Sample size log linear analysis? Is there a rule of thumb for the sample size for a log linear analysis? For example, would it be inappropriate to use this analysis for a sample size of 50 with 3 predictors?
 A: The current question cannot be fully answered. Those "you need this many if you have this many independent variables" are very roughly generalized rules at best and should not be followed without a deeper understanding on how sample size calculation works.
There are, roughly, three components at work:
First, what is the expected strength of the association? The stronger it is, the fewer sample you'll need. If you talk to a statistician, you may be asked to provide an expected regression coefficient, or in the case of log-linear an expected risk ratio for your main predictor of interest.
Second, what are the power and type I error rate? These two concern the chance of committing type I and type II errors. The lower the power (aka higher type II error rate) and the higher the type I error rate will lead to fewer sample size, and vice versa.
Third, what is the sample size?
These three operate together. And if one wants to find out either one of them, the other two must be known or be assumed. For instance, if you want to know the sample, you'll need to provide the effect size and the expected type I error rate (usually 5%, but not a fixed rule) and power (usually 80%, but again not a rule.)
And in your case specifically, you have 50 and want to know if it's appropriate (aka, powerful enough to detect the association,) then you will need to provide sample size (50) and expected strength in association for the statistician to tell you if the study is properly powered or not.
It's just a simplified summary; depending on the complexity of the model and formula used to compute the sample, some more information may be required as well. I'd strongly recommend you to talk to a statistician for some more relevant guidance.
