# Logistic regression sub-group size parameters

Someone in my lab has a sample of 500 older kids and he wants to investigate what factors are related to the probability that they will bully. Groups:

        bullied  not
bully       22    28
don't      200   250


They created an interaction variable using age*not bullied/bullied and added 14 other "predictors" to the mode. Interaction of age and bullying is sig but the prototypical plot looks weird, the group who were bullied have a 0 slope by age and the line starts and ends at 0. My guess is the the bullied/bullying group is way too small for all the info in the model. IF so, what are the group size parameters or ratio to total group parameters for logistic regression? Thank you very much!

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Could you explain what you mean by a 'prototypical plot'? –  onestop May 2 '12 at 14:15
The plot generated to indicate any interaction effect - pls see link - google.com/… –  Glenlivet May 2 '12 at 14:36
I don't really follow the question. Looking at the data reported here, you have a simple 2x2 contingency table setup. I'm not sure how that works w/ whatever was done next. Did they try to turn this into multinomial logistic regression? I don't think that would be appropriate. Also, can you post the plot that you think is problematic? –  gung May 3 '12 at 14:12
@gung - I think what we have is a bullying/non-bullying outcome with predictors that include whether bullied, age, and 14 others, plus the interaction term. I agree that we'd need to see the plot to comment on it. –  rolando2 May 3 '12 at 14:51
Something appears to have gone awry as from your data, the probability of bullying among those who were bullied is 22/222 = 0.099, but the plot shows it as 0. Suggests to me that the problem must be related to the 14 other 'predictors'. I suggest you try taking them all out initially, then adding them back one at a time to try to indentify what's causing the problem. –  onestop May 3 '12 at 15:11
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500 seems like a good-sized sample, but in this case it may not be. IF @rolando2 is right that this is a logistic regression of bullying onto having been bullied, plus the interaction with age (is age also a covariate on its own?), plus 14 other covariates, that's 16 predictors and only 50 instances of the phenomenon in question. Logistic regression tends to work best if the numbers of successes and failures are fairly similar (this is discussed on CV here). Another potential problem is separation, or quasi-separation (and here is a discussion of that problem). With so many covariates, you may end up with combinations in which there are simply no cases of bullying at all, and that will cause lots of problems. Based on your counts, at first blush it looks like having been bullied is almost perfectly irrelevant. I would try to rethink this project based on the original ideas and prior research (i.e., not taking into account what these data have shown thus far), and refit a model based on at most a few covariates. Unfortunately, there is a limit to how much information you can get from a dataset. They say that in art school, one of the crucial lessons for students is when to stop painting; there can be an analogy drawn to data analysis.

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I think that a small group size can be a major problem and probably is here. I don't know of any rules of thumb for exceptable sizes. But anytime you are interested in a statistical rule of thumb consult Van Belle's book that is titled "Statistical Rules of Thumb".

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