title: Comparison of mixed-effects model and a combination of two mixed-effects models
body: <p>I hope this question fits into here because it is not only about a coding problem, but also digs into some theoretical questions concerning linear mixed-effects models. Assume the linear mixed-effects model:</p>
  <pre><code>model1 &lt;- lmer(RT ~ word_duration + RT_prev + trial + stem + 
                         (1|Subject) + (1|Word), data = df_whole)
  </code></pre>
  <p>I can compute its AIC score and use it to compare the model with other models. In my case, I have another model:</p>
  <pre><code>model2 &lt;- lmer(RT ~ word_duration + RT_prev + trial + form + 
                         (1|Subject) + (1|Word), data = df_subset)
  </code></pre>
  <p>The predictions of my <code>model3</code> are the minimum of the predictions of model1 and model2 = <code>min[model1, model2]</code>. I would like to compare <code>model3</code> with <code>model1</code> and I know that I could use the mean square error (MSE) for instance. However, the MSE does not take into account that <code>model3</code> is a combination of two models and a difference in MSE might not justify the increased complexity. So can I compute a measurement that takes a model's complexity into account such as the AIC in order to compare the models?</p>
  <p>Note: <code>model1</code> is trained on all the data, <code>model2</code> only for a subset. This is done because I assume the items in the subset might be processed differently. Thus, for some items <code>stem</code> and for other <code>form</code> is the better predictor (as discussed in the literature).</p>