Comment/question on degeneracy

[vasishth]

"To reiterate, this model can be reduced to a linear model because the random effects are inert, in the sense that they have a variance of zero." Is this sentence correct? The random effects don't necessarily have a variance of zero, the estimate of the variance from the data is zero.

Also, regarding the model being called degenerate, is it the model that is degenerate or the variance covariance matrix? In Pinheiro and Bates I think degenerate was only used in the context of the vcov matrix of random effects.

Finally, it may be worth mentioning that the 0 estimate of the random effect sd is just due to sparse data. If we had lots more data, the estimate would probably be non-zero. Simulation can demonstrate this point.