title: How to unscale the coefficients from an lmer()-model fitted with a scaled response
body: <p>I fitted a model in <code>R</code> with the <code>lmer()</code>-function from the <code>lme4</code> package. I scaled the dependent variable:</p>
  
  <pre><code>    mod &lt;- lmer(scale(Y)
                  ~ X
                  + (X | Z),
                  data = df,
                  REML = FALSE)
  </code></pre>
  
  <p>I look at the fixed-effect coefficients with <code>fixef(mod)</code>:</p>
  
  <pre><code>    &gt; fixef(mod)
      (Intercept)      X1          X2         X3           X4 
       0.08577525 -0.16450047 -0.15040043 -0.25380073  0.02350007
  </code></pre>
  
  <p>It is quite easy to calculate the means by hand from the fixed-effects coefficients. However, I want them to be unscaled and I am unsure how to do this exactly. I am aware that scaling means substracting the mean from every <code>Y</code> and deviding by the standard deviation. But both, mean and standard deviation, were calculated from the original data. Can I simply reverse this process after I fitted an <code>lmer()</code>-model by using the mean and standard deviation of the original data?</p>
  
  <p>Thanks for any help!</p>
  
  <hr>
  
  <p>Update: The way I presented the model above seems to imply that the dependent variable is scaled by taking the mean over all responses and dividing by the standard deviation of all the responses. Usually, it is done differently. Rather than taking the overall mean and standard deviation the responses are standardized per subject by using the mean and standard deviation of the responses of that subject. (This is odd in an <code>lmer()</code> I think as the random intercept should take care of that... Not to mention the fact that we are talking about calculating means on an ordinal scale...) The problem however stays the same: Once I fitted such a model, is there a clean way to rescale the coefficients of the fitted model?</p>