If I understand correctly the ContourLines function gives you the contour lines when you put in the data. But before this I need to data to put into that function. I think this is something like a 2D CDF of the data that then leads to the 2D quantiles but I am not 100% sure. What I am basically looking for is the 2D curve that encloses say 95% of the data in a similar fashion to a 1D quantile where the quantile represents the value that x% of the data is below. I think what I am looking for is the 2D bivariate version of the 1D quantile plot (where the quantile value is plotted vs the % value). I hope this makes some sense. Bernard McGarvey Director, Fort Myers Beach Lions Foundation, Inc. Retired (Lilly Engineering Fellow).> On March 27, 2019 at 3:57 PM Paul Murrell <paul at stat.auckland.ac.nz> wrote: > > > > Are you looking for the contourLines() function ? > > Paul > > On 28/03/19 8:37 AM, Bernard McGarvey wrote: > > John, I have attached a pdf of the plot. Hopefully you can read this. > > > > If I understand correctly, this plot is basically the 2-D version of the 1-D quantile plot. > > > > Thanks > > > > Bernard McGarvey > > > > > > Director, Fort Myers Beach Lions Foundation, Inc. > > > > > > Retired (Lilly Engineering Fellow). > > > > > >> On March 27, 2019 at 7:44 AM John Kane <jrkrideau at gmail.com> wrote: > >> > >> > >> The figure did not get through. Perhaps try a pdf? > >> > >> On Tue, 26 Mar 2019 at 13:41, Bernard McGarvey > >> <mcgarvey.bernard at comcast.net> wrote: > >>> > >>> I want to see if I can reproduce the plot below in R. If I understand it correctly, i takes my bivariate data and creates quantile density contours. My interpretation of these contours is that they enclose a certain % of the total data. I am using the bkde2D function in library KernSmooth which gives density values that can be plotted on a contour plot but I would like the curves that enclose a given % of the data, if that is possible > >>> > >>> > >>> Thanks > >>> > >>> > >>> > >>> > >>> > >>> Bernard McGarvey > >>> > >>> Director, Fort Myers Beach Lions Foundation, Inc. > >>> > >>> Retired (Lilly Engineering Fellow). > >>> > >>> > >>> ______________________________________________ > >>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > >>> 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. > >> > >> > >> > >> -- > >> John Kane > >> Kingston ON Canada > >> > >> ______________________________________________ > >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > >> 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. > > -- > Dr Paul Murrell > Department of Statistics > The University of Auckland > Private Bag 92019 > Auckland > New Zealand > 64 9 3737599 x85392 > paul at stat.auckland.ac.nz > http://www.stat.auckland.ac.nz/~paul/
You are missing a crucial point. The reals are well ordered; higher dimensions are not. Therefore 2d quantile contours are not unique. Of course assuming I understand your query correctly. Bert On Wed, Mar 27, 2019, 13:55 Bernard McGarvey <mcgarvey.bernard at comcast.net> wrote:> If I understand correctly the ContourLines function gives you the contour > lines when you put in the data. But before this I need to data to put into > that function. I think this is something like a 2D CDF of the data that > then leads to the 2D quantiles but I am not 100% sure. What I am basically > looking for is the 2D curve that encloses say 95% of the data in a similar > fashion to a 1D quantile where the quantile represents the value that x% of > the data is below. I think what I am looking for is the 2D bivariate > version of the 1D quantile plot (where the quantile value is plotted vs the > % value). > > I hope this makes some sense. > > Bernard McGarvey > > > Director, Fort Myers Beach Lions Foundation, Inc. > > > Retired (Lilly Engineering Fellow). > > > > On March 27, 2019 at 3:57 PM Paul Murrell <paul at stat.auckland.ac.nz> > wrote: > > > > > > > > Are you looking for the contourLines() function ? > > > > Paul > > > > On 28/03/19 8:37 AM, Bernard McGarvey wrote: > > > John, I have attached a pdf of the plot. Hopefully you can read this. > > > > > > If I understand correctly, this plot is basically the 2-D version of > the 1-D quantile plot. > > > > > > Thanks > > > > > > Bernard McGarvey > > > > > > > > > Director, Fort Myers Beach Lions Foundation, Inc. > > > > > > > > > Retired (Lilly Engineering Fellow). > > > > > > > > >> On March 27, 2019 at 7:44 AM John Kane <jrkrideau at gmail.com> wrote: > > >> > > >> > > >> The figure did not get through. Perhaps try a pdf? > > >> > > >> On Tue, 26 Mar 2019 at 13:41, Bernard McGarvey > > >> <mcgarvey.bernard at comcast.net> wrote: > > >>> > > >>> I want to see if I can reproduce the plot below in R. If I > understand it correctly, i takes my bivariate data and creates quantile > density contours. My interpretation of these contours is that they enclose > a certain % of the total data. I am using the bkde2D function in library > KernSmooth which gives density values that can be plotted on a contour plot > but I would like the curves that enclose a given % of the data, if that is > possible > > >>> > > >>> > > >>> Thanks > > >>> > > >>> > > >>> > > >>> > > >>> > > >>> Bernard McGarvey > > >>> > > >>> Director, Fort Myers Beach Lions Foundation, Inc. > > >>> > > >>> Retired (Lilly Engineering Fellow). > > >>> > > >>> > > >>> ______________________________________________ > > >>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > > >>> 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. > > >> > > >> > > >> > > >> -- > > >> John Kane > > >> Kingston ON Canada > > >> > > >> ______________________________________________ > > >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > > >> 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. > > > > -- > > Dr Paul Murrell > > Department of Statistics > > The University of Auckland > > Private Bag 92019 > > Auckland > > New Zealand > > 64 9 3737599 x85392 > > paul at stat.auckland.ac.nz > > http://www.stat.auckland.ac.nz/~paul/ > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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. >[[alternative HTML version deleted]]
That thought had crossed my mind so thanks for that clarification Bert. i think you are correct and so the plot I am looking at must be doing something different than I was thinking. Thanks Bernard Sent from my iPhone so please excuse the spelling!"> On Mar 27, 2019, at 5:18 PM, Bert Gunter <bgunter.4567 at gmail.com> wrote: > > You are missing a crucial point. The reals are well ordered; higher dimensions are not. Therefore 2d quantile contours are not unique. > > Of course assuming I understand your query correctly. > > > Bert > >> On Wed, Mar 27, 2019, 13:55 Bernard McGarvey <mcgarvey.bernard at comcast.net> wrote: >> If I understand correctly the ContourLines function gives you the contour lines when you put in the data. But before this I need to data to put into that function. I think this is something like a 2D CDF of the data that then leads to the 2D quantiles but I am not 100% sure. What I am basically looking for is the 2D curve that encloses say 95% of the data in a similar fashion to a 1D quantile where the quantile represents the value that x% of the data is below. I think what I am looking for is the 2D bivariate version of the 1D quantile plot (where the quantile value is plotted vs the % value). >> >> I hope this makes some sense. >> >> Bernard McGarvey >> >> >> Director, Fort Myers Beach Lions Foundation, Inc. >> >> >> Retired (Lilly Engineering Fellow). >> >> >> > On March 27, 2019 at 3:57 PM Paul Murrell <paul at stat.auckland.ac.nz> wrote: >> > >> > >> > >> > Are you looking for the contourLines() function ? >> > >> > Paul >> > >> > On 28/03/19 8:37 AM, Bernard McGarvey wrote: >> > > John, I have attached a pdf of the plot. Hopefully you can read this. >> > > >> > > If I understand correctly, this plot is basically the 2-D version of the 1-D quantile plot. >> > > >> > > Thanks >> > > >> > > Bernard McGarvey >> > > >> > > >> > > Director, Fort Myers Beach Lions Foundation, Inc. >> > > >> > > >> > > Retired (Lilly Engineering Fellow). >> > > >> > > >> > >> On March 27, 2019 at 7:44 AM John Kane <jrkrideau at gmail.com> wrote: >> > >> >> > >> >> > >> The figure did not get through. Perhaps try a pdf? >> > >> >> > >> On Tue, 26 Mar 2019 at 13:41, Bernard McGarvey >> > >> <mcgarvey.bernard at comcast.net> wrote: >> > >>> >> > >>> I want to see if I can reproduce the plot below in R. If I understand it correctly, i takes my bivariate data and creates quantile density contours. My interpretation of these contours is that they enclose a certain % of the total data. I am using the bkde2D function in library KernSmooth which gives density values that can be plotted on a contour plot but I would like the curves that enclose a given % of the data, if that is possible >> > >>> >> > >>> >> > >>> Thanks >> > >>> >> > >>> >> > >>> >> > >>> >> > >>> >> > >>> Bernard McGarvey >> > >>> >> > >>> Director, Fort Myers Beach Lions Foundation, Inc. >> > >>> >> > >>> Retired (Lilly Engineering Fellow). >> > >>> >> > >>> >> > >>> ______________________________________________ >> > >>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >> > >>> 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. >> > >> >> > >> >> > >> >> > >> -- >> > >> John Kane >> > >> Kingston ON Canada >> > >> >> > >> ______________________________________________ >> > >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >> > >> 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. >> > >> > -- >> > Dr Paul Murrell >> > Department of Statistics >> > The University of Auckland >> > Private Bag 92019 >> > Auckland >> > New Zealand >> > 64 9 3737599 x85392 >> > paul at stat.auckland.ac.nz >> > http://www.stat.auckland.ac.nz/~paul/ >> >> ______________________________________________ >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >> 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.[[alternative HTML version deleted]]
Regardless of how many dimensions you have for independent variables, the density is one-dimensional, and if you assume the density function has been determined (e.g. by kernel estimation or by a Gaussian copula) then if you integrate the density function along that dimension there will be unique slices of the multivariate input domain determined by those slices. They might in general be disjoint regions of the independent variable space, but that is what the contour function does. I am not seeing your point, Bert, unless you are unwilling to assume a density function model? On March 27, 2019 2:18:18 PM PDT, Bert Gunter <bgunter.4567 at gmail.com> wrote:>You are missing a crucial point. The reals are well ordered; higher >dimensions are not. Therefore 2d quantile contours are not unique. > >Of course assuming I understand your query correctly. > > >Bert > >On Wed, Mar 27, 2019, 13:55 Bernard McGarvey ><mcgarvey.bernard at comcast.net> >wrote: > >> If I understand correctly the ContourLines function gives you the >contour >> lines when you put in the data. But before this I need to data to put >into >> that function. I think this is something like a 2D CDF of the data >that >> then leads to the 2D quantiles but I am not 100% sure. What I am >basically >> looking for is the 2D curve that encloses say 95% of the data in a >similar >> fashion to a 1D quantile where the quantile represents the value that >x% of >> the data is below. I think what I am looking for is the 2D bivariate >> version of the 1D quantile plot (where the quantile value is plotted >vs the >> % value). >> >> I hope this makes some sense. >> >> Bernard McGarvey >> >> >> Director, Fort Myers Beach Lions Foundation, Inc. >> >> >> Retired (Lilly Engineering Fellow). >> >> >> > On March 27, 2019 at 3:57 PM Paul Murrell ><paul at stat.auckland.ac.nz> >> wrote: >> > >> > >> > >> > Are you looking for the contourLines() function ? >> > >> > Paul >> > >> > On 28/03/19 8:37 AM, Bernard McGarvey wrote: >> > > John, I have attached a pdf of the plot. Hopefully you can read >this. >> > > >> > > If I understand correctly, this plot is basically the 2-D version >of >> the 1-D quantile plot. >> > > >> > > Thanks >> > > >> > > Bernard McGarvey >> > > >> > > >> > > Director, Fort Myers Beach Lions Foundation, Inc. >> > > >> > > >> > > Retired (Lilly Engineering Fellow). >> > > >> > > >> > >> On March 27, 2019 at 7:44 AM John Kane <jrkrideau at gmail.com> >wrote: >> > >> >> > >> >> > >> The figure did not get through. Perhaps try a pdf? >> > >> >> > >> On Tue, 26 Mar 2019 at 13:41, Bernard McGarvey >> > >> <mcgarvey.bernard at comcast.net> wrote: >> > >>> >> > >>> I want to see if I can reproduce the plot below in R. If I >> understand it correctly, i takes my bivariate data and creates >quantile >> density contours. My interpretation of these contours is that they >enclose >> a certain % of the total data. I am using the bkde2D function in >library >> KernSmooth which gives density values that can be plotted on a >contour plot >> but I would like the curves that enclose a given % of the data, if >that is >> possible >> > >>> >> > >>> >> > >>> Thanks >> > >>> >> > >>> >> > >>> >> > >>> >> > >>> >> > >>> Bernard McGarvey >> > >>> >> > >>> Director, Fort Myers Beach Lions Foundation, Inc. >> > >>> >> > >>> Retired (Lilly Engineering Fellow). >> > >>> >> > >>> >> > >>> ______________________________________________ >> > >>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, >see >> > >>> 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. >> > >> >> > >> >> > >> >> > >> -- >> > >> John Kane >> > >> Kingston ON Canada >> > >> >> > >> ______________________________________________ >> > >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, >see >> > >> 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. >> > >> > -- >> > Dr Paul Murrell >> > Department of Statistics >> > The University of Auckland >> > Private Bag 92019 >> > Auckland >> > New Zealand >> > 64 9 3737599 x85392 >> > paul at stat.auckland.ac.nz >> > http://www.stat.auckland.ac.nz/~paul/ >> >> ______________________________________________ >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >> 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. >> > > [[alternative HTML version deleted]] > >______________________________________________ >R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >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.-- Sent from my phone. Please excuse my brevity.
Hallo Bernard I did not follow all emails in this thread but it seems to me that your request is similar to Bioconductor packages dealing with Flow Cytometry data. Especially flowViz package is designed to visualise such data. Cheers Petr> -----Original Message----- > From: R-help <r-help-bounces at r-project.org> On Behalf Of Bernard McGarvey > Sent: Wednesday, March 27, 2019 9:55 PM > To: Paul Murrell <paul at stat.auckland.ac.nz>; John Kane > <jrkrideau at gmail.com> > Cc: R. Help Mailing List <r-help at r-project.org> > Subject: Re: [R] [FORGED] Re: Quantile Density Contours > > If I understand correctly the ContourLines function gives you the contour lines > when you put in the data. But before this I need to data to put into that > function. I think this is something like a 2D CDF of the data that then leads to > the 2D quantiles but I am not 100% sure. What I am basically looking for is the > 2D curve that encloses say 95% of the data in a similar fashion to a 1D quantile > where the quantile represents the value that x% of the data is below. I think > what I am looking for is the 2D bivariate version of the 1D quantile plot (where > the quantile value is plotted vs the % value). > > I hope this makes some sense. > > Bernard McGarvey > > > Director, Fort Myers Beach Lions Foundation, Inc. > > > Retired (Lilly Engineering Fellow). > > > > On March 27, 2019 at 3:57 PM Paul Murrell <paul at stat.auckland.ac.nz> > wrote: > > > > > > > > Are you looking for the contourLines() function ? > > > > Paul > > > > On 28/03/19 8:37 AM, Bernard McGarvey wrote: > > > John, I have attached a pdf of the plot. Hopefully you can read this. > > > > > > If I understand correctly, this plot is basically the 2-D version of the 1-D > quantile plot. > > > > > > Thanks > > > > > > Bernard McGarvey > > > > > > > > > Director, Fort Myers Beach Lions Foundation, Inc. > > > > > > > > > Retired (Lilly Engineering Fellow). > > > > > > > > >> On March 27, 2019 at 7:44 AM John Kane <jrkrideau at gmail.com> wrote: > > >> > > >> > > >> The figure did not get through. Perhaps try a pdf? > > >> > > >> On Tue, 26 Mar 2019 at 13:41, Bernard McGarvey > > >> <mcgarvey.bernard at comcast.net> wrote: > > >>> > > >>> I want to see if I can reproduce the plot below in R. If I > > >>> understand it correctly, i takes my bivariate data and creates > > >>> quantile density contours. My interpretation of these contours is > > >>> that they enclose a certain % of the total data. I am using the > > >>> bkde2D function in library KernSmooth which gives density values > > >>> that can be plotted on a contour plot but I would like the curves > > >>> that enclose a given % of the data, if that is possible > > >>> > > >>> > > >>> Thanks > > >>> > > >>> > > >>> > > >>> > > >>> > > >>> Bernard McGarvey > > >>> > > >>> Director, Fort Myers Beach Lions Foundation, Inc. > > >>> > > >>> Retired (Lilly Engineering Fellow). > > >>> > > >>> > > >>> ______________________________________________ > > >>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > > >>> 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. > > >> > > >> > > >> > > >> -- > > >> John Kane > > >> Kingston ON Canada > > >> > > >> ______________________________________________ > > >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > > >> 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. > > > > -- > > Dr Paul Murrell > > Department of Statistics > > The University of Auckland > > Private Bag 92019 > > Auckland > > New Zealand > > 64 9 3737599 x85392 > > paul at stat.auckland.ac.nz > > http://www.stat.auckland.ac.nz/~paul/ > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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.Osobn? ?daje: Informace o zpracov?n? a ochran? osobn?ch ?daj? obchodn?ch partner? PRECHEZA a.s. jsou zve?ejn?ny na: https://www.precheza.cz/zasady-ochrany-osobnich-udaju/ | Information about processing and protection of business partner?s personal data are available on website: https://www.precheza.cz/en/personal-data-protection-principles/ D?v?rnost: Tento e-mail a jak?koliv k n?mu p?ipojen? dokumenty jsou d?v?rn? a podl?haj? tomuto pr?vn? z?vazn?mu prohl??en? o vylou?en? odpov?dnosti: https://www.precheza.cz/01-dovetek/ | This email and any documents attached to it may be confidential and are subject to the legally binding disclaimer: https://www.precheza.cz/en/01-disclaimer/
Thanks Petr Bernard Sent from my iPhone so please excuse the spelling!"> On Mar 28, 2019, at 2:26 AM, PIKAL Petr <petr.pikal at precheza.cz> wrote: > > Hallo Bernard > > I did not follow all emails in this thread but it seems to me that your request is similar to Bioconductor packages dealing with Flow Cytometry data. > > Especially flowViz package is designed to visualise such data. > > Cheers > Petr > > >> -----Original Message----- >> From: R-help <r-help-bounces at r-project.org> On Behalf Of Bernard McGarvey >> Sent: Wednesday, March 27, 2019 9:55 PM >> To: Paul Murrell <paul at stat.auckland.ac.nz>; John Kane >> <jrkrideau at gmail.com> >> Cc: R. Help Mailing List <r-help at r-project.org> >> Subject: Re: [R] [FORGED] Re: Quantile Density Contours >> >> If I understand correctly the ContourLines function gives you the contour lines >> when you put in the data. But before this I need to data to put into that >> function. I think this is something like a 2D CDF of the data that then leads to >> the 2D quantiles but I am not 100% sure. What I am basically looking for is the >> 2D curve that encloses say 95% of the data in a similar fashion to a 1D quantile >> where the quantile represents the value that x% of the data is below. I think >> what I am looking for is the 2D bivariate version of the 1D quantile plot (where >> the quantile value is plotted vs the % value). >> >> I hope this makes some sense. >> >> Bernard McGarvey >> >> >> Director, Fort Myers Beach Lions Foundation, Inc. >> >> >> Retired (Lilly Engineering Fellow). >> >> >>> On March 27, 2019 at 3:57 PM Paul Murrell <paul at stat.auckland.ac.nz> >> wrote: >>> >>> >>> >>> Are you looking for the contourLines() function ? >>> >>> Paul >>> >>>> On 28/03/19 8:37 AM, Bernard McGarvey wrote: >>>> John, I have attached a pdf of the plot. Hopefully you can read this. >>>> >>>> If I understand correctly, this plot is basically the 2-D version of the 1-D >> quantile plot. >>>> >>>> Thanks >>>> >>>> Bernard McGarvey >>>> >>>> >>>> Director, Fort Myers Beach Lions Foundation, Inc. >>>> >>>> >>>> Retired (Lilly Engineering Fellow). >>>> >>>> >>>>> On March 27, 2019 at 7:44 AM John Kane <jrkrideau at gmail.com> wrote: >>>>> >>>>> >>>>> The figure did not get through. Perhaps try a pdf? >>>>> >>>>> On Tue, 26 Mar 2019 at 13:41, Bernard McGarvey >>>>> <mcgarvey.bernard at comcast.net> wrote: >>>>>> >>>>>> I want to see if I can reproduce the plot below in R. If I >>>>>> understand it correctly, i takes my bivariate data and creates >>>>>> quantile density contours. My interpretation of these contours is >>>>>> that they enclose a certain % of the total data. I am using the >>>>>> bkde2D function in library KernSmooth which gives density values >>>>>> that can be plotted on a contour plot but I would like the curves >>>>>> that enclose a given % of the data, if that is possible >>>>>> >>>>>> >>>>>> Thanks >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> Bernard McGarvey >>>>>> >>>>>> Director, Fort Myers Beach Lions Foundation, Inc. >>>>>> >>>>>> Retired (Lilly Engineering Fellow). >>>>>> >>>>>> >>>>>> ______________________________________________ >>>>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >>>>>> 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. >>>>> >>>>> >>>>> >>>>> -- >>>>> John Kane >>>>> Kingston ON Canada >>>>> >>>>> ______________________________________________ >>>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >>>>> 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. >>> >>> -- >>> Dr Paul Murrell >>> Department of Statistics >>> The University of Auckland >>> Private Bag 92019 >>> Auckland >>> New Zealand >>> 64 9 3737599 x85392 >>> paul at stat.auckland.ac.nz >>> http://www.stat.auckland.ac.nz/~paul/ >> >> ______________________________________________ >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >> 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. > Osobn? ?daje: Informace o zpracov?n? a ochran? osobn?ch ?daj? obchodn?ch partner? PRECHEZA a.s. jsou zve?ejn?ny na: https://www.precheza.cz/zasady-ochrany-osobnich-udaju/ | Information about processing and protection of business partner?s personal data are available on website: https://www.precheza.cz/en/personal-data-protection-principles/ > D?v?rnost: Tento e-mail a jak?koliv k n?mu p?ipojen? dokumenty jsou d?v?rn? a podl?haj? tomuto pr?vn? z?vazn?mu prohl??en? o vylou?en? odpov?dnosti: https://www.precheza.cz/01-dovetek/ | This email and any documents attached to it may be confidential and are subject to the legally binding disclaimer: https://www.precheza.cz/en/01-disclaimer/ >