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

[Jeffrey Evans]

Good question.
 
They are similar
 
Compare models with nested fixed effects structures
Full model = lnsdlmaxd + lnadultssdld + lnsdlmaxd:lnadultssdld
Reduced model = lnsdlmaxd + lnadultssdld

AIC		R		SAS
Full		1150		1663.9
Reduced	1159		1673.4
-------------------------------
deltaAIC	9		9.5


________________________________

From: almost at gmail.com [mailto:almost at gmail.com] On Behalf Of Andy Fugard
Sent: Thursday, July 01, 2010 12:16 PM
To: Jeffrey Evans
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] different aic and LL in glmer(lme4) and
glimmix(SAS)?


Hi Jeff, 

Can't answer the question, but out of interest, what happens when you
compare nested models in R and SAS, e.g., models with and without the
lnsdlmaxd:lnadultssdld interaction?  Would be interesting to see the
log-likehood ratio (and maybe /change/ in AIC and BIC between the models).

Cheers,

Andy


On Thu, Jul 1, 2010 at 18:03, Jeffrey Evans <Jeffrey.Evans at dartmouth.edu>
wrote:


	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
	
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