The question in logistic regression is how much more frequent the outcome is one rather than zero. We are used to think of relative frequencies as proportions, which are numbers between 0 and 1.

Another way to express a proportion (or probability) p is: odds = p/(1-p). For example, the probability of Six on a dice is 1/6. The odds of Six is therefore:

(1/6)/(5/6) = 1/5.

Imagine you want to test whether your participant can use paranormal powers to get more Sixes. In your experiment you find that the proportion of Sixes is now 1/5 and the odds are 1/4. Then this change can be expressed as ratio-of-odds:

(1/4)/(1/5) = 5/4

In logistic regression, coefficients are typically on a log-odds (or logit) scale: log(p/(1-p)). By taking the exponent coefficients are converted to odds and odds ratios. Intercept parameters are odds, whereas treatment coefficients are odds ratios, representing change in odds.

More on logistic regression in my online book, chapter 7.4:

https://www.researchgate.net/project/Book-New-statistics-for-the-design-researcher

To fit a logistic regression model in R, you can use the function glm and specify family = binomial. The documentation is available here: https://www.rdocumentation.org/packages/stats/versions/3.6.1/topics/glm.

You can get the odds ratios from the variable coefficients in R by running exp(coef(mylogit)) where mylogit is the name of your model. See https://stats.idre.ucla.edu/r/dae/logit-regression/ for a worked example of fitting a logistic regression model in R.

Multilevel models are suitable when you have observations that have a hierarchical structure, for example pupils are nested in classes which are nested in schools. An introduction to situations in which multilevel modelling is useful can be found here: http://www.bristol.ac.uk/cmm/learning/multilevel-models/what-why.html A free interactive training course developed at the University of Bristol for learning multilevel modelling can be found here: https://www.cmm.bris.ac.uk/lemma/

To fit a multilevel logistic regression model in R, you can use the glmer function and specify family = binomial("logit"). Documentation is available here: https://www.rdocumentation.org/packages/lme4/versions/1.1-21/topics/glmer.

There are quite a lot of tricky issues with multilevel logit largely stemming from the fact that the level-1 variance is not really estimated but constrained and the other values are scaled to that result. These issues are very well covered in this free online material:

http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#discrete

In addition , multilevel estimates are cluster specific rather than population average, and this is especially important with repeated measures where the level 2 (subject) variance is more likely to be large. The estimate s cannot necessarily be interpreted in the same way as single level logit models.

Kindly Find the Attached

You can use the 'lme4' package