Assessing sources of variation with variance components

Variance components assess the amount of variation in the response because of random factors. To analyze a model with random factors, you usually use Fit Mixed Effects Model. While Fit General Linear Model also estimates variance components for random factors, Fit Mixed Effects Model provides better estimates when the designs are unbalanced. Fit General Linear Model and Fit Mixed Effects Model calculate the same variance components for balanced data.

What is a random factor?

Random factors have levels that are selected at random; whereas fixed factors have levels that are the only levels of interest. For example, you do a study on the effect of two levels of pressure on output measured by randomly chosen operators. Pressure is fixed (2 levels); and operator is random. The variance components output lists the estimated variance for the operator and error term. For more information on fixed and random factors, go to What is the difference between fixed and random factors?.

Interpret a negative variance component

The calculations for Fit General Linear Model allow negative variance components. In general, use Fit Mixed Effects Model instead of Fit General Linear Model when the model includes random factors. If you use Fit General Linear Model and get negative variance components, the following are possible ways to deal with the negative estimates:
  • Accept the estimate as evidence of a true value of zero and use zero as the estimate, recognizing that the estimator will no longer be unbiased.
  • Retain the negative estimate, recognizing that subsequent calculations using the results might not make much sense.
  • Interpret that the negative component estimate indicates an incorrect statistical model.
  • Collect more data and analyze them separately or in conjunction with the existing data and hope that increased information will yield positive estimates.