# How to check for heterogeneity over time and location for rate data

I have data that consists of different locations, with repeated observations over time, of counts (and a denominator to make a rate). eg

CENTRE -- YEAR ---- DENOMINATOR -- CASES

a    ---- 1995 ---- 2531 --------  8

a    ---- 1996 ---- 2364 --------  12

a    ---- 1997 ---- 1264 --------  7

b    ---- 1995 ---- 5012 --------- 20

...

...


I want to know if there is a difference across centres (a-z) and/or over time. I am not entirely sure how to do this, but my thought is to fit a negative binomial model (as the variance is somewhat larger than the mean). with an offset of the ln(denominator)? In R this might look like

nbmodyear = glm.nb(CASES ~ YEAR + offset(log(DENOMINATOR)), data)


and

nbmodcentre = glm.nb(CASES ~ CENTRE + offset(log(DENOMINATOR)), data)


and having centre as factor. If this is a reasonable method, would this be enough to tell me if there is heterogeneity between year or centre location? If not, can anyone advise what method I should use? Thank you.