Is there a general rule about max nr of variables to use in (generalized) linear model?

Question

I am running a generalized linear model on a dataset with 19 individuals and have 4 variables of interest. There are furthermore a number of interactions that might be interesting to look at. I was wondering if there is a general rule of thumb (with reference please) about the nr of terms you can use in a model based on the sample size. Thanks.

Answer 1

There's Tukey's suggestion of a minimum of 5 observations per mean parameter (he also suggested 25 observations per variance or covariance parameter). I don't recall the exact location of that suggestion, sorry.

But it really depends on the accuracy you want. If you want to be able to get a reasonable idea of actual effects sizes, this suggests that for a logistic regression something more like 50 observations per parameter might be more in the ballpark.

This has sample-size-related rules of thumb; if you can specify the required information you might be able to figure out what you need.