Proc Genmod offset vs. weight

[mcs]

I'd like to better understand the OFFSET and WEIGHT options in PROC GENMOD Poisson regression.  I'm using SAS/STAT 13.2.

Say I have a dataset with y observed counts, x1-x10 predictors, t time observed, and log_t.  What's the difference between the following two models?

proc genmod;
  model y = x1-x10 / d=p offset=log_t;

proc genmod;
  model y = x1-x10 / d=p;
  weight t;

Also, are there any differences when data is split across multiple observations, i.e., do I get the same result from fitting

  y  x1-x10  t

and

  y1  x1-x10 t1

  y2  x1-x10 t2

where y = y1 + y2, t = t1 + t2, and x1-x10 are the same?

[Ksharp]

offset variable will fix its parameter at 1 always. It is usually taken as a measure unit. For example:
y=1 , log_t=2  means in two hours, event occur once.
y=2,  log_t=8 means in eight hours, event occur twice.

these two obs 's time interval is different, so you need take log_t as a offset variable(its parameter=1)


weight variable means this obs is measured more accurate and exactly .
Check Rick's blog , there are several blog have talked about it.

For your last question, I don't think you gonna get the same result.

[JacobSimonsen · Accepted solution]

As @Ksharp says, offset and weight are two different things. Nevertheless, in Poisson regression and with "log" as link function, you can use weight or offset as you suggested to fit exactly same model.

It doesnt matter if you split one observation into two observations, if just the original time value equals the sum of the two new time values, and both new timevalues are greater than zero. Though, the fit statistics will give some different results. - This is not a problem since in such Poisson regression models the fit statistics are meaningless anyway.