Negative Binomial Regression with Time Variable

#1
I am running a regression in R and I am confused. I am trying to understand what factors affect debate participation in parliament and how this has changed over time. I want to run a regression in R, with a count variable as the dependent variable (the number of times each member has participated in debate in a specific policy area per year) and 4 explanatory variables - sex of the member (dummy variable), political party of the member (dummy variables for each of the 3 main parties), whether or not they hold a leadership position in their party (dummy variable) and the number of years since they were elected (categorical variable).

I want to run a regression analysis over 11 years (2000 - 2010) to understand if changes have taken place over time. I have another categorical variable for the years. I was going to do a negative binomial regression (as my dependent variable is a count variable), but I am not sure how to analyse how the debate participation has changed over time. I don't think I can just include my year variable as an explanatory variable? Should I do a two step regression? Any help is much appreciated.
 
#2
I think the canonical answer would be GEE (generalized estimating equation) to account for the correlations across time. The thing is, you have a categorical predictor measured at each time point as im reedin it? Well I think things are gunna work out alot better if there is some functional relationship associated with time (ie y = m*time + b or something) rather than treating tie as categorical. Withouth this, my 'confounding' stats sense is being triggered.