We know the generalized linear models (GLMs) are a broad class of models. When fitting GLMs in R, we need to specify which family function to use from a bunch of options like gaussian, poisson, binomial, quasi, etc. I would like to have your advice regarding how to determine the optional family function used for GLM fitting in R. Thanks!
Usually the dispositive consideration is the nature of the dependent variable. For example, if the response variable is binomial in nature, you might use logistic regression with a binomial family. If the response variable is count, you might use Poisson or negative binomial regression. If you have proportion data between 0 and 1, you might use beta regression. If you have data that's left-limited, say at zero, and potentially skewed, you might use Gamma regression.
A simple empirical rule:
Gaussian family : for continuous decimal data with normal distribution, like weight, length, et al.
Poisson or quasipoisson family: for positive integer or small natural number like count, individual number, frequency.
Binomial or quasibinomial family: binary data like 0 and 1, or proportion like survival number vs death number, positive frequency vs negative frequency, winning times vs the number of failtures, et al...
Gamma family : usually describe time data like the time or duration of the occurrence of the event.
If your model is overdispered, you should make a correction by choosing quasi-binomial or quasi-poisson.
In addition to what Salvatore S. Mangiafico has said, you should also choose the model based on its dispersion status (Over-dispersed or under-dispersed).
Thank you all for your responses. As you mentioned, it depends on what kind of distribution the data belongs to. So the next problem is to how to identify the distribution of your data. Here is a link of the answer to this question for whom might be interested: https://www.spcforexcel.com/knowledge/basic-statistics/deciding-which-distribution-fits-your-data-best
Which type of family link can be used for a dependent variable that has a skewed distribution such as CRP levels or the absolute value of body weight changes during a time interval?
