16.1 Properly constrained models

Specification of a properly constrained model with a unique solution is the responsibility of the user because MARSS() has no way to tell if you have specified an insufficiently constrained model—with correspondingly an infinite number of solutions.

How do you know if the model is properly constrained? If you are using a MARSS model form that is widely used, then you can probably assume that it is properly constrained. If you go to papers where someone developed the model or method, the issue of constraints necessary to ensure “identifiability” will likely be addressed if it is an issue. Are you fitting novel MARSS models? Then you will need to do some study on identifiability in this class of models using textbooks. Often textbooks do not address identifiability explicitly. Rather it is addressed implicitly by only showing a model constructed in such a way that it is identifiable. In our work, if we suspect identification problems, we will often first do a Bayesian analysis with flat priors and look for oddities in the posteriors, such as ridges, plateaus or bimodality.