Autoregressive distributed lag model with different duration of lag

#1
Hi,
I have observations for individuals at two points in times. I want to model the probability of smoking at time t, giving characteristics at time t-a, so the model looks like this:
Smokingt = B0 + B1*Smokingt-a + BiXi

The problem is that for some individuals, the duration "a" between two observations is 2 years, for other it's 3 years and for some others 4.
Since I want a model that can predict the annual probability to stop smoking (or to start smoking for non smokers), I am thus wondering what should I do. Can I just add in the model a linear regressor for the number of years between two observations? The model would thus be:

Smokingt = B0 + B1*Smokingt-a B2*a + BiXi
 

noetsi

Fortran must die
#2
I think that any software is going to have standardized lag for everyone. I don't think there is any way to tell it that a lag is two years [two periods] for one individual and three years for another. If you specify t+2 2 is going to be two periods [be the period years months or whatever].

Having said that I have never seen this issue raised in time series. They talk about generic lags.
 

hlsmith

Not a robit
#3
Welcome to the forum @Demographer12

Yes, entering a time variable seems like the best option.

Side note, If you had multiple measurements and everyone had obs taken at the approximate same time, which you don't, you can create a power structure weight to account for different lengths of time, (follow-up: 1 month, 3 months, 6 months, 12 months, given everyone has the same followup. I think I have seen this label as something like toepes (sp?).