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A client measured greenhouse gas emissions from all phases of 6 cropping systems over 2 growing seasons (a cropping system is a crop rotation plus management e.g. notill v conventional tillage, organic v conventional, etc.).  Phases were nested within cropping systems so linear contrasts of similar phases (such as corn versus other crops) across cropping systems are singular and SAS simply outputs "nonestimable".  We can override the singularity check in the Proc Mixed nested analysis or we can create a new treatment variable (corn/other) which makes a factorial combination (unbalanced, but no missing cells) to run as a new analysis.  The singularity check override is the simpler way and there are more such comparisons so it is worth asking "Are there more reasons to prefer one method over the other"?
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Jon Baldock
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I'm probably exposing my level of ignorance but while I can see an estimate of the mean level of a factor (using the ESTIMATE statement) becoming estimable when, say, the one uses the NOINT model option (i.e., one particular type of reparameterization), I don't see how any CONTRAST statement (with the coefficients summing to zero) would become estimable with a reparameterization.  In short, I wouldn't override the singularity check.

Can you reparameterize the model as a "cell means" model and then construct the contrasts?

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James Baldwin
Station Statistician
US Forest Service
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At the risk of overstating my appreciation of the problem, it's been my experience that singularities in the design matrix indicate that things have been lumped together in the model which would actually be desirable to distinguish statistically, if possible.  In that situation, a re-parameterization is advisable, usually to the full extent possible (i.e. more than just corn/other if you know them and any covariates), because you can always re-lump factors later and you will probably only reedit this data set once.  Although time consuming to add to a data set after the fact, I am inferring that the newly available factor and covariate information will offer the opportunity to analyze a factorial design structure.  This is always desirable when possible.   Other PROCs such as GLM can then be invoked for analysis.  In general, re-parameterization is preferable to overriding the singularity constraint, because even the results from a SAS procedure, while reproducible and well documented, are not likely to be comparable with the output of other software, and may prove less defensible statistically.  In other words, the analysis will always be vulnerable to future criticism statistically unless you at least try the re-parameterization approach.  Easier may be simpler for the analyst, but it isn't always better for the problem or the customer.

Thomas D. Sandry

Industrial Statistical Consultant, Retired

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Thomas Sandry
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