title: Strange glmulti results: Why are interaction variables from the candidate model dropped/not included?
body: <p>I have been using <code>glmulti</code> to obtain model averaged estimates and relative importance values for my variables of interest. In running <code>glmulti</code> I specified a candidate model for which all variables and interactions were included based on a priori knowledge (see code below). </p>
  
  <p>After running the <code>glmutli</code> model I studied the results by using the functions <code>summary()</code> and <code>weightable()</code>. There seem to be a number of strange things going on with the results which I do not understand. </p>
  
  <p>First of all, when I run my candidate model with <code>lme4</code> <code>glmer()</code> function I obtain an AIC value of 2086. In the glmulti output this candidate model (with exactly the same formula) has a lower AIC value (2107), as a result of which it appears at position 8 out of 26 in the list of all potential models (as obtained through the weigtable() function). </p>
  
  <p>What seems to be causing this problem is that the logArea:Habitat interaction is  dropped from the candidate model, despite <code>level=2</code> being specified. The function <code>summary(output_new@objects[[8]])</code>  provides a different formula (without the logArea:Habitat interaction variable) compared to the formula provided through <code>weightable()</code>. This explains why the candidate model AIC value is not the same as obtained through <code>lme4</code>, but I do not understand why the interaction variables logArea:Habitat is missing from the formula. The same is happening for other possible models. It seems that for all models with 2 or more interactions, one interaction is dropped. </p>
  
  <p>Does anyone have an explanation for what is going on? Any help would be much appreciated!</p>
  
  <p>Best,
  Robert</p>
  
  <p>Note: I have created a subset of my data (<a href="https://drive.google.com/open?id=1rc0Gkp7TPdnhW6Bw87FskL5SSNp21qxl" rel="nofollow noreferrer">https://drive.google.com/open?id=1rc0Gkp7TPdnhW6Bw87FskL5SSNp21qxl</a>) and simplified the candidate model by removing variables in order to decrease model run time. (The problem remains the same)</p>
  
  <pre><code>     newdat &lt;- Data_ommited2[, c("Presabs","logBodymass", "logIsolation", "Matrix", "logArea", "Protection","Migration", "Habitat", "Guild", "Study","Species", "SpeciesStudy")] 
  
       glmer.glmulti &lt;- function (formula, data, random, ...) {
       glmer(paste(deparse(formula), random), data = data, family=binomial(link="logit"),contrasts=list(Matrix=contr.sum, Habitat=contr.treatment, Protection=contr.treatment, Guild=contr.sum),glmerControl(optimizer="bobyqa", optCtrl = list(maxfun = 100000)))
       }
  
     output_new &lt;- glmulti(y = Presabs ~  Matrix  + logArea*Protection + logArea*Habitat,
      data = sampledata,
      random = '+(1|Study)+(1|Species)+(1|SpeciesStudy)',
      family = binomial,
      method = 'h',
      level=2,
      marginality=TRUE,
      crit = 'aic',
      fitfunc = glmer.glmulti,
      confsetsize = 26)
  
      print(output_new)
  
      summary(output_new)
  
      weightable(output_new)
  </code></pre>