Between sleep deprivation and it having been years since my last stats class, I cannot wrap my mind around what should be an easy problem of curve fitting. In school I did have econometrics, but now I'm not quite figuring out how to set this up. (Yes, if you don't use what you learn you can forget it all. sigh.)
Can the following problem be done as a weighted least squares? And if not, in general can I do what I need to do in Excel (with stats add-ins)? Most stand-alone stats programs are expensive (although some have free trials). I've got data on the adoption rate of technologies by year and country. I want to estimate the adoption curve for certain countries, and then forecast out just a few years (again, by country). The literature on technology diffusion and the raw data itself suggest using a logistic curve with a ceiling: Penetration at time t Pt = L / (1 + a exp(-bt)) L is the ceiling, a is the timing variable, b is the slope. For each country I have the penetration rate (per 100 or 1000 people) of the technology for each year since the technology was introduced. The probability of success here is this rate which is binary at the individual level-- does a person have a computer (or internet access or a cellular phone) or not? I have the population growth rate, and for now will assume that the max penetration (ceiling) is a fixed % of total population. As this is more of an exploratory / qualitative look at the data I'm not using any other explanatory variables, just time. In many of the countries the technology is mature-- the growth rate is past its the inflection point-- but none have reached their ceilings. So essentially this is a logit with pre grouped data, or is it? My Gujarati textbook has an example of estimating a and b for a logit with grouped data using WLS. For each Xi, one obtains the logit LN(Pi/(1-Pi) = A + B Xi + Ui. One then multiplies both sides by the square root of the weight: Wi = Ni(Pi*)(1-Pi*) where Ni = samples at X=i, Pi* = relative frequency at X=i to account for heteroscedasticity. I can understand how this works when you are grouping individual data. By with my data there isn't a Ni per se: this is population data already. Can I still uses WLS- what would be the weight? (As a side question, can't the inflection point in the change of the growth rate be used to estimate total time to full penetration, given the assumptions of logistic curves?) And if not WLS, how should I think about approaching this data? This sort of curve fitting + slight forecasting should be easy, if I could just see over the mental block I've got about it. Thank you. Catharine . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
