How to use Custom-defined link function with poisson regression

I want to use Poisson regression on a model that looks like following:

    y = a * b^X1 * X2^c

Where a, b and c are constants.

I assume that I need to use 'glmfit' and make use of a link function, but I dont know how to write the code to get it right.

Answer 1

[Philip Caplan]

From my understanding of the question, it seems you would like to model the average, mu, of a response, y, to input variables, X, with a Poisson distribution. For a Poisson regression, the model is transformed with the log link:

log(mu) = beta1 +Z1*beta2 +Z2*beta3

where

beta1 = log(a)
beta2 = log(b)
beta3 = c
Z1    = X1
Z2    = log(X2)

with a, b, c, X1, X2 corresponding to your variables. You can then use "glmfit" (or "fitglm") with 'Distribution' as 'Poisson' and 'Link' as 'Log' with the above transformation to get the desired result. For more information, please see:

http://www.mathworks.com/help/stats/glmfit.html