I have a problem related to measuring likelihood between
-an observed presence absence dataset (containing 0 or 1)
-a predicted simulation matrix of the same dimensions (containing values from 0
to 1)
This must be a common problem but I am struggling to find the answer in the
literature.
Within the simulation model I have a parameter 'm' which I can alter to find
the best fit (maximum likelihood).
Currently I just use a 'sum of squares of difference' to measure likelihood.
ie likelihood = sum (obs-pred)^2
This is then very easy to find (using numerical optimisation techniques) the
value of 'm' which gives my maximum likelihood (least sum of squares)
However I do not think my likelihood function is the correct one to be using
for this purpose.
Firstly, if sum of squares is the correct method, maybe I should be taking the
square root of the likelihood (makes no difference) and possibly the 'mean'
values of the datasets may need to be included in my calculatons.
However, sum of squares suggests my data are normally distributed (which it is
clearly not)
Obs (boolean O or 1)
Pred (beta O to 1)
Difference (beta -1 to 1)
My guess is that I should be using a beta (or uniform) defined likelihood
measure.
Or maybe just a simple transformation.
Any help greatly appreciated
Mark
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