Obtaining correct parameter estimates for loglinear mixed model with proc glimmix

[RobertF]

I'm running a loglinear multiple regression model on episode level hospital claims data with a random effect for the subject IDs.

My regression formula has the form:

E[ln(Length of Stay)] = Beta* X_matrix + Gamma*(Subject ID)

My code:

proc glimmix data=sasdata.RPT_CTBH15041_CTPAR_CY2015_2017;
  class membno provnam grpnum sexcod racecd svccls;
  model total_los = provnam grpnum memage sexcod racecd svccls / cl e solution dist=lognormal;
  random int / subject=membno;
  lsmeans provnam / e cl ilink diff=anom;
  ods output ParameterEstimates=ParmEst;
  ods output LSMeans=MeanDiff;
run;

Question: Since I specified a loglinear model, not a GLM, does the "ilink" option in the lsmeans statement return the correct parameter estimates and standard errors of the mean LOS (not the median LOS) for the final model?

[sld · Accepted solution]

When you choose DIST=LOGNORMAL, the GLIMMIX procedure models the logarithm of the response variable as a normal random variable, The GLIMMIX Procedure | Model options  Because the default link is the identity link, the ILINK option has no effect: the inverse-linked estimates are on the lognormal scale. You have to do the inverse-transformation yourself.