# [R] logistic regression - glm.fit: fitted probabilities numerically 0 or 1 occurred

peter dalgaard pdalgd at gmail.com
Fri Dec 2 00:32:07 CET 2011

```On Dec 1, 2011, at 23:43 , Ben quant wrote:

> I'm not proposing this as a permanent solution, just investigating the warning. I zeroed out the three outliers and received no warning. Can someone tell me why I am getting no warning now?

It's easier to explain why you got the warning before. If the OR for a one unit change is 3000, the OR for a 14 unit change is on the order of 10^48 and that causes over/underflow in the conversion to probabilities.

I'm still baffled at how you can get that model fitted to your data, though. One thing is that you can have situations where there are fitted probabilities of one corresponding to data that are all one and/or fitted zeros where data are zero, but you seem to have cases where you have both zeros and ones at both ends of the range of x. Fitting a zero to a one or vice versa would make the likelihood zero, so you'd expect that the algorithm would find a better set of parameters rather quickly. Perhaps the extremely large number of observations that you have has something to do with it?

You'll get the warning if the fitted zeros or ones occur at any point of the iterative procedure. Maybe it isn't actually true for the final model, but that wouldn't seem consistent with the OR that you cited.

Anyways, your real problem lies with the distribution of the x values. I'd want to try transforming it to something more sane. Taking logarithms is the obvious idea, but you'd need to find out what to do about the zeros -- perhaps log(x + 1e-4) ? Or maybe just cut the outliers down to size with pmin(x,1).

>
> I did this 3 times to get rid of the 3 outliers:
> mx_dims = arrayInd(which.max(l_yx), dim(l_yx))
> l_yx[mx_dims] = 0
>
> Now this does not produce an warning:
> l_logit = glm(y~x, data=as.data.frame(l_yx), family=binomial(link="logit"))
>
> Can someone tell me why occurred?
>
> Also, again, here are the screen shots of my data that I tried to send earlier (two screen shots, two pages):
> http://scientia.crescat.net/static/ben/warn%20num%200%20or%201.pdf
>
> Thank you for your help,
>
> Ben
>
> On Thu, Dec 1, 2011 at 3:25 PM, Ben quant <ccquant at gmail.com> wrote:
> Oops! Please ignore my last post. I mistakenly gave you different data I was testing with. This is the correct data:
>
> Here you go:
>
> > attach(as.data.frame(l_yx))
> >  range(x[y==0])
> [1]  0.00000 14.66518
> > range(x[y==1])
> [1]  0.00000 13.49791
>
>
> How do I know what is acceptable?
>
> Also, here are the screen shots of my data that I tried to send earlier (two screen shots, two pages):
> http://scientia.crescat.net/static/ben/warn%20num%200%20or%201.pdf
>
> Thank you,
>
> Ben
>
> On Thu, Dec 1, 2011 at 3:07 PM, Ben quant <ccquant at gmail.com> wrote:
> Here you go:
>
> > attach(as.data.frame(l_yx))
> > range(x[y==1])
> [1] -22500.0000    746.6666
> >  range(x[y==0])
> [1] -10076.5303    653.0228
>
> How do I know what is acceptable?
>
> Also, here are the screen shots of my data that I tried to send earlier (two screen shots, two pages):
> http://scientia.crescat.net/static/ben/warn%20num%200%20or%201.pdf
>
> Thank you,
>
> Ben
>
>
> On Thu, Dec 1, 2011 at 2:24 PM, peter dalgaard <pdalgd at gmail.com> wrote:
>
> On Dec 1, 2011, at 21:32 , Ben quant wrote:
>
> > Thank you for the feedback, but my data looks fine to me. Please tell me if I'm not understanding.
>
> Hum, then maybe it really is a case of a transition region being short relative to the range of your data. Notice that the warning is just that: a warning. I do notice that the distribution of your x values is rather extreme -- you stated a range of 0--14 and a mean of 0.01. And after all, an odds ratio of 3000 per unit is only a tad over a doubling per 0.1 units.
>
> Have a look at  range(x[y==0]) and range(x[y==1]).
>
>
> >
> > I followed your instructions and here is a sample of the first 500 values : (info on 'd' is below that)
> >
> > >  d <- as.data.frame(l_yx)
> > > x = with(d, y[order(x)])
> > > x[1:500] # I have 1's and 0's dispersed throughout
> >   [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0
> > [101] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> > [201] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0
> > [301] 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> > [401] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
> >
> > # I get the warning still
> > > l_df = as.data.frame(l_yx)
> > >     l_logit = glm(y~x, data=l_df, family=binomial(link="logit"))
> >
> > Warning message:
> > glm.fit: fitted probabilities numerically 0 or 1 occurred
> >
> > # some info on 'd' above:
> >
> > > d[1:500,1]
> >   [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> > [101] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> > [201] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> > [301] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> > [401] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> > > d[1:500,2]
> >   [1] 3.023160e-03 7.932130e-02 0.000000e+00 1.779657e-02 1.608374e-01 0.000000e+00 5.577064e-02 7.753926e-03 4.018553e-03 4.760918e-02 2.080511e-02 1.642404e-01 3.703720e-03  8.901981e-02 1.260415e-03
> >  [16] 2.202523e-02 3.750940e-02 4.441975e-04 9.351171e-03 8.374567e-03 0.000000e+00 8.440448e-02 5.081017e-01 2.538640e-05 1.806017e-02 2.954641e-04 1.434859e-03 6.964976e-04 0.000000e+00 1.202162e-02
> >  [31] 3.420300e-03 4.276100e-02 1.457324e-02 4.140121e-03 1.349180e-04 1.525292e-03 4.817502e-02 9.515717e-03 2.232953e-02 1.227908e-01 3.293581e-02 1.454352e-02 1.176011e-03 6.274138e-02 2.879205e-02
> >  [46] 6.900926e-03 1.414648e-04 3.446349e-02 8.807174e-03 3.549332e-02 2.828509e-03 2.935003e-02 7.162872e-03 5.650050e-03 1.221191e-02 0.000000e+00 2.126334e-02 2.052020e-02 7.542409e-02 2.586269e-04
> >  [61] 5.258664e-02 1.213126e-02 1.493275e-02 8.152657e-03 1.774966e-02 2.433198e-02 1.371257e-02 6.732339e-02 9.747677e-03 8.180594e-03 1.882473e-01 1.682596e-03 1.410170e-02 8.429676e-03 3.520589e-01
> >  [76] 1.865160e-02 2.389941e-02 3.301558e-02 4.896605e-03 6.826244e-03 9.151337e-02 1.722270e-02 1.764039e-01 3.554063e-02 7.338532e-03 9.577793e-03 3.632366e-03 1.422400e-02 3.020497e-02 1.797096e-02
> >  [91] 2.577899e-03 1.338365e-01 8.202223e-03 1.088335e-02 2.137259e-02 6.829797e-03 3.104860e-04 8.927160e-03 5.626881e-02 1.197682e-02 6.140553e-02 2.729364e-02 1.377913e-02 3.018277e-03 1.188304e-02
> > [106] 2.029268e-03 2.108815e-02 1.765503e-03 2.449253e-02 3.677046e-03 1.013463e-02 4.286642e-02 1.238931e-02 3.072090e-03 1.509613e-02 3.609885e-02 5.537268e-03 3.151614e-02 3.703148e-03 1.409401e-01
> > [121] 1.473365e-02 9.160461e-03 1.035099e-01 3.005865e-02 1.332199e-02 6.936535e-03 2.433539e-02 4.935373e-03 4.822740e-03 1.597643e-03 3.805619e-03 1.092683e-02 1.760635e-01 5.565614e-03 7.739213e-04
> > [136] 4.529198e-03 5.110359e-03 7.391258e-02 5.018207e-03 2.071417e-02 1.825787e-02 9.141405e-03 1.078386e-01 2.171470e-04 7.164583e-03 2.522077e-02 1.994428e-03 6.044653e-03 1.778078e-04 5.797706e-03
> > [151] 1.526778e-02 1.595897e-02 1.995627e-01 1.946735e-03 6.711582e-02 2.722350e-02 3.127499e-02 1.074904e-01 2.477414e-03 5.015375e-02 3.417810e-02 2.046643e-02 1.644832e-02 5.220166e-03 1.217752e-02
> > [166] 1.187352e-02 1.634016e-02 2.349568e-03 3.451811e-02 2.593540e-03 6.868595e-03 1.311236e-02 6.457757e-03 2.942391e-04 1.628352e-02 8.288831e-03 3.170856e-04 1.251331e+00 1.706954e-02 1.063723e-03
> > [181] 1.374416e-02 2.140507e-02 2.817009e-02 2.272793e-02 4.365562e-02 6.089414e-03 2.498083e-02 1.360471e-02 1.884079e-02 1.448660e-02 2.341314e-02 8.167064e-03 4.109117e-02 2.660633e-02 7.711723e-03
> > [196] 9.590278e-03 2.515490e-03 1.978033e-02 3.454990e-02 8.072748e-03 4.718885e-03 1.621131e-01 4.547743e-03 1.081195e-02 9.572051e-04 1.790391e-02 1.618026e-02 1.910230e-02 1.861914e-02 3.485475e-02
> > [211] 2.844890e-03 1.866889e-02 1.378208e-02 2.451514e-02 2.535044e-03 3.921364e-04 1.557266e-03 3.315892e-03 1.752821e-03 6.786187e-03 1.360921e-02 9.550702e-03 8.114506e-03 5.068741e-03 1.729822e-02
> > [226] 1.902033e-02 8.196564e-03 2.632880e-03 1.587969e-02 8.354079e-04 1.050023e-03 4.236195e-04 9.181120e-03 4.995919e-04 1.092234e-02 1.207544e-02 2.187243e-01 3.251349e-02 1.269134e-03 1.557751e-04
> > [241] 1.232498e-02 2.654449e-02 1.049324e-03 8.442729e-03 6.331691e-03 1.715609e-02 1.017800e-03 9.230006e-03 1.331373e-02 5.596195e-02 1.296551e-03 5.272687e-03 2.805640e-02 4.790665e-02 2.043011e-02
> > [256] 1.047226e-02 1.866499e-02 9.323001e-03 8.920536e-03 1.582911e-03 2.776238e-03 2.914762e-02 4.402356e-03 9.555274e-04 1.681966e-03 7.584319e-04 6.758914e-02 1.505431e-02 2.213308e-02 1.329330e-02
> > [271] 7.284363e-03 2.687818e-02 2.997535e-03 7.470007e-03 2.070569e-03 3.441944e-02 1.717768e-02 4.523364e-02 1.003558e-02 1.365111e-02 1.906845e-02 1.676223e-02 3.506809e-04 9.164257e-02 9.008416e-03
> > [286] 1.073903e-02 4.855937e-03 8.618043e-03 2.529247e-02 1.059375e-02 5.834253e-03 2.004309e-02 1.460387e-02 2.899190e-02 5.867984e-03 1.983956e-02 6.834339e-03 1.925821e-03 9.231870e-03 6.839616e-03
> > [301] 1.029972e-02 2.009769e-02 9.458785e-03 1.183901e-02 8.911549e-03 1.264745e-02 2.995451e-03 7.657983e-04 5.315853e-03 1.325039e-02 1.044103e-02 2.307236e-02 2.780789e-02 1.735145e-02 9.053126e-03
> > [316] 5.847638e-02 3.815715e-03 5.087690e-03 1.040513e-02 4.475672e-02 6.564791e-02 3.233571e-03 1.076193e-02 8.283819e-02 5.370256e-03 3.533256e-02 1.302812e-02 1.896783e-02 2.055282e-02 3.572239e-03
> > [331] 5.867681e-03 5.864974e-04 9.715807e-03 1.665469e-02 5.082044e-02 3.547168e-03 3.069631e-03 1.274717e-02 1.858226e-03 3.104809e-04 1.247831e-02 2.073575e-03 3.544110e-04 7.240736e-03 8.452117e-05
> > [346] 8.149151e-04 4.942461e-05 1.142303e-03 6.265512e-04 3.666717e-04 3.244669e-02 7.242018e-03 6.335951e-04 2.329072e-02 3.719716e-03 2.803425e-02 1.623981e-02 6.387102e-03 8.807679e-03 1.214914e-02
> > [361] 6.699341e-03 1.148082e-02 1.329736e-02 1.537364e-03 2.004390e-02 1.562065e-02 1.655465e-02 9.960172e-02 2.174588e-02 1.209472e-02 2.328413e-02 2.012760e-04 1.422327e-02 2.194455e-03 2.307362e-02
> > [376] 4.315764e-03 3.208576e-02 3.826598e-02 1.828001e-02 3.935978e-03 5.294211e-04 1.392423e-02 6.588394e-03 1.040147e-03 1.260787e-02 9.051757e-04 5.353215e-02 6.049058e-02 1.382630e-01 1.064124e-01
> > [391] 3.380742e-03 1.798038e-02 1.557048e-01 1.217146e-02 4.140520e-02 4.707564e-02 2.786042e-02 8.836988e-03 5.542879e-03 1.862664e-02 8.858770e-03 1.026681e-03 1.692105e-02 8.849238e-03 7.143816e-03
> > [406] 1.630118e-02 1.165920e-01 9.471496e-03 4.879998e-02 1.388216e-02 1.453267e-02 4.845224e-04 1.415190e-03 1.208627e-02 1.372348e-02 2.573131e-02 1.169595e-02 1.825447e-02 2.574299e-02 5.301360e-02
> > [421] 6.961110e-03 7.781891e-03 1.013308e-03 3.160916e-03 1.090344e-02 1.530841e-02 9.398088e-04 9.143726e-04 1.286683e-02 2.006193e-02 1.774378e-02 5.681591e-02 9.584676e-03 7.957152e-02 4.485609e-03
> > [436] 1.086684e-02 2.930273e-03 6.085481e-03 4.342320e-03 1.319999e-02 2.120402e-02 4.477545e-02 1.991814e-02 8.893947e-03 7.790133e-03 1.610199e-02 2.441280e-02 2.781231e-03 1.410080e-02 1.639912e-02
> > [451] 1.797498e-02 1.185382e-02 2.775063e-02 3.797315e-02 1.428883e-02 1.272659e-02 2.390500e-03 7.503478e-03 8.965356e-03 2.139452e-02 2.028536e-02 6.916416e-02 1.615986e-02 4.837412e-02 1.561731e-02
> > [466] 7.130332e-03 9.208406e-05 1.099934e-02 2.003469e-02 1.395857e-02 9.883482e-03 4.110852e-02 1.202052e-02 2.833039e-02 1.233236e-02 2.145801e-02 7.900161e-03 4.663819e-02 4.410819e-03 5.115056e-04
> > [481] 9.100270e-04 4.013683e-03 1.227139e-02 3.304697e-03 2.919099e-03 6.112390e-03 1.922229e-02 1.208282e-03 1.164037e-02 2.166888e-02 4.381615e-02 5.318929e-03 7.226343e-03 2.732819e-02 2.385092e-04
> > [496] 4.905250e-02 1.159876e-02 4.068228e-03 3.349013e-02 1.273468e-03
> >
> >
> > Thanks for your help,
> >
> > Ben
> >
> > On Thu, Dec 1, 2011 at 11:55 AM, peter dalgaard <pdalgd at gmail.com> wrote:
> >
> > On Dec 1, 2011, at 18:54 , Ben quant wrote:
> >
> > > Sorry if this is a duplicate: This is a re-post because the pdf's mentioned
> > > below did not go through.
> >
> > Still not there. Sometimes it's because your mailer doesn't label them with the appropriate mime-type (e.g. as application/octet-stream, which is "arbitrary binary"). Anyways, see below
> >
> > [snip]
> > >
> > > With the above data I do:
> > >>    l_logit = glm(y~x, data=as.data.frame(l_yx),
> > > Warning message:
> > > glm.fit: fitted probabilities numerically 0 or 1 occurred
> > >
> > > Why am I getting this warning when I have data points of varying values for
> > > y=1 and y=0?  In other words, I don't think I have the linear separation
> > > issue discussed in one of the links I provided.
> >
> > I bet that you do... You can get the warning without that effect (one of my own examples is  the probability of menarche in a data set that includes infants and old age pensioners), but not with a huge odds ratio as well. Take a look at
> >
> > d <- as.data.frame(l_yx)
> > with(d, y[order(x)])
> >
> > if it comes out as all zeros followed by all ones or vice versa, then you have the problem.
> >
> >
> > >
> > > PS - Then I do this and I get a odds ratio a crazy size:
> > >>    l_sm = summary(l_logit) # coef pval is \$coefficients[8], log odds
> > > \$coefficients[2]
> > >>    l_exp_coef = exp(l_logit\$coefficients)[2] # exponentiate the
> > > coeffcients
> > >>    l_exp_coef
> > >       x
> > > 3161.781
> > >
> > > So for one unit increase in the predictor variable I get 3160.781%
> > > (3161.781 - 1 = 3160.781) increase in odds? That can't be correct either.
> > > How do I correct for this issue? (I tried multiplying the predictor
> > > variables by a constant and the odds ratio goes down, but the warning above
> > > still persists and shouldn't the odds ratio be predictor variable size
> > > independent?)
> >
> >
> > --
> > Peter Dalgaard, Professor,
> > Center for Statistics, Copenhagen Business School
> > Solbjerg Plads 3, 2000 Frederiksberg, Denmark
> > Phone: (+45)38153501
> > Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com
> >
> >
> >
> >
> >
> >
> >
> >
> >
>
> --
> Peter Dalgaard, Professor,
> Center for Statistics, Copenhagen Business School
> Solbjerg Plads 3, 2000 Frederiksberg, Denmark
> Phone: (+45)38153501
> Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com
>
>
>
>
>
>
>
>
>
>
>

--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

```