Modelling Repeated Measures with Poisson Distribution

[doctortimi]

Hello SAS Community,

I am trying to model a count event that occurs in different states over time. I believe the appropriate model is a generalized linear mixed model with Poisson distribution (using proc mixed or glimmix). Below is an arbitrary dataset and the code I wrote. I just need input on the best way to model this information. Thank you!

Data

state year count_event population
AL 2010 2 20010
AL 2011 4 20399
AL 2012 8 20589
AR 2010 5 40322
AR 2012 8 43222
CA 2010 19 64032
CA 2011 32 68004
CA 2012 34 69333

Code

proc glimmix data = dsn;
class year state;
model count_event = year state / dist = poisson solution offset = newvar; /*Note: newvar = log(population)*/
random int / subject = state;
run;

[StatDave]

Your data appears to be binomial with observed probabilities event_count/population. A random effects model in PROC GLIMMIX is one modeling approach you can use. Another is a GEE model in PROC GEE or PROC GENMOD. Here is an example using an AR correlation structure, but you could select a different one.

proc genmod data = dsn;
class year state;
model count_event/population = year state / dist = binomial;
repeated state / type=ar within=year;
run;

[doctortimi]

Thank you for your response, StatDave_sas. So with your approach, there is no need for an offset? 

[StatDave]

Right...  "/population" on the response side takes care of it. 

[doctortimi · Accepted solution]

Thank you for the clarification. I just ran this code. Added the "repeated subject = state" portion.

proc genmod data = dsn1;
class dyr state;
model cohort_sample_size/population_size = dyr state / dist = binomial type3;
repeated subject = state /type = ar within = dyr;
run;