I have fitted a logistic regression model showing the probability of flight given distance to a disturbance event. My sample size is 140 observations of which 45 were observed to fly. Distance to the disturbance is the only significant predictor among many explored (biologically relevant interactions as well). Here is the out from the R console
Call: glm(formula = flight ~ approach_km, family = binomial) Deviance Residuals: Min 1Q Median 3Q Max -1.1233 -0.9317 -0.7460 1.3538 1.9400 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -0.1233 0.3438 -0.359 0.7199 approach_km -0.4530 0.2225 -2.036 0.0418 * Null deviance: 175.82 on 139 degrees of freedom Residual deviance: 171.30 on 138 degrees of freedom AIC: 175.3 Number of Fisher Scoring iterations: 4
Here is a plot of the predicted probabilities of flight.
As you can see there is no point along the distance continuum in which the probability of flight exceeds 0.5. Since this is the case the classification tables will never predict a flight (it predicts 67.9% correctly, ALL THE NO FLIGHT EVENTS!). McFadden's psuedo R2 = 0.026. I am happy with the fit of the model but I am under the belief that I need to include these types of goodness of fit statistics when publishing. I would rather show that within a certain range of the data, say 1 km, there is roughly a 0.40 probability of flight. If there were 20 observations associated with this estimate there would be 8 flight events and 12 non-flight events. Is there a way to show this? How can I write up these results to show my findings without referee's balking at my lack of fit tests? Any thoughts or references would be greatly appreciated.
UPDATE: In response to @Drew75.
Here is the ROC curve. Does this mean that the model does not perform as well I has thought?