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

[Jeffrey Evans]

I see. Thank you for the clarification.  


I did just try lme4 on a[n expanded] binary version of the same data, but
the numbers are still not coming out the same as in SAS.

No matter. The deltaAIC values are the same, so I am content that they are
doing similar things.

Cheers,
Jeff


-----Original Message-----
From: dmbates at gmail.com [mailto:dmbates at gmail.com] On Behalf Of Douglas
Bates
Sent: Thursday, July 01, 2010 12:24 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)?

On Thu, Jul 1, 2010 at 11:03 AM, 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?

The difference is probably due to the way that the deviance is defined for
the binomial family in R.  A glm family object is a list of functions and
expressions.  One of the functions, called "dev.resids"
has arguments y, mu and weights.  You can specify the response for a
binomial family as the 0/1 responses or as a matrix with two columns as you
did here.  When you use the two column specification the response y is
transformed to the fraction of successes and the number of cases is
incorporated in the weights.  It turns out that this is all the information
necessary for obtaining the mle's of the parameters but it does not give the
same deviance as you would get by listing the 0/1 responses.

I'll write an example using the cbpp data from the lme4 package.
> 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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