I am trying to implement the Generalized Bass Model (GBM) in R with price as a decision variable. Price is decreasing and product adoption is increasing through the years in my dataset. However, I am finding the price sensitivity (alpha) sign as positive which is strange. My scaling function is the following:

T + alpha * ln(P(t)/P(0))

where T is is number of years since the initial adoption; .

Then, I am implementing the GBM as follows:

(1 - exp(-(p + q) * (T + alpha * ln(P(t)/P(0)))))/(1 + q / p *exp(- (p + q) * (T + alpha * ln(P(t)/P(0)))))

Am I missing something?

Thanks in advance.