[R-sig-ME] different aic and LL in glmer(lme4) and glimmix(SAS)?

[Jeffrey Evans]

Hello All,
 
I have read several posts related to this previously, but haven't found any
resolution yet. When running the same GLMM in glmer and in SAS PROC GLIMMIX,
both programs return comparable parameter estimates, but wildly different
likelihoods and AIC values.

In SAS I specify use of the Laplace approximation. In R, I believe this is
the default (no?).

What's the difference, and [how] can I reproduce the SAS -2ll in glmer?

Thanks,
Jeff
 
\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/
> R_GLMM = glmer(cbind(SdlFinal, SdlMax-SdlFinal) ~ lnsdlmaxd*lnadultssdld +
 (1|ID),data=sdlPCAdat,family="binomial")
> R_GLMM
Generalized linear mixed model fit by the Laplace approximation 
Formula: cbind(SdlFinal, SdlMax - SdlFinal) ~ lnsdlmaxd * lnadultssdld +
(1 | ID) 
   Data: sdlPCAdat 
  AIC  BIC logLik deviance
 1150 1165   -570     1140        <------------------ this line!!
Random effects:
 Groups Name        Variance Std.Dev.
 ID     (Intercept) 1.2491   1.1176  
Number of obs: 144, groups: ID, 48
 
Fixed effects:
                       Estimate Std. Error z value Pr(>|z|)    
(Intercept)             4.56964    0.43148  10.591  < 2e-16 ***
lnsdlmaxd              -0.65936    0.05686 -11.595  < 2e-16 ***
lnadultssdld           -0.64534    0.15861  -4.069 4.73e-05 ***
lnsdlmaxd:lnadultssdld  0.07393    0.02166   3.414  0.00064 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
 
Correlation of Fixed Effects:
            (Intr) lnsdlm lndlts
lnsdlmaxd   -0.923              
lnadltssdld -0.461  0.479       
lnsdlmxd:ln  0.482 -0.508 -0.994

 
 \/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/
title 'SAS GLMM';
proc glimmix data=sdlPCAdat ic=pq noitprint method=laplace;
class site id;
model sdlfinal/sdlmax = lnsdlmaxd|lnadultssdld/ solution dist=binomial;
random ID /;
covtest glm/wald;
run;

//////////////////////////////////////////////////////////////////////

                      SAS GLMM      19:36 Wednesday, June 30, 2010 88

                   The GLIMMIX Procedure

            Data Set           WORK.SDLPCADAT
            Response Variable (Events)  SdlFinal
            Response Variable (Trials)  SdlMax
            Response Distribution     Binomial
            Link Function         Logit
            Variance Function       Default
            Variance Matrix        Not blocked
            Estimation Technique     Maximum Likelihood
            Likelihood Approximation   Laplace
            Degrees of Freedom Method   Containment



                  Optimization Information

             Optimization Technique    Dual Quasi-Newton
             Parameters in Optimization  5
             Lower Boundaries       1
             Upper Boundaries       0
             Fixed Effects         Not Profiled
             Starting From         GLM estimates

             Convergence criterion (GCONV=1E-8) satisfied.

                     Fit Statistics

               -2 Log Likelihood        1653.90  <------------------ this
line!!
               AIC (smaller is better)  1663.90
               AICC (smaller is better) 1664.33
               BIC (smaller is better)  1673.25
               CAIC (smaller is better) 1678.25
               HQIC (smaller is better) 1667.43


              Fit Statistics for Conditional Distribution

              -2 log L(SdlFinal | r. effects)   1436.44
              Pearson Chi-Square          908.07
              Pearson Chi-Square / DF        6.31


                 Covariance Parameter Estimates

            Cov         Standard     Z
            Parm  Estimate    Error   Value   Pr > Z

            ID    1.2491   0.2746   4.55   <.0001


                 Solutions for Fixed Effects

                              Standard
     Effect         Estimate    Error    DF  t Value  Pr > |t|

     Intercept           4.5696   0.4333    47    10.55  <.0001
     lnsdlmaxd          -0.6594   0.05717   93   -11.53  <.0001
     lnadultssdld       -0.6453   0.1593    93   -4.05   0.0001
     lnsdlmaxd*lnadultssd0.07394  0.02174   93    3.40   0.0010