myself in a reasonable
>>>> period of time. I will therefore ask one short question: Are all the
>>>> variable names in the "nlsList" call either columns of "mydata" or
>>>> parameters to be estimated and therefore spelled out in "start"? If I
>>>> were you, I'd check this all very carefully, being especially careful
>>>> about the distinction between "lCl" and "lC1", in particular.
>>>>
>>>> If you'd like further help with this, I suggest you try to find
>>>> the simplest possible example that generates problem you don't
>>>> understand, then try to recast that example into one that is
>>>> completely self contained, either a data set in the standard R or nlme
>>>> distribution or numbers that one can generate with a very few lines
>>>> of code. If you use random numbers, please "set.seed", to increase
>>>> your confidence that someone else will see what you see. (And please
>>>> review the posting guide! "www.R-project.org/posting-guide.html".
>>>> Doing so may increase your chances of getting more useful information
>>>> more quickly.)
>>>>
>>>> spencer graves
>>>>
>>>> Patrick Giraudoux wrote:
>>>>
>>>>> Dear listers,
>>>>>
>>>>> I am trying to fit a model using nlsList() using alternately a
>>>>> SSfol() selfstart function or its developped equivalent formulae.
>>>>>
>>>>> This preliminary trial works well
>>>>>
>>>>> mydata<-groupedData(Conc~Tps|Organ,data=mydata)
>>>>> mymod1<-nls(Conc~SSfol(Dose,Tps,lKe,lKa,lCl),data=mydata)
>>>>>
>>>>> as well as a developped form:
>>>>>
>>>>> mymod2<-nls(Conc~Dose * exp(lKe+lKa-lCl) *
>>>>> (exp(-exp(lKe)*Tps)-exp(-exp(lKa)*Tps)) /(exp(lKa)-exp(lKe)),
>>>>> data=mydata,
>>>>> start= c(lKe=-2.77, lKa=-1.41, lCl=-1.13)
>>>>> )
>>>>>
>>>>> However when trying to fit the model with nlsList, I get:
>>>>>
>>>>> mymod3<-nlsList(Conc~Dose * exp(lKe+lKa-lCl) *
>>>>> (exp(-exp(lKe)*Tps)-exp(-exp(lKa)*Tps)) /(exp(lKa)-exp(lKe)),
>>>>> data=mydata,
>>>>> start= c(lKe=-2.77, lKa=-1.41, lCl=-1.13)
>>>>> )
>>>>> Error in model.frame(formula, rownames, variables, varnames, extras,
>>>>> extranames, :
>>>>> variable lengths differ
>>>>> Error in model.frame(formula, rownames, variables, varnames, extras,
>>>>> extranames, :
>>>>> variable lengths differ
>>>>> Error in model.frame(formula, rownames, variables, varnames, extras,
>>>>> extranames, :
>>>>> variable lengths differ
>>>>>
>>>>> Or specifying the grouping factor explicitely:
>>>>>
>>>>> mymod3<-nlsList(Conc~Dose * exp(lKe+lKa-lCl) *
>>>>> (exp(-exp(lKe)*Tps)-exp(-exp(lKa)*Tps)) /(exp(lKa)-exp(lKe))|Organ,
>>>>> data=mydata,
>>>>> start= c(lKe=-2.77, lKa=-1.41, lCl=-1.13)
>>>>> )
>>>>>
>>>>> Error in model.frame(formula, rownames, variables, varnames, extras,
>>>>> extranames, :
>>>>> variable lengths differ
>>>>> Error in model.frame(formula, rownames, variables, varnames, extras,
>>>>> extranames, :
>>>>> variable lengths differ
>>>>> Error in model.frame(formula, rownames, variables, varnames, extras,
>>>>> extranames, :
>>>>> variable lengths differ
>>>>>
>>>>>
>>>>> I cannot find out why the grouping factor cannot be used (it has the
>>>>> same length as the other variables...)
>>>>>
>>>>> Another strange thing occurs: in the example given in the help of
>>>>> nlsList.selfstart, the following command works well:
>>>>>
>>>>> fm1 <- nlsList(SSasympOff, CO2)
>>>>>
>>>>> However its seemingly equivalent applied to the case above fails:
>>>>>
>>>>> mymod4<-nlsList(SSfol,data=mydata)
>>>>> Error in eval(expr, envir, enclos) : object "input" not found
>>>>> Error in eval(expr, envir, enclos) : object "input" not found
>>>>> Error in eval(expr, envir, enclos) : object "input" not found
>>>>>
>>>>>
>>>>> Any hint/suggestion appreciated.
>>>>>
>>>>> Kind regards,
>>>>>
>>>>> Patrick Giraudoux
>>>>>
>>>>> ______________________________________________
>>>>> R-help at stat.math.ethz.ch mailing list
>>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>>> PLEASE do read the posting guide!
>>>>> http://www.R-project.org/posting-guide.html
>>>>
>>>
>>> ______________________________________________
>>> R-help at stat.math.ethz.ch mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide!
>>> http://www.R-project.org/posting-guide.html
>>>
>>
>
>
>
--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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