attached paper should be useful

Article Log-binomial models: Exploring failed convergence

Let us begin with a logit and binomial model: the Logit binomial is a suitable method for analysing proportions with a varying denominator. For example 2 (numerator ) out of 20 people in the village (the denominator) have the disease (the response). The random term in this model is assumed to binomial so that variance depends on the expected value of the proportion and the denominator. The expected value is the modelled underlying proportion of having the disease.

If you are dealing with individual data, the denominator is all 1's and you could use a logit Bernoulli model. A case is 1 out of 1; a non-case is 0 out of 1 but you still modelling the underlying proportion having the disease. The random term is now expected to follow a Bernoulli distribution (as the denominator is all 1s)

In practice if you had individual data and you could turned it into proportions you would get the same results with either method ; some software does this behind the scenes to make for quicker estimation. For example 10,000 observations on disease presence and sex could be reduced to 4 observations in a 2 by 2 table.

Have a look at my replies to

https://www.researchgate.net/post/What-is-the-difference-between-linear-regression-and-logistics-regression

Now for the log bit; it is usual for the log to be used with counts (with a NBD or Poisson random term) and the logit (or probit or log-log ) to be used with binary outcomes and proportions (with a binomial or Bernoulli random terms; the term canonical link is often used

have a look at the table Common distributions with typical uses and canonical link functions on this site

https://en.wikipedia.org/wiki/Generalized_linear_model

and this explains more:

https://www.r-bloggers.com/2018/10/generalized-linear-models-understanding-the-link-function/

https://www.sagepub.com/sites/default/files/upm-binaries/21121_Chapter_15.pdf

The log binomial is sometimes preferred so as to estimate relative risks, rather than the relative odds of the logit, but estimation may be tricky. as the paper cited by @James Leigh describes.

You may also be interested in taking this free online course; it includes logit modelling:

http://www.bristol.ac.uk/cmm/learning/online-course/

@Tanvir The same topic had been discussed earlier on research gate. Kindly go through the thread below.

https://www.researchgate.net/post/What_is_the_difference_between_binary_logistic_regression_and_binomial_logistic_regression

Hi Imran Anwar. That thread is addressing a different question, IMO. It asks about the distinction between binary and binomial logistic regression models. In both cases, the model is a GzLM with a logit link and binomial error distribution.

In the current thread, on the other hand, both models have a binomial error distribution, but one has a logit link, and the other has a log link. The former is logistic regression, and Exp(B) = the odds ratio (OR). For the latter, Exp(B) = the risk ratio (RR).

Tanvir Ahammed, which model people prefer might be related to study design. E.g., for a case-control study, the OR is indicated. For clinical trials or cohort studies with binary outcomes, investigators might prefer to report the RR. It is sometimes argued that clinicians have an easier time understanding risk and RRs than odds and ORs. This article discusses some of these issues.

Article Statistical notes for clinical researchers: Risk difference,...

HTH.

EDIT

PS- I might have added that a GzLM with binomial error distribution and log link function (i.e., the log-binomial model) is one way to model the RR. As these UCLA webpages show, Poisson regression with a robust variance estimator is another way.

• https://stats.idre.ucla.edu/stata/faq/how-can-i-estimate-relative-risk-using-glm-for-common-outcomes-in-cohort-studies/
• https://stats.idre.ucla.edu/sas/faq/how-can-i-estimate-relative-risk-in-sas-using-proc-genmod-for-common-outcomes-in-cohort-studies/