# Reference category and prediction

I am struggling a little bit at the moment with a question related to logistic regression. I have a model that predicts the occurrence of animal based on land cover with reference to forest. I am not grasping the concept of a reference class and struggle to extrapolate the model onto a new area. Any explanations or guidance towards papers, lecture notes etc would be highly appreciated.

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Maybe you can precise your problem? –  mbq Jul 28 '10 at 12:44

I'm not sure I exactly understand your question, but I'm assuming your confusion involves a categorical predictor in your model. When it comes to continuous variables in a regression, the coefficients for each predictor are weights for the value of the predictor to produce the predicted y value:e.g. y = 2*x

However, with a categorical variable, weights are meaningless. What does 2*Male mean, or in your case, 2*forest.

So, the coefficients returned for levels of categorical variables represent how different they are from some reference level. In experimental settings, your reference level would be the control group, and then you would get a coefficient for every treatment group, indicating what the size of the effect of each treatment was.

In my own research, and I'm guessing in yours too, there isn't always a meaningful control category for the reference level. So, what I'd do is set the reference level to whatever category would make exposition of the comparisons easiest. Or, you could use different contrasts, like sum contrasts, but those have their own difficulties especially if you have sparse data for one or more categories.

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Thannks a lot for this very detailed answer. It does make perfect sense to me. If I have a model know. For example:

y = - 2.8 - 1.2 * urban - 3 * forest


with the reference category grassland and I would like to predict the model for a new environment.

If I have a point with grassland, the probability of y would be like:

y = 1 / (1 + exp(2.8))


Is that right?

And lets say for a point in in a forest

y = 1 / (1+ exp(-(-2.8 - 3*1)))


Thanks a lot again

Mike

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Didn't see this for a while. Users don't get notifications about new answers to questions they've contributed answers to themselves. If you leave a followup as a comment instead, you might get an additional response sooner. –  JoFrhwld Aug 4 '10 at 19:18
Actually, P(y | grassland) would be exp(-2.8) / (1 + exp(-2.8)) A point in the forest would be exp(-2.8 - 3) / (1 + exp(-2.8 - 3)) However, you could estimate those probabilities without doing a logistic regression. What would be more interesting would be to look at exp(-3), or 1/exp(-3). This says that an animal is 20x more likely on grassland than forest, and if the p-value is <0.05, then that difference is significant. –  JoFrhwld Aug 4 '10 at 19:23