6: Random Effects and Introduction to Mixed Models

Overview Section

So far in our discussion of treatment designs, we have assumed (though unstated) that the treatment levels were chosen intentionally by the researcher dictated by their specific interests. In this situation, the scope of inference is limited to the specific (or fixed) treatment levels used in the study. However in practice, this is not always the case. Sometimes treatment levels may be a (random) sample of possible levels, and the scope of inference should be to a larger population of all possible levels.

If it is clear that the researcher is interested in comparing specific, chosen levels of treatment, that treatment is called a fixed effect. On the other hand, if the levels of the treatment are a sample from a larger population of possible levels, then the treatment is called a random effect.

Objectives

Upon completion of this lesson, you should be able to:

  1. Extend the treatment design to include random effects.
  2. Understand the basic concepts of random-effects models.
  3. Calculate and interpret the intraclass correlation coefficient.
  4. Combining fixed and random effects in the mixed model. 
  5. Work with mixed models that include both fixed and random effects.