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I try to understand how is calculated residual deviance after a glm with binomial distribution and logit link: I am not able to reproduce the value that is reported by R (I do not blame R; I am sure that the output is right!). Thanks if someone can help me:

A <- c(10, 12, 15, 0, 1, 2, 3)
B <- c(2, 5, 3, 14, 15, 20, 30)
S <- c(25, 26, 27, 28, 29, 30, 31)

g <- glm(cbind(A=A, B=B) ~ S, 
         family = binomial(link = "logit"))
g$deviance
g$null.deviance

The values are: 

> g$deviance
[1] 22.16312
> g$null.deviance
[1] 77.99713

Residual deviance being -2*(LnL - LnLSat), I estimate LnL and LnLSat:

invlogit <- function (n) 1/(1 + exp(-n))
LnL <- sum(pbinom(q=A, size = A+B, 
           prob = invlogit(predict(g)), log.p = TRUE))
LnLSat <- sum(pbinom(q=A, size = A+B, 
           prob = A/(A+B), log.p = TRUE))
-2*(LnL - LnLSat)

Error here; it was obviously dbinom() not pbinom() that should be used !

The correct code is :

invlogit <- function (n) 1/(1 + exp(-n))
LnL <- sum(dbinom(x=A, size = A+B, 
           prob = invlogit(predict(g)), log = TRUE))
LnLSat <- sum(dbinom(x=A, size = A+B, 
           prob = A/(A+B), log = TRUE))
-2*(LnL - LnLSat)

All is ok now

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  • $\begingroup$ It's usually helpful to look at the source code for the whichever function you're using. $\endgroup$
    – assumednormal
    Aug 27, 2019 at 13:46
  • $\begingroup$ I found !!! it was just stupid error !I used pbinom() whereas it should be dbinom()! And it works perfectly now... sorry. I was stuck during 3 hours about this. $\endgroup$
    – MarcG
    Aug 27, 2019 at 14:18

1 Answer 1

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I made a mistake: pbinom() is for the cumulative distribution function whereas I should use dbinom() for the density/mass function.

And all is ok now !

I do not delete the question just in case someone did the same mistake as me !

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  • $\begingroup$ Don't beat yourself up about this. Why not develop a full answer that explains (conceptually) how the deviances are calculated, & illustrates that w/ R code that's made as transparent as possible (not everyone will use R, or be able to read it well)? $\endgroup$
    – gung - Reinstate Monica
    Aug 27, 2019 at 15:13

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