Chapter 4 Model specification

The argument model specifies the structure of the MARSS model. It is a list where the list elements for each model parameter specify the form of that parameter matrix.

MARSS(data, model=list(...))

There are text shortcuts for common matrix structures:

• "identity", "diagonal and equal", "diagonal and unequal", "unconstrained", "equalvarcov", "zero", "unequal", "equal"
• Then there are some special shortcuts for \(\mathbf{Z}\) and \(\mathbf{a}\).

The default model structures are

• Z="identity" each \(y\) in \(\mathbf{y}\) corresponds to one \(x\) in \(\mathbf{x}\)
• B="identity" no interactions among the \(x\)’s in \(\mathbf{x}\)
• U="unequal" the \(u\)’s in \(\mathbf{u}\) are all different
• Q="diagonal and unequal" process errors are independent but have different variances
• R="diagonal and equal" the observations are i.i.d.
• A="scaling" \(\mathbf{a}\) is a set of scaling factors
• C="zero" and D="zero" no inputs.
• c="zero" and d="zero" no inputs.
• x0="unequal" all initial states are different
• V0="zero" the initial condition on the states (\(\mathbf{x}_0\) or \(\mathbf{x}_1\)) is fixed but unknown
• tinitx=0 the initial state refers to \(t=0\) instead of \(t=1\).

The shortcuts and general specifications for each parameter are discussed below.