title: rank deficiency warning mixed model lmer
body: <p>I have a dataset with 142 data entries: 121 individuals measured on two occasions (two years, before and after treatment, Year = 0 or 1), in the second year 46 individuals were in treated plots and the rest were in control plots (treatment = 0 or 1). Here's some example data:</p>
  
  <pre><code>ID &lt;- c("480", "480", "620", "620","712","712")
  Year &lt;- c("0", "1", "0", "1","0", "1")
  Plot &lt;- c("14", "14", "13", "13","20","20")
  Treat &lt;- c("0", "0", "0", "1", "0", "1")
  Exp &lt;- c("31", "43", "44", "36", "29", "71")
  ExpSqrt &lt;- c("5.567764", "6.557439", "6.633250", "6.000000", "5.385165", "8.426150")
  
  Winter &lt;- data.frame(ID, Year, Plot, Treat,
                    Exp, ExpSqrt,
                    stringsAsFactors = TRUE) 
  </code></pre>
  
  <p>Plots and individuals are random factors and I'm trying to fit a mixed model to determine the effect of Year, Treatment and the interaction between them:</p>
  
  <pre><code>model_Exp &lt;- lmer(ExpSqrt~Year+Treat+Year*Treat+(1|ID)+(1|Plot),data=Winter)
  </code></pre>
  
  <p>but I keep getting the warning message:</p>
  
  <pre><code>"fixed-effect model matrix is rank deficient so dropping 1 column / coefficient"
  </code></pre>
  
  <p>This removes the interaction. </p>
  
  <p>I have no NA values in my dataset and Exp is always positive but I have sqrt transformed this as the distribution was non-normal. It's not a particularly small dataset, I have tried the using the function findLinearCombos from the caret package but it returns no result.</p>
  
  <p>My understanding is that there is some problem because treatment 1 only occurs under condition year=1 (but not in all instances: Year=1 also contains 75 control individuals).</p>
  
  <p>I am not sure a) how or if this can be resolved?
  or b) if it can't be resolved how to interpret this?</p>
  
  <p>I have read some responses about this warning but have done everything I found suggested to resolve it, I've also read a bit about the Hauck-Donner effect, but I'm not sure if this is my problem and being relatively new to stats I can't admit I entirely understand it.</p>