# Wrongly converging glm()

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## Wrongly converging glm()

 Dear R-core, I have found an edge-case where the glm function falsely concludes that the model has converged. The issue is the following: my data contains a number of covariates, one of these covariates has a very small variance. For most of the rows of this covariate, the value is 0, except for one of the rows, where it is 1. The glm function correctly determines the beta and standard error estimates for all other covariates. I've placed the data here: http://www.harmjanwestra.nl/rtestdata.txtThe model I'm using is very simple: data <- read.table("rtestdata.txt") model <- glm(data[,1] ~ data[,2] + data[,3] + data[,4] + data[,5] + data[,6] + data[,7] + data[,8] + data[,9] + data[,10] + data[,11] + data[,12] + data[,13] + data[,14], family=binomial("logit")) summary(model) You will see that for covariate data[,13], the beta/coefficient estimate is around -9. The number of iterations that has been performed is 8, and model\$converged returns TRUE. I've used some alternate logistic regression code in C (https://github.com/czep/mlelr/blob/master/src/mlelr.c), which produces identical estimates for the other covariates and comparable deviance values. However, using this C code, I'm seeing that the estimate for data[,13] is around -100 (since I'm allowing a maximum of 100 MLE iterations). There, the conclusion is that the model does not converge. The difference between the two pieces of code is that in R, the glm() function determines convergence of the whole model by measuring the difference between deviance of the current iteration versus the deviance of the prior iteration, and calls the model converged when it reaches a certain epsilon value. In the C++ code, the model is converged when all parameters haven't changed markedly compared to the previous iteration. I think both approaches are valid, although the R variant (while faster) makes it vulnerable to wrongly concluding convergence in edge cases such as the one presented above, resulting in wrong coefficient estimates. For people wanting to use logistic regression in a training/prediction kind of setting, using these estimates might influence their predictive performance. The problem here is that the glm function does not return any warnings when one of the covariates in the model does not converge. For someone who is not paying attention, this may lead them to conclude there is nothing wrong with their data. In my opinion, the default behavior in this case should therefore be to conclude that the model did not converge, or at least to show a warning message. Please let me know whether you believe this is an issue, and whether I can provide additional information. With kind regards, Harm-Jan Westra         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
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## Re: Wrongly converging glm()

 Allow me to chime in. That's an interesting case you present, but as far as I'm concerned the algorithm did converge. The estimate of -9.25 has an estimated standard error of 72.4, meaning that frequentists would claim the true value would lie anywhere between appx. -151 and 132 (CI) and hence the estimate from the glm algorithm is perfectly compatible with the one from the C++ code. And as the glm algorithm uses a different convergence rule, the algorithm rightfully reported it converged. It's not because another algorithm based on another rule doesn't converge, that the one glm uses didn't. On top of that: In both cases the huge standard error on that estimate clearly tells you that the estimate should not be trusted, and the fit is unstable. That's to be expected, given the insane inbalance in your data, especially for the 13th column. If my students would incorporate that variable in a generalized linear model and tries to formulate a conclusion based on that coefficient, they failed the exam. So if somebody does this analysis and tries to draw any conclusion whatsoever on that estimate, maybe they should leave the analysis to somebody who does know what they're doing. Cheers Joris On Thu, Jul 20, 2017 at 5:02 PM, Harm-Jan Westra <[hidden email] > wrote: > Dear R-core, > > > I have found an edge-case where the glm function falsely concludes that > the model has converged. The issue is the following: my data contains a > number of covariates, one of these covariates has a very small variance. > For most of the rows of this covariate, the value is 0, except for one of > the rows, where it is 1. > > > The glm function correctly determines the beta and standard error > estimates for all other covariates. > > > I've placed the data here: http://www.harmjanwestra.nl/rtestdata.txt> > > The model I'm using is very simple: > > > data <- read.table("rtestdata.txt") > > model <- glm(data[,1] ~ data[,2] + data[,3] + data[,4] + data[,5] + > data[,6] + data[,7] + data[,8] + data[,9] + data[,10] + data[,11] + > data[,12] + data[,13] + data[,14], family=binomial("logit")) > > summary(model) > > > You will see that for covariate data[,13], the beta/coefficient estimate > is around -9. The number of iterations that has been performed is 8, and > model\$converged returns TRUE. > > > I've used some alternate logistic regression code in C ( > https://github.com/czep/mlelr/blob/master/src/mlelr.c), which produces > identical estimates for the other covariates and comparable deviance > values. However, using this C code, I'm seeing that the estimate for > data[,13] is around -100 (since I'm allowing a maximum of 100 MLE > iterations). There, the conclusion is that the model does not converge. > > > The difference between the two pieces of code is that in R, the glm() > function determines convergence of the whole model by measuring the > difference between deviance of the current iteration versus the deviance of > the prior iteration, and calls the model converged when it reaches a > certain epsilon value. In the C++ code, the model is converged when all > parameters haven't changed markedly compared to the previous iteration. > > > I think both approaches are valid, although the R variant (while faster) > makes it vulnerable to wrongly concluding convergence in edge cases such as > the one presented above, resulting in wrong coefficient estimates. For > people wanting to use logistic regression in a training/prediction kind of > setting, using these estimates might influence their predictive performance. > > > The problem here is that the glm function does not return any warnings > when one of the covariates in the model does not converge. For someone who > is not paying attention, this may lead them to conclude there is nothing > wrong with their data. In my opinion, the default behavior in this case > should therefore be to conclude that the model did not converge, or at > least to show a warning message. > > > Please let me know whether you believe this is an issue, and whether I can > provide additional information. > > > With kind regards, > > > Harm-Jan Westra > > > > > > > > > >         [[alternative HTML version deleted]] > > ______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-devel> -- Joris Meys Statistical consultant Ghent University Faculty of Bioscience Engineering Department of Mathematical Modelling, Statistics and Bio-Informatics tel :  +32 (0)9 264 61 79 [hidden email] ------------------------------- Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php        [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
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## Re: Wrongly converging glm()

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## Re: Wrongly converging glm()

 In reply to this post by Joris FA Meys In defence of Harma-Jan's original post I would say that there is a difference between true convergence and satisfying a convergence criterion. In my view the algorithm has not converged. This is a case of quasi-complete separate -- there are both successes and failures when x13=0 but only failures when x13=1. As a result, the likelihood has no maximum and increases, albeit slightly, as the associated coefficient tends to infinity while maximizing over the other parameters. The estimate given is not the MLE and the standard error is not meaningful because the conditions for convergence of MLEs to their asymptotic normal distribution has been violated. I agree with Joris that someone familiar with logistic regression should be able to identify this situation -- though the solution is not as simple as throwing out the covariate. Suppose that there had been many failures when x13=1, not just 1. The same problem would arise, but x13 is clearly an important covariate. Removing it from the analysis is not the thing to do. A better solution is to penalize the likelihood or (and I'm showing my true colours here) conduct a Bayesian analysis. Regarding the statement that the algorithm has converged, perhaps R should say more truthfully that the convergence criterion has been satisfied -- but that might lead to more confusion. In this case, any convergence criterion will be satisfied eventually. If you increase the maximum number of iterations in the C implementation then the other convergence criterion will be satisfied and the code will say that the algorithm has converged. In the end, it's up to the analyst to be aware of the pitfalls and how to address them. Cheers, Simon > -----Original Message----- > From: R-devel [mailto:[hidden email]] On Behalf Of Joris Meys > Sent: July 20, 2017 11:39 AM > To: Harm-Jan Westra <[hidden email]> > Cc: [hidden email] > Subject: Re: [Rd] Wrongly converging glm() > > Allow me to chime in. That's an interesting case you present, but as far as I'm > concerned the algorithm did converge. The estimate of -9.25 has an estimated > standard error of 72.4, meaning that frequentists would claim the true value > would lie anywhere between appx. -151 and 132 (CI) and hence the estimate > from the glm algorithm is perfectly compatible with the one from the C++ code. > And as the glm algorithm uses a different convergence rule, the algorithm > rightfully reported it converged. It's not because another algorithm based on > another rule doesn't converge, that the one glm uses didn't. > > On top of that: In both cases the huge standard error on that estimate clearly > tells you that the estimate should not be trusted, and the fit is unstable. That's > to be expected, given the insane inbalance in your data, especially for the 13th > column. If my students would incorporate that variable in a generalized linear > model and tries to formulate a conclusion based on that coefficient, they failed > the exam. So if somebody does this analysis and tries to draw any conclusion > whatsoever on that estimate, maybe they should leave the analysis to > somebody who does know what they're doing. > > Cheers > Joris > > On Thu, Jul 20, 2017 at 5:02 PM, Harm-Jan Westra > <[hidden email] > > wrote: > > > Dear R-core, > > > > > > I have found an edge-case where the glm function falsely concludes > > that the model has converged. The issue is the following: my data > > contains a number of covariates, one of these covariates has a very small > variance. > > For most of the rows of this covariate, the value is 0, except for one > > of the rows, where it is 1. > > > > > > The glm function correctly determines the beta and standard error > > estimates for all other covariates. > > > > > > I've placed the data here: http://www.harmjanwestra.nl/rtestdata.txt> > > > > > The model I'm using is very simple: > > > > > > data <- read.table("rtestdata.txt") > > > > model <- glm(data[,1] ~ data[,2] + data[,3] + data[,4] + data[,5] + > > data[,6] + data[,7] + data[,8] + data[,9] + data[,10] + data[,11] + > > data[,12] + data[,13] + data[,14], family=binomial("logit")) > > > > summary(model) > > > > > > You will see that for covariate data[,13], the beta/coefficient > > estimate is around -9. The number of iterations that has been > > performed is 8, and model\$converged returns TRUE. > > > > > > I've used some alternate logistic regression code in C ( > > https://github.com/czep/mlelr/blob/master/src/mlelr.c), which produces > > identical estimates for the other covariates and comparable deviance > > values. However, using this C code, I'm seeing that the estimate for > > data[,13] is around -100 (since I'm allowing a maximum of 100 MLE > > iterations). There, the conclusion is that the model does not converge. > > > > > > The difference between the two pieces of code is that in R, the glm() > > function determines convergence of the whole model by measuring the > > difference between deviance of the current iteration versus the > > deviance of the prior iteration, and calls the model converged when it > > reaches a certain epsilon value. In the C++ code, the model is > > converged when all parameters haven't changed markedly compared to the > previous iteration. > > > > > > I think both approaches are valid, although the R variant (while > > faster) makes it vulnerable to wrongly concluding convergence in edge > > cases such as the one presented above, resulting in wrong coefficient > > estimates. For people wanting to use logistic regression in a > > training/prediction kind of setting, using these estimates might influence > their predictive performance. > > > > > > The problem here is that the glm function does not return any warnings > > when one of the covariates in the model does not converge. For someone > > who is not paying attention, this may lead them to conclude there is > > nothing wrong with their data. In my opinion, the default behavior in > > this case should therefore be to conclude that the model did not > > converge, or at least to show a warning message. > > > > > > Please let me know whether you believe this is an issue, and whether I > > can provide additional information. > > > > > > With kind regards, > > > > > > Harm-Jan Westra > > > > > > > > > > > > > > > > > > > >         [[alternative HTML version deleted]] > > > > ______________________________________________ > > [hidden email] mailing list > > https://stat.ethz.ch/mailman/listinfo/r-devel> > > > > > -- > Joris Meys > Statistical consultant > > Ghent University > Faculty of Bioscience Engineering > Department of Mathematical Modelling, Statistics and Bio-Informatics > > tel :  +32 (0)9 264 61 79 > [hidden email] > ------------------------------- > Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php> > [[alternative HTML version deleted]] > > ______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-devel______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
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## Re: Wrongly converging glm()

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## Re: Wrongly converging glm()

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## Re: Wrongly converging glm()

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## Re: Wrongly converging glm()

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## Re: Wrongly converging glm()

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## Re: Wrongly converging glm()

 In reply to this post by Harm-Jan Westra On Thu, Jul 20, 2017 at 8:32 PM, Harm-Jan Westra <[hidden email] > wrote: > My apologies if I seemed to ‘blame R’. This was in no way my intention. I > get the feeling that you’re missing my point as well. > I get that now. But you're on R-devel and you started with the claim that R "falsely reports...". That looks like a bug report, and that's why I initially answered that R correctly reports it converged. Maybe to the wrong value, but it converged. > > > What strikes me as odd is that R would warn you when your data is faulty > for a function such as cor(), but not for glm(). I don’t see why you > wouldn’t want to check both convergence criteria if you know multiple of > such criteria exist. It would make the software more user friendly in the > end. > The unfitness of the data bears no relation to the convergence criterium and vice versa. These data checks should be done before the convergence algorithm is even started, and as Mark Leeds also indicated, that's one hell of a job to do. That said, the glm function has an argument "method" by which you can provide an alternative version of glm.fit().  Adapting that one to use another convergence criterium is rather trivial, so technically R even allows you to do that out of the box. No patches needed. > > > I agree ‘that everybody using R should first do the effort of learning > what they're doing’, but it is a bit of a non-argument, because we all know > that, the world just doesn’t work that way, plus this is one of the > arguments that has held for example the Linux community back for quite a > while (i.e. let’s not make the software more user friendly because the user > should be more knowledgeable). > That's a wrong analogy imho. You can expect Linux to be user friendly, but not "I will detect every logical fallacy in the article you're writing in this text editor" friendly. And honestly, that's a bit what you're asking R to do here. I understand why, but there's always cases that will be missed. And I wouldn't dare to speak in the name of the R core team, but I can imagine they have a little more urgent issues than helping my students to pass their statistics course ;-) Cheers Joris -- Joris Meys Statistical consultant Ghent University Faculty of Bioscience Engineering Department of Mathematical Modelling, Statistics and Bio-Informatics tel :  +32 (0)9 264 61 79 [hidden email] ------------------------------- Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php        [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
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## Re: Wrongly converging glm()

 Dear Joris, I’ll be more careful in my wording next time; thanks for the pointer, and thanks for the discussion. This whole process has been quite educational! 😉. I think we’ve reached a consensus here, where the situation as it is right now has been chosen to allow for flexibility of R’s glm() function. With kind regards, Harm-Jan From: Joris Meys Sent: Thursday, July 20, 2017 16:06 To: Harm-Jan Westra Cc: [hidden email] Subject: Re: [Rd] Wrongly converging glm() On Thu, Jul 20, 2017 at 8:32 PM, Harm-Jan Westra <[hidden email]> wrote: My apologies if I seemed to ‘blame R’. This was in no way my intention. I get the feeling that you’re missing my point as well. I get that now. But you're on R-devel and you started with the claim that R "falsely reports...". That looks like a bug report, and that's why I initially answered that R correctly reports it converged. Maybe to the wrong value, but it converged. What strikes me as odd is that R would warn you when your data is faulty for a function such as cor(), but not for glm(). I don’t see why you wouldn’t want to check both convergence criteria if you know multiple of such criteria exist. It would make the software more user friendly in the end. The unfitness of the data bears no relation to the convergence criterium and vice versa. These data checks should be done before the convergence algorithm is even started, and as Mark Leeds also indicated, that's one hell of a job to do. That said, the glm function has an argument "method" by which you can provide an alternative version of glm.fit().  Adapting that one to use another convergence criterium is rather trivial, so technically R even allows you to do that out of the box. No patches needed. I agree ‘that everybody using R should first do the effort of learning what they're doing’, but it is a bit of a non-argument, because we all know that, the world just doesn’t work that way, plus this is one of the arguments that has held for example the Linux community back for quite a while (i.e. let’s not make the software more user friendly because the user should be more knowledgeable). That's a wrong analogy imho. You can expect Linux to be user friendly, but not "I will detect every logical fallacy in the article you're writing in this text editor" friendly. And honestly, that's a bit what you're asking R to do here. I understand why, but there's always cases that will be missed. And I wouldn't dare to speak in the name of the R core team, but I can imagine they have a little more urgent issues than helping my students to pass their statistics course ;-) Cheers Joris -- Joris Meys Statistical consultant Ghent University Faculty of Bioscience Engineering Department of Mathematical Modelling, Statistics and Bio-Informatics tel :  +32 (0)9 264 61 79 [hidden email] ------------------------------- Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php        [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
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## Re: Wrongly converging glm()

 In reply to this post by Harm-Jan Westra I'm chiming in late since I read the news in digest form, and I won't copy the entire conversation to date. The issue raised comes up quite often in Cox models, so often that the Therneau and Grambsch book has a section on the issue (3.5, p 58).  After a few initial iterations the offending coefficient will increase by a constant at each iteration while the log-likelihood approaches an asymptote (essentially once the other coefficients "settle down"). The coxph routine tries to detect this case and print a warning, and this turns out to be very hard to do accurately.  I worked hard at tuning the threshold(s) for the message several years ago and finally gave up; I am guessing that the warning misses > 5% of the cases when the issue is true, and that 5% of the warnings that do print are incorrect.   (And these estimates may be too optimistic.)   Highly correlated predictors tend to trip it up, e.g., the truncated power spline basis used by the rcs function in Hmisc. All in all, I am not completely sure whether the message does more harm than good.  I'd be quite reluctant to go down the same path again with the glm function. Terry Therneau ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
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## Re: Wrongly converging glm()

 Please allow me to add my 3 cents.  Stopping an iterative optimization algorithm at an "appropriate" juncture is very tricky.  All one can say is that the algorithm terminated because it triggered a particular stopping criterion.  A good software will tell you why it stopped - i.e. the stopping criterion that was triggered.  It is extremely difficult to make a failsafe guarantee that the triggered stopping criterion is the correct one and that the answer obtained is trustworthy. It is up to the user to determine whether the answer makes sense.  In the case of maximizing a likelihood function, it is perfectly reasonable to stop when the algorithm has not made any progress in increasing the log likelihood.  In this case, the software should print out something like "algorithm terminated due to lack of improvement in log-likelihood."  Therefore, I don't see a need to issue any warning, but simply report the stopping criterion that was applied to terminate the algorithm. Best, Ravi -----Original Message----- From: R-devel [mailto:[hidden email]] On Behalf Of Therneau, Terry M., Ph.D. Sent: Friday, July 21, 2017 8:04 AM To: [hidden email]; Mark Leeds <[hidden email]>; [hidden email]; [hidden email] Subject: Re: [Rd] Wrongly converging glm() I'm chiming in late since I read the news in digest form, and I won't copy the entire conversation to date. The issue raised comes up quite often in Cox models, so often that the Therneau and Grambsch book has a section on the issue (3.5, p 58).  After a few initial iterations the offending coefficient will increase by a constant at each iteration while the log-likelihood approaches an asymptote (essentially once the other coefficients "settle down"). The coxph routine tries to detect this case and print a warning, and this turns out to be very hard to do accurately.  I worked hard at tuning the threshold(s) for the message several years ago and finally gave up; I am guessing that the warning misses > 5% of the cases when the issue is true, and that 5% of the warnings that do print are incorrect.   (And these estimates may be too optimistic.)   Highly correlated predictors tend to trip it up, e.g., the truncated power spline basis used by the rcs function in Hmisc. All in all, I am not completely sure whether the message does more harm than good.  I'd be quite reluctant to go down the same path again with the glm function. Terry Therneau ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-devel______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
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## Re: Wrongly converging glm()

 Hi Ravi: Well said. In John's Rvmmin package, he has codes for explaining the cause of the termination. The codes returned were fine. The problem was that the model I was using could have multiple solutions ( regardless of the data sent in ) so, even though the stopping criteria was reached, it turned out that one of the parameters ( there were two parameters ) could have really been anything and the same likelihood value would  be returned. So, what I learned the hard way was  termination due to reasonable stopping  criteria DOES NOT NECESSARILY EQUAL OPTIMAL. But I lived in the dark about this for a long time and only happened to notice it when playing around with the likelihood by fixing the offending parameter to various values and optimizing over the non-offending parameter. Thanks for eloquent explanation.       Mark On Fri, Jul 21, 2017 at 9:22 AM, Ravi Varadhan <[hidden email]> wrote: > Please allow me to add my 3 cents.  Stopping an iterative optimization > algorithm at an "appropriate" juncture is very tricky.  All one can say is > that the algorithm terminated because it triggered a particular stopping > criterion.  A good software will tell you why it stopped - i.e. the > stopping criterion that was triggered.  It is extremely difficult to make a > failsafe guarantee that the triggered stopping criterion is the correct one > and that the answer obtained is trustworthy. It is up to the user to > determine whether the answer makes sense.  In the case of maximizing a > likelihood function, it is perfectly reasonable to stop when the algorithm > has not made any progress in increasing the log likelihood.  In this case, > the software should print out something like "algorithm terminated due to > lack of improvement in log-likelihood."  Therefore, I don't see a need to > issue any warning, but simply report the stopping criterion that was > applied to terminate the algorithm. > > Best, > Ravi > > -----Original Message----- > From: R-devel [mailto:[hidden email]] On Behalf Of > Therneau, Terry M., Ph.D. > Sent: Friday, July 21, 2017 8:04 AM > To: [hidden email]; Mark Leeds <[hidden email]>; > [hidden email]; [hidden email] > Subject: Re: [Rd] Wrongly converging glm() > > I'm chiming in late since I read the news in digest form, and I won't copy > the entire conversation to date. > > The issue raised comes up quite often in Cox models, so often that the > Therneau and Grambsch book has a section on the issue (3.5, p 58).  After a > few initial iterations the offending coefficient will increase by a > constant at each iteration while the log-likelihood approaches an asymptote > (essentially once the other coefficients "settle down"). > > The coxph routine tries to detect this case and print a warning, and this > turns out to be very hard to do accurately.  I worked hard at tuning the > threshold(s) for the message several years ago and finally gave up; I am > guessing that the warning misses > 5% of the cases when the issue is true, > and that 5% of the warnings that do print are incorrect. > (And these estimates may be too optimistic.)   Highly correlated > predictors tend to trip > it up, e.g., the truncated power spline basis used by the rcs function in > Hmisc. > > All in all, I am not completely sure whether the message does more harm > than good.  I'd be quite reluctant to go down the same path again with the > glm function. > > Terry Therneau > > ______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-devel>         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-devel