I would like to model on a rate outcome, with a number of covariates. I also have the number of counts which generate the rate outcome. Like below:

Good.Egg Bad.Egg Total.Egg   Good.Rate   Covariate1   Covariate2...

 2         2        4         0.5           1             22.3
 2         1        3         0.66          1             12.1
 0         1        1         0             0              8.0
 4         2        6         0.666         0              7.5
 3         5        8         0.375         1              6.6
 2         2        4         0.5           0              18.8
 0         2        2         0             1              14.6
 1         0        1         1             1              7.0

I would like to fit a model, which looks like

Good.Rate ~ covariate1 + covariate2 +......

And obtain P-values for each covariates.(The P-values will be used for a second step analysis)

I am doing the analysis in R.

Originally I am thinking of a GLM regression with family="binomial", but that does not take the number of counts into consideration. And I also considered beta-binomial regression, but it seems not possible to obtain P-value for each covariate?

My question is:

  1. Should I care about the number of the total counts? Say, the good egg rate of 1.0 derived from 1 out of 1 is less "reliable" than a good egg rate of 1.0 derived from 5 out of 5?

  2. If the answer to the above question is "yes". Then how do I model the data to achieve my goal (obtain P-value for each single covariate)?

Thank you!

  1. Yes, your intuition is right.

  2. Logistic regression (family = binomial(link = "logit")) is the way to go, but instead of making the dependent variable the rate, make it the number of good and bad eggs (i.e., use cbind(Good.Egg, Bad.Egg) on the left-hand side of ~). This is equivalent to recoding the data to have one row for each egg, with the dependent variable being a flag indicating whether the egg is bad or good.

Of course, without context, I don't know if this is the specific model you should use for your specific case. I'm supplying an answer to the general problem of binary outcomes.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.