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Random Effects Model

A factor in an experiment can be described by the way in which factor levels are chosen for inclusion in the experiment:

• Fixed factor. The experiment includes all factor levels about which inferences are to be made.
• Random factor. The experiment includes a random sample of levels from a much bigger population of factor levels.

Experiments can be described by the presence or absence of fixed or random factors:

• Fixed-effects model. All of the factors in the experiment are fixed.
• Random-effects model. All of the factors in the experiment are random.
• Mixed model. At least one factor in the experiment is fixed, and at least one factor is random

The use of fixed factors versus random factors has implications for how experimental results are interpreted. With a fixed factor, results apply only to selected factor levels. With a random factor, results apply to every factor level.

For example, consider the blood pressure experiment described above. Suppose the experimenter only wanted to test the effect of three particular dosage levels - 0 mg, 50 mg, and 100 mg. He would include those dosage levels in the experiment, and any research conclusions would apply to only those particular dosage levels. This would be an example of a fixed-effects model.

On the other hand, suppose the experimenter wanted to test the effect of any dosage level. Since it is not practical to test every dosage level, the experimenter might choose three dosage levels at random from the population of possible dosage levels. Any research conclusions would apply not only to the selected dosage levels, but also to other dosage levels that were not included explicitly in the experiment. This would be an example of a random-effects model.

See also:

Experimental Design and ANOVA