The form of MARSS models for users is "marxss", the MARSS models with inputs. See MARSS.marxss
. In the internal algorithms (e.g. MARSSkem
), the "marss" form is used and the D and d are incorporated into the A matrix and C and c are incorporated into the U matrix.
This is a MARSS(1) model of the marss form:
$$x(t+1) = B(t) x(t) + U(t) + G(t) w(t), where w(t) ~ MVN(0,Q(t))$$
$$y(t) = Z(t) x(t) + A(t) + H(t) v(t), where v(t) ~ MVN(0,R(t))$$
$$x(1) ~ MVN(x0, V0) or x(0) ~ MVN(x0, V0) $$
Note, by default \(V0\) is a matrix of all zeros and thus \(x(1)\) or \(x(0)\) is treated as an estimated parameter not a diffuse prior.
Note, "marss" is a model form. A model form is defined by a collection of form functions discussed in marssMODEL
. These functions are not exported to the user, but are called by MARSS()
using the argument form
. These internal functions convert the users model list into the vec form of a MARSS model and do extensive error-checking.