Talk:Deviance (statistics)

message: It isn´t defined as log likelihood. it is the log likelihood ratio!! of the submodel divided by the fullmodel.
:Reformulated to meet above point Melcombe (talk) 15:52, 12 September 2008 (UTC)
thread_title: 2008

message: The First edition of the McCullagh & Nelder reference certainly defines the deviance using the log-likelihood ratio (p17)... I can't access the 2nd Edition. In addition the two external links also agree with this. Melcombe (talk) 10:20, 15 September 2008 (UTC)
replies: text: You are right! Got confused about the definition of "full model." I tried to clear this up to prevent others from having this confusion. Pdbailey (talk) 01:00, 16 September 2008 (UTC)
thread_title:  Definition 

message: I believe the definition given here is scaled deviance, not deviance. Deviance would be scaled deviance times the scale parameter in the GLM. Schomerus (talk) 18:27, 23 November 2011 (UTC)
replies: text: This seems to follow on from the comment immediately above in that different sources may be using different definitions for deviance and/or scaled deviance. The definition presently in the article agrees with the citations given. Melcombe (talk) 11:25, 24 November 2011 (UTC)
replies: text: Hmmm, McCullough and Nelder 1989, the source cited, defines scaled deviance as deviance over the dispersion parameter on pp 33-34,  and it's clear there that  -2 [\log \lbrace p(y|\hat \theta_0)\rbrace -\log \lbrace p(y|\hat \theta_s)\rbrace ]\, is equal to scaled deviance. I haven't come across any sources which define it differently. But if the term is used inconsistently I would think that should be noted. Also of relevance to the discussion above, McCullough and Nelder  on p 119 note, "The chi-squared approximation is usually quite accurate for differences of [scaled] deviance [for nested models] even though it is inaccurate for the deviances themselves." Schomerus (talk) 00:02, 25 November 2011 (UTC)
replies: text: . . . which is another way of saying that the likelihood ratio test becomes unreliable when the number of parameters approaches the number of observations (i.e. saturation). Schomerus (talk) 15:43, 25 November 2011 (UTC)
replies: text: The 1983 edition of McCullough and Nelder definitely defines "deviance" in the way presently stated, and has no "scaled deviance". I am unable to see specific pages in the Google citations you give, and still unable to access the 1989 edition. I have found [], which uses thew "1983" version on page 15, and then does something very strange on page 17. However, I have also found webpages that seem to be using the "1989" form. Melcombe (talk) 10:56, 28 November 2011 (UTC)
replies: text: I've had a chance to compare the 1983 and 1989 editions of McCullagh and Nelder. You're right that in the 1983 edition there appears to be no mention of scaled deviance. However I believe that was an error, because they give two definitions of deviance, which are not consistent with each other. On p 17 (1983 ed.) they suggest that deviance is equal to 2 times the difference of log-likelihoods and there is no mention of the scale parameter, but on p. 24 (1983 ed.) deviance is divided by the scale parameter. This error was evidently corrected in the 1989 edition, as 2 times the difference of log-likelihoods is defined explicitly as "scaled deviance" (D*) on p 24 (1989 ed.). I've also checked a few other references from Alan Agresti and Yudi Pawitan and they agree with the latter definition. At any rate, since the 1989 edition is what's cited, I think the definition should agree with what's given there.Schomerus (talk) 20:11, 28 November 2011 (UTC)

text:  I have the impression that M&N tend to be sloppy with the terminology, which is leading to some of the confusion. For models that assume unit dispersion (eg Bernoulli, Poisson, etc), deviance and scaled deviance are of course equal. So in that context one can use them interchangeably, which McCullagh and Nelder seem to do (cf. p 119, 1989 ed.). When speaking of GLMs in general, though, it's important to make the distinction.  Schomerus (talk) 20:48, 28 November 2011 (UTC)
replies: text: Are there any other "text book" sources that might be consulted? I agree that M&N are a good basic source for GLMs, but there may be doubt about other contexts, where there is no obvious scale factor. Indeed, starting from scratch, it seems that the adjective "scaled" has been applied to the wrong version of  "deviance". But your thought that the usage in the 1983 edition was an error is incorrect, as that is exactly the terminology being used at the time (I attended seminars given by Nelder): of course that terminology may well have changed later. However, as to other uses, I note that the few papers I have seen on "Bayesian deviance" use the twice log-likelihood basis: see for example Deviance information criterion and its references. I will post a note on the Stats project talk page to see if others can contribute here. Melcombe (talk) 10:07, 1 December 2011 (UTC)
thread_title: Deviance vs scaled deviance

message: This article is very important for diagnostics of GLM models. I've mentioned Wilks' theorem, but it should also have examples showing it. If someone else will get to adding it, that would be great. Tal Galili (talk) 20:02, 19 August 2018 (UTC)
thread_title:  Lacking examples