Singularities in the Average Information Matrix


!AISINGULARITIES forces ASReml to calculate Average Information (AI) updates even though a singularity was detected in the AI matrix. The AI matrix is used to give updates to the variance parameter estimates. In release 1, if singularities were present in the AI matrix, a generalised inverse was used which effectively conditioned on whichever parameters were identified as singular. ASReml now aborts processing if such singularities appear unless the !AISINGULARITIES qualifier is set. Which particular parameter is singular is reported in the variance component table printed in the .asr file.

The most common reason for singularities is that the user has overspecified the model and is likely to misinterpret the results if not fully aware of the situation. Overspecification will occur in a direct product of two unconstrained variance matrices, when a random term is confounded with a fixed term and when there is no information in the data on a particular component. The best action is to revise the variance model so that the ambiguity is removed, or to fix one of the parameters in the variance model so that the model can be fitted. For instance, if !ASUV is specified, you may also need !S2==1. Only rarely will it be reasonable to specify the !AISINGULARITIES qualifier.

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