The variance components estimated by PROC VARCOMP should theoretically be nonnegative because they are assumed to represent the variance of a random variable. Nevertheless, when you are using METHOD=MIVQUE0, TYPE1, or GRR, some estimates of variance components might become negative. (Due to the nature of the algorithms used for METHOD=ML and METHOD=REML, negative estimates are constrained to zero.) These negative estimates might arise for a variety of reasons:

• The variability in your data might be large enough to produce a negative estimate, even though the true value of the variance component is positive.

• Your data might contain outliers. Refer to Hocking (1983) for a graphical technique for detecting outliers in variance components models by using the SAS System.

• A different model for interpreting your data might be appropriate. Under some statistical models for variance components analysis, negative estimates are an indication that observations in your data are negatively correlated. Refer to Hocking (1984) for further information about these models.

Assuming you are satisfied that the model that PROC VARCOMP is using is appropriate for your data, it is common practice to treat negative variance components as if they are zero.