# theoretical concerns in logistic regression

I have a dataset with 260 patients. I aim to study factors associated the certain finding in magnetic resonance imaging. I use logistic regression with six predictors. Regression yields to several significant predictors. I have philosophical concerns however.

Nagelkerke´s R is only 20%. My model is however significant compared to empty model. Only 7% of the positive outcomes can be predicted. However diagnostics show that just ten cases has normalized residuals outside 1.96 SD. Moreover leverage criteria of 3x mean value is met in 250 cases.

However I have been told that I do not have look too deeply to this fact with low R2 (http://www.theanalysisfactor.com/small-r-squared/

I would like to think so. My aim is not to construct a PREDICTIVE model but instead to study RELATIONSHIP between predictors and outcome. Therefore low R2 can be tolerated as far as my model is better than empty model. Moreover this is a highly clinical issue and it is impossible to include all relevant predictors. These most likely contribute much of the variance. My predictors are those which can be measured in reasonable manner. This fact highlights more the impossibility to construct a PREDICTIVE model.

Is it valid to draw any conclusions from my analysis with statistical findings stated above? And is there any basis to differentiate between predictive logistic regression versus logistic regression studying relationship?

• As long as the model assumptions are valid (you must check this), a low $R^2$ does not affect the validity of interpreting regression coefficients. – ved Jul 2 '14 at 14:59
• The use and interpretation of the Nagelkerke pseudo $R^2$ in logistic regression is discussed at stats.stackexchange.com/questions/3559. IMHO it's worth reading all the answers and comments, not just the most popular ones. – whuber Jul 2 '14 at 15:04
• Your post does not indicate that you have spent enough time studying logistic regression. It is not reasonable to ask others to do your work. – Frank Harrell Jul 2 '14 at 16:04
• @Frank Harrel: Certainly I was not asking others to do my work. I would like to assume I understand the basics of logistic regression. All the literature I have read about logistic regression have mentioned examples using logistic regression to construct models regarding outcome event. Therefore I was asking that does the logistic regression always have to produce predictive model since my model is doing poorly with it. – arkiaamu Jul 2 '14 at 16:36
• @Frank Harrel: I understand that low pseudo-R2 does not indicate that ORs obtained Are invalid. I am not that familiar with statistics to understand whether poor predictive ability is always equal to low pseudo-R2 in logistic regression. – arkiaamu Jul 2 '14 at 17:11