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I am developing a predictive model to apply to raster layers for land cover classification. So, I have a thematic category that is classified as agriculture but an accuracy assessment indicates commission error, savanna incorrectly classified as ag. I randomly sampled the category and have 177 observations of ag and savanna. I extracted reflectance values from 6 predictive raster layers at the observation locations. So that's my dataset. I selected 4 variables that all significantly contribute to the model. Percentage correct for selected and unselected cases are approx 90% and Nagelkerke R square is 0.880. Odds ratios for the predictors are between .599 and 1.127 but the odds ratio for the constant is very high, 564830031.5. The predictors cannot all take the value of zero. I'm not sure what to make of the odds ratio. Any insight would be greatly appreciated.

Cheers

Sean Sweeney
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  • Very high odds ratio is probably overfitting, or perfect separation in the data. You can find some information here: http://stats.stackexchange.com/questions/11109/how-to-deal-with-perfect-separation-in-logistic-regression/68917#68917 – kjetil b halvorsen Jan 16 '15 at 18:43
  • If it's only the odds ratio for the constant, this probably isn't separation, but rather most observations are in the positive class. – gung - Reinstate Monica Jan 16 '15 at 18:47
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    The discussion of odds and odds ratios at http://stats.stackexchange.com/questions/133623 might help you interpret this. – whuber Jan 16 '15 at 20:38

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The exponentiated coefficient of the constant is not an odds ratio but an odds, to be precise: the odds "success" when all predictors are 0. You say that some of your predictors cannot be 0, so that will be an extrapolation.

Say one of those predictors is year, so the constant refers to ground cover in the year 0, which is probably way way way outside the range of your data. In that case the fact that you get weird numbers is not surprising and not a problem. Personally, I still prefer to center those variables at some meaningful value within the range of your data. Say your earliest observation was in 1990, then I would just subtract 1990 from year. That way the value 0 refers to 1990, and your constant refers to the odds of success in 1990. Strictly speaking this is not necessary, but I find it easier to spot errors (I make lots of those, the trick is to find them before I publish...) if I make sure all coefficients are interpretable.

Maarten Buis
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