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

[Ebert,Timothy Aaron]

Time is often used in this sort of problem, but really time is not relevant. A better choice is accumulated thermal units. The insect will molt when X thermal units have been accumulated. This is often expressed as degree days, but could as easily be other units like degree seconds. However, I suspect that fine time units exceeds the accuracy of the measurement system. A growth chamber might maintain 28 C, but the temperature the insect experiences might be somewhat different thereby introducing additional variability in the outcome. No thermal units accumulated, no development, so that is not an issue.
    This approach allows one to predict life stage over a large temperature range. Accuracy can be improved if one knows the lower development threshold. At high temperatures development stops, and a mortality function can be added.

Tim

-----Original Message-----
From: R-help <r-help-bounces using r-project.org> On Behalf Of Rolf Turner
Sent: Wednesday, July 27, 2022 8:26 PM
To: r-help <r-help using r-project.org>
Subject: [R] Predicted values from glm() when linear predictor is NA.

[External Email]

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

--
Honorary Research Fellow
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276