From westra.harmjan at outlook.com  Thu Jul 20 18:21:54 2017
From: westra.harmjan at outlook.com (Harm-Jan Westra)
Date: Thu, 20 Jul 2017 16:21:54 +0000
Subject: [Rd] Wrongly converging glm()
In-Reply-To: <CAO1zAVa5uOEswx8b8HhHMwGNazz8Pgq3nmYhR2okTiCM4+-cRg@mail.gmail.com>
References: <DM3PR20MB05722D6CF8D15F73CC4CE65987A70@DM3PR20MB0572.namprd20.prod.outlook.com>,
 <CAO1zAVa5uOEswx8b8HhHMwGNazz8Pgq3nmYhR2okTiCM4+-cRg@mail.gmail.com>
Message-ID: <DM3PR20MB0572B9357503F0401CC5EABF87A70@DM3PR20MB0572.namprd20.prod.outlook.com>

Dear Joris,


I agree that such a covariate should not be used in the analysis, and fully agree with your assessment. However, your response assumes that everybody who uses R knows what they're doing, which is a dangerous assumption to make. I bet there are a lot of people who blindly trust the output from R, even when there's clearly something wrong with the estimates.


In terms of your conclusion that the C++ estimate corresponds to a value within the R estimated confidence interval: if I allow the C++ code to run for 1000 iterations, it's estimate would be around -1000. It simply never converges.


I think there's nothing wrong with letting the user know there might be something wrong with one of the estimates, especially if your code can easily figure it out for you, by adding an additional rule. Not everyone is always paying attention (even if they know what they're doing).


With kind regards,


Harm-Jan


________________________________
From: Joris Meys <jorismeys at gmail.com>
Sent: Thursday, July 20, 2017 11:38 AM
To: Harm-Jan Westra
Cc: r-devel at r-project.org
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 <westra.harmjan at outlook.com<mailto:westra.harmjan at outlook.com>> 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









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Joris Meys
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[Rd] Wrongly converging glm()
Harm-Jan Westra