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I have an area which is divided into polygons of different sizes. Each polygon has the same associated features/predictors and I know whether something occurs within the polygon or not. If something occurs in the polygon I have a number between 1 ... n which indicates the ‘amount of evidence’.

I am trying to use logistic regression (or GAMs later on) to model the occurrence probability given a polygon’s features $(X_1, ..., X_n)$. At the moment I do not adjust for polygon size and ‘amount of evidence’ so I have just a vector $(X_1, ..., X_n)$ plus a zero or one value for the response.

I am just wondering whether it may be useful to adjust the data (somehow?) to account of the different sizes of the polygons and the amount of evidence. Perhaps one should repeat the data rows more often depending on the size and the amount of evidence?

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What exactly does "amount of evidence" mean? It sounds like this question cannot adequately be answered without knowing something more about the data-generation process; specifically, how the outcomes may be associated with geometric features of the polygons and with the "amount of evidence" value. – whuber♦ Mar 1 '12 at 18:41
Thanks. Basically a program has determined the number of papers which indicate whether something occurs in the polygon. Number of papers indicate strength of evidence. – csetzkorn Mar 2 '12 at 7:27
Strength of evidence...or merely amount of interest? Or size of polygon? To make progress, it would help to have a quantitative model of what this number implies. For instance, if each "paper" represents an attempt to identify whether "something occurs" and typically a paper can fail to identify an occurrence with probability $p$, then $n$ independent papers will fail to identify the occurrence with probability $1-(1-p)^n$. (I bet nobody's software combines weights this way!) Such a model would indicate how to estimate your parameters. – whuber♦ Mar 2 '12 at 14:21
Thanks. This all sounds very interesting - I will try to digest it. Yes it could also mean amount of interest and papers are not necessarily independent as they may be written by the same (co)authors etc. – csetzkorn Mar 3 '12 at 7:10

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