[R-sig-ME] Binominal GLMM in Lmer

[Ben Bolker]

Claire M. Sheridan wrote:
>   
> I am new to the use of R and to GLMM's. I am not sure how to interpret my
> results. I first modeled my most complex model with all of my hypothesized
> fixed effects(print out below). From my Pr(>|z|) values I feel that I should
> be able to say that none of the fixed effects significantly affects
> presence. I also ran models in which I took out one fixed effect at a time
> and compare using ANOVA. 

  Do you mean anova()? (This runs a likelihood ratio test, confusingly
enough.)

I also started with more basic models (1 fixed
> effect) 

  with no random effect?  or do you mean 1 fixed effect + random effects?

and compared it to a model with only random effects (with the #1 in
> place of where the fixed effect would be). Using ANOVA I also compared those
> models. What is confusing to me is that I sometimes get lower AIC values and
> significant p-values for the ANOVA with the model with a single fixed effect
> vs. a model with no fixed effect. I was expecting based on the Pr(>|z|)
> values that I would get lower AIC values for the no fixed effects model. For
> any variation that I run on the model (1-7 fixed effects), the Pr(>|z|)
> values are always >0.05. Can someone help explain this to me? I'm really
> sorry if this something that has already been addressed, but I couldn't find
> anything on the message boards similar to my question. 

  Which other variables are included matters in GLMMs (it matters in any
  modeling framework where the effects are not perfectly orthogonal,
which includes most regression models, any nonlinear model, and GLMMs).
 It is not shocking that you find some cases where adding some variables
to the simplest/null model improves prediction, but adding the same
variables to a model with the other 6 variables present does not.  In
addition, AIC and Likelihood ratio test p-values are completely
different frameworks, my fairly strong advice is to pick one or the
other & not to use them in the same analysis.

  These issues are fairly generic to modeling/model selection problems
as soon as one leaves the balanced/orthogonal/designed experiment case.
Zuur et al (mixed models book), Harrell (applied regression modeling)
are both recommended.  Others may have other recommendations.

> print(m1<-lmer(Presence ~FixedEffect1 + FixedEffect2 + FixedEffect3 +
> FixedEffect4 + FixedEffect5 + FixedEffect6 + FixedEffect7 + (1|Site) +
> (1|Year), family=binomial, REML=FALSE))
> 
> Generalized linear mixed model fit by the Laplace approximation 
> 
> Formula: Presence ~FixedEffect1 + FixedEffect2 + FixedEffect3 + FixedEffect4
> + FixedEffect5 + FixedEffect6 + FixedEffect7  + (1 | Site) + (1 | Year) 
> 
>   AIC   BIC logLik deviance
> 
>  88.9 110.8 -34.45     68.9
> 
> Random effects:
> 
>  Groups Name        Variance Std.Dev.
>  Site   (Intercept)  0        0      
>  Year   (Intercept)  0        0      
> 
> Number of obs: 66, groups: Site, 4; Year, 2

   The zero variances here suggest fairly strongly that you're
overfitting.  It's hard to fit a random-effects term with only 4 sites,
and even harder with only 2 years (e.g. search for "Are there enough
levels" in <http://glmm.wikidot.com/faq>)

> Fixed effects:
> 
>                   Estimate Std. Error z value Pr(>|z|)  
> 
> (Intercept)     -17.793834   9.299257  -1.914   0.0557 . 
> FixedEffect1        0.164940   0.175818   0.938   0.3482  
> FixedEffect2         0.068806   0.057713   1.192   0.2332  
> FixedEffect3      -0.004817   0.004070  -1.183   0.2367  
> FixedEffect4          0.375625   0.399966   0.939   0.3477  
> FixedEffect5          -0.112683   0.658858  -0.171   0.8642  
> FixedEffect6  2.672537   2.158679   1.238   0.2157  
> FixedEffect7       -0.175103   0.132223  -1.324   0.1854  
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-- 
Ben Bolker
Associate professor, Biology Dep't, Univ. of Florida
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