title: Extract reference levels from linear mixed model
body: <p>How do I extract the combination of reference levels for fixed factors in <code>lmer()</code> ? </p>
  
  <p>Let's assume we have model: </p>
  
  <pre><code>fx &lt;- lmer(RT ~ size + response + noise:size + noise:prime
                   + (1+noise|subject) + (1+noise|picture),
                   data=df, REML=FALSE)
  </code></pre>
  
  <p>Levels in <code>df</code>:</p>
  
  <pre><code>levels(size) = c('1', '2')
  levels(noise) = c('0', '4')
  levels(prime) = c('yes', 'incorr', 'no')
  levels(response) = c('left', 'up', 'right', 'down')
  levels(picture) = rep(1:7)
  levels(subject) = rep(1:20)
  </code></pre>
  
  <p>In model's summary we see:</p>
  
  <pre><code>Fixed effects:
                                 Estimate Std. Error t value
  (Intercept)                 381.409     38.675   9.862
  size_2                      -46.914     14.814  -3.167
  responce_up                  60.028     17.633   3.404
  responce_right                5.640     16.764   0.336
  responce_down                87.455     17.073   5.123
  size_1:noise_4               91.443     38.346   2.385
  size_2:noise_4              141.050     37.765   3.735
  noise_0:prime_incorr          4.758     22.278   0.214
  noise_4:prime_incorr         72.849     35.988   2.024
  noise_0:prime_no             16.736     22.407   0.747
  noise_4:prime_no             90.058     34.427   2.616
  </code></pre>
  
  <p>Now we need to count what effect size every fixed factor causes if it included to model. </p>
  
  <p>If I understand correctly <code>(Intercept)</code> estimates target variable based on levels of fixed effects chosen in alphabetical order. 
  It is quite easy to guess this levels if we have only simple fixed factors. But what <code>(Intercept)</code> contains if we also use interactions like <code>size:nose</code> in a model?</p>