I am using the LinearModel class in R2012a to create a generalized linear model. I am specifying the model by way of a formula in Wilkinson notation, and I'm passing a Dataset struct with both numeric and categorical columns. The latter are indicated to LinearModel.fit() by way of the CategoricalVars option.
The problem is that one of the terms in my formula involves interactions between two categorical variables (e.g. 'A:B'), which when expanded via dummyvars internally and multiplied out, leads to the creation of columns in the design matrix that are all zeros. This of course leads to a singular design matrix.
Is there a simple way to tell MATLAB how to handle problematic categorical interactions, or at least remove them without breaking the linear model object? I'm surprised this is apparently unhandled (no warnings even), as the situation could easily come up.
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When I try an example like this I see:
Warning: Regression design matrix is rank deficient to within machine precision.
The coefficients table has coefficients fixed at zero. The step method may remove the singular terms. The anova method can help reveal which terms don't have full degrees of freedom.
Can you elaborate on what you see?