[R] Predicted values from glm() when linear predictor is NA.

[John Fox]

Dear Rolf,

The coefficient of TrtTime:LifestageL1 isn't estimable (as you explain) 
and by setting it to NA, glm() effectively removes it from the model. An 
equivalent model is therefore

 > fit2 <- glm(cbind(Dead,Alive) ~ TrtTime + Lifestage +
+               I((Lifestage == "Egg + L1")*TrtTime) +
+               I((Lifestage == "L1 + L2")*TrtTime) +
+               I((Lifestage == "L3")*TrtTime),
+             family=binomial, data=demoDat)
Warning message:
glm.fit: fitted probabilities numerically 0 or 1 occurred

 > cbind(coef(fit, complete=FALSE), coef(fit2))
                                   [,1]         [,2]
(Intercept)                -0.91718302  -0.91718302
TrtTime                     0.88846195   0.88846195
LifestageEgg + L1         -45.36420974 -45.36420974
LifestageL1                14.27570572  14.27570572
LifestageL1 + L2           -0.30332697  -0.30332697
LifestageL3                -3.58672631  -3.58672631
TrtTime:LifestageEgg + L1   8.10482459   8.10482459
TrtTime:LifestageL1 + L2    0.05662651   0.05662651
TrtTime:LifestageL3         1.66743472   1.66743472

There is no problem computing fitted values for the model, specified 
either way. That the fitted values when Lifestage == "L1" all round to 1 
on the probability scale is coincidental -- that is, a consequence of 
the data.

I hope this helps,
  John

On 2022-07-27 8:26 p.m., Rolf Turner wrote:
> 
> I have a data frame with a numeric ("TrtTime") and a categorical
> ("Lifestage") predictor.
> 
> Level "L1" of Lifestage occurs only with a single value of TrtTime,
> explicitly 12, whence it is not possible to estimate a TrtTime "slope"
> when Lifestage is "L1".
> 
> Indeed, when I fitted the model
> 
>      fit <- glm(cbind(Dead,Alive) ~ TrtTime*Lifestage, family=binomial,
>                 data=demoDat)
> 
> I got:
> 
>> as.matrix(coef(fit))
>>                                    [,1]
>> (Intercept)                -0.91718302
>> TrtTime                     0.88846195
>> LifestageEgg + L1         -45.36420974
>> LifestageL1                14.27570572
>> LifestageL1 + L2           -0.30332697
>> LifestageL3                -3.58672631
>> TrtTime:LifestageEgg + L1   8.10482459
>> TrtTime:LifestageL1                 NA
>> TrtTime:LifestageL1 + L2    0.05662651
>> TrtTime:LifestageL3         1.66743472
> 
> That is, TrtTime:LifestageL1 is NA, as expected.
> 
> I would have thought that fitted or predicted values corresponding to
> Lifestage = "L1" would thereby be NA, but this is not the case:
> 
>> predict(fit)[demoDat$Lifestage=="L1"]
>>        26       65      131
>> 24.02007 24.02007 24.02007
>>
>> fitted(fit)[demoDat$Lifestage=="L1"]
>>   26  65 131
>>    1   1   1
> 
> That is, the predicted values on the scale of the linear predictor are
> large and positive, rather than being NA.
> 
> What this amounts to, it seems to me, is saying that if the linear
> predictor in a Binomial glm is NA, then "success" is a certainty.
> This strikes me as being a dubious proposition.  My gut feeling is that
> misleading results could be produced.
> 
> Can anyone explain to me a rationale for this behaviour pattern?
> Is there some justification for it that I am not currently seeing?
> Any other comments?  (Please omit comments to the effect of "You are as
> thick as two short planks!". :-) )
> 
> I have attached the example data set in a file "demoDat.txt", should
> anyone want to experiment with it.  The file was created using dput() so
> you should access it (if you wish to do so) via something like
> 
>      demoDat <- dget("demoDat.txt")
> 
> Thanks for any enlightenment.
> 
> cheers,
> 
> Rolf Turner
> 
> 
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-- 
John Fox, Professor Emeritus
McMaster University
Hamilton, Ontario, Canada
web: https://socialsciences.mcmaster.ca/jfox/