[R] How to obtain individual log-likelihood value from glm?

[John Fox]

Dear John,

On 2020-08-29 1:30 a.m., John Smith wrote:
> Thanks Prof. Fox.
> 
> I am curious: what is the model estimated below?

Nonsense, as Peter explained in a subsequent response to your prior posting.

> 
> I guess my inquiry seems more complicated than I thought: with y being 0/1, how to fit weighted logistic regression with weights <1, in the sense of weighted least squares? Thanks

What sense would that make? WLS is meant to account for non-constant 
error variance in a linear model, but in a binomial GLM, the variance is 
purely a function for the mean.

If you had binomial (rather than binary 0/1) observations (i.e., 
binomial trials exceeding 1), then you could account for overdispersion, 
e.g., by introducing a dispersion parameter via the quasibinomial 
family, but that isn't equivalent to variance weights in a LM, rather to 
the error-variance parameter in a LM.

I guess the question is what are you trying to achieve with the weights?

Best,
  John

> 
>> On Aug 28, 2020, at 10:51 PM, John Fox <jfox using mcmaster.ca> wrote:
>>
>> Dear John
>>
>> I think that you misunderstand the use of the weights argument to glm() for a binomial GLM. From ?glm: "For a binomial GLM prior weights are used to give the number of trials when the response is the proportion of successes." That is, in this case y should be the observed proportion of successes (i.e., between 0 and 1) and the weights are integers giving the number of trials for each binomial observation.
>>
>> I hope this helps,
>> John
>>
>> John Fox, Professor Emeritus
>> McMaster University
>> Hamilton, Ontario, Canada
>> web: https://socialsciences.mcmaster.ca/jfox/
>>
>>> On 2020-08-28 9:28 p.m., John Smith wrote:
>>> If the weights < 1, then we have different values! See an example below.
>>> How  should I interpret logLik value then?
>>> set.seed(135)
>>>   y <- c(rep(0, 50), rep(1, 50))
>>>   x <- rnorm(100)
>>>   data <- data.frame(cbind(x, y))
>>>   weights <- c(rep(1, 50), rep(2, 50))
>>>   fit <- glm(y~x, data, family=binomial(), weights/10)
>>>   res.dev <- residuals(fit, type="deviance")
>>>   res2 <- -0.5*res.dev^2
>>>   cat("loglikelihood value", logLik(fit), sum(res2), "\n")
>>>> On Tue, Aug 25, 2020 at 11:40 AM peter dalgaard <pdalgd using gmail.com> wrote:
>>>> If you don't worry too much about an additive constant, then half the
>>>> negative squared deviance residuals should do. (Not quite sure how weights
>>>> factor in. Looks like they are accounted for.)
>>>>
>>>> -pd
>>>>
>>>>> On 25 Aug 2020, at 17:33 , John Smith <jswhct using gmail.com> wrote:
>>>>>
>>>>> Dear R-help,
>>>>>
>>>>> The function logLik can be used to obtain the maximum log-likelihood
>>>> value
>>>>> from a glm object. This is an aggregated value, a summation of individual
>>>>> log-likelihood values. How do I obtain individual values? In the
>>>> following
>>>>> example, I would expect 9 numbers since the response has length 9. I
>>>> could
>>>>> write a function to compute the values, but there are lots of
>>>>> family members in glm, and I am trying not to reinvent wheels. Thanks!
>>>>>
>>>>> counts <- c(18,17,15,20,10,20,25,13,12)
>>>>>      outcome <- gl(3,1,9)
>>>>>      treatment <- gl(3,3)
>>>>>      data.frame(treatment, outcome, counts) # showing data
>>>>>      glm.D93 <- glm(counts ~ outcome + treatment, family = poisson())
>>>>>      (ll <- logLik(glm.D93))
>>>>>
>>>>>        [[alternative HTML version deleted]]
>>>>>
>>>>> ______________________________________________
>>>>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>>> PLEASE do read the posting guide
>>>> http://www.R-project.org/posting-guide.html
>>>>> and provide commented, minimal, self-contained, reproducible code.
>>>>
>>>> --
>>>> Peter Dalgaard, Professor,
>>>> Center for Statistics, Copenhagen Business School
>>>> Solbjerg Plads 3, 2000 Frederiksberg, Denmark
>>>> Phone: (+45)38153501
>>>> Office: A 4.23
>>>> Email: pd.mes using cbs.dk  Priv: PDalgd using gmail.com
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>     [[alternative HTML version deleted]]
>>> ______________________________________________
>>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.