title: Backtransforming response for plotting allEffects
body: <p>I have fitted a few models using <code>glmer</code> from the<code>lme4</code> package and did model selection with <code>MuMIn::dredge()</code> followed by model averaging. My response is frequency of occurrence of an animal in front of camera traps (continuous, number of photos per 100 hours of camera time); the predictors are minimum distances from a camera trap to landscape categories in meters, sometimes with an interaction with the day phase (day/night).</p>
  
  <p>The response shows Gamma-distribution, but to make the model work I had to transform my response by adding 1, as the Gamma distribution can't handle non-positive data and quite a few of my data points were zeros as shown in this histogram:</p>
  
  <p><img src="https://i.stack.imgur.com/aLxun.jpg" alt="in this histogram"> </p>
  
  <p>Also, I had to scale the predictors, otherwise I got convergence warnings like </p>
  
  <blockquote>
    <p>Model is nearly unidentifiable: large eigenvalue ratio - Rescale variables?</p>
  </blockquote>
  
  <p>I did this with <code>scale(..., center = TRUE)</code>. </p>
  
  <p>My model formula looks like this:</p>
  
  <pre><code>mod &lt;- glmer(Species_Frequency ~ scaled_Minimal_Distance1 + 
     scaled_Minimal_Distance2 + 
     (scaled_Minimal_Distance3 * Dayphase), 
  data = data, 
  na.action = na.fail, 
  family = Gamma(link = "log"), 
  control = glmerControl(optimizer = "bobyqa"))
  </code></pre>
  
  <p>Now I want to plot the results of <code>mod</code>  using <code>plot(allEffects(mod))</code>. </p>
  
  <p>For plotting, I am backscaling my predictors in the <code>allEffects</code>-object by accessing </p>
  
  <p><code>allEffects(mod)[["scaled_Minimal_Distance1"]][["x"]][["scaled_Minimal_Distance1"]]</code> and doing as shown <a href="https://stackoverflow.com/questions/10287545/backtransform-scale-for-plotting">Here</a>. I would also like to back-transform my response, to make the plot more understandable. Otherwise one would always have to keep in mind that 1 on the y-axis is actually 0, 2 is 1 etc. Can someone help me on how to do this, as I hit a roadblock and can't seem to figure it out myself. </p>
  
  <p>Thank you very much in advance. </p>