Estimation of Variance Components - Singular Hessian Matrix at Point of Conversion in Maximum Likelihood Estimation

In some cases you may see this message at the top of the spreadsheet reporting the estimates of the variance components; usually, you will also see at least one component with a reported asymptotic standard error of 0 (zero). This message indicates that during the iterative computations, at least two components were found to be entirely redundant, and that no unique estimates can be derived for those components. This may, for example, happen when there are 0 (zero) degrees of freedom for the error term, and hence, the error variance is not defined.

The computational algorithm used in STATISTICA always attempts to resolve any redundancies so as to retain a positive (>0) estimate for the Error variance component (otherwise, if during the estimation an intermediate solution makes the Error component equal to 0 [zero], the algorithm may prematurely terminate with a non-maximum likelihood solution). However, when this message appears in the header of a results spreadsheet in your analysis, you should carefully review the current model (e.g., click the SS and MS for Effects button on the Variance Components and Mixed Model ANOVA/ANCOVA Results dialog - Estimation tab), and interpret the estimates of the variance components with caution (as they are not unique).