MARSS (version 3.11.9)

is.marssMODEL: Test Model Objects

Description

These are model objects and utility functions for model objects in the package MARSS-package. is.marssMODEL() ensures model consistency. MARSS_formname() translates a model list as passed in call to MARSS() into a marssMODEL model object.

Usage

is.marssMODEL(MODELobj, method = "kem")

Value

A vector of error messages or NULL is no errors.

Arguments

MODELobj

An object of class marssMODEL.

method

Method used for fitting in case there are special constraints for that method.

Author

Eli Holmes, NOAA, Seattle, USA.

Details

A marssMODEL object is an R representation of a MARSS model along with the data. Data in a marssMODEL object consists of multivariate time series data in which time is across columns and the n observed time series are in the n different rows.

The base MARSS model (form=marss) is

x(t) = B(t) x(t-1) + U(t) + w(t), where w(t) ~ MVN(0,Q(t))

y(t) = Z(t) x(t) + A(t) + v(t), where v(t) ~ MVN(0,R(t))

x(0) ~ MVN(x0, V0) or x(1) ~ MVN(x0, V0)

The marssMODEL(form=marss) object describes this MARSS model but written in vec form:

x(t) = kron(x(t-1),I)(f_b(t)+D_b(t)b) + (f_u(t)+D_u(t)u) + w(t), where w(t) ~ MVN(0,Q)

vec(Q) = f_q(t)+D_q(t)q

y(t) = kron(x(t),I)(f_z(t)+D_z(t)z) + (f_a(t)+D_a(t)a) + v(t), where v(t) ~ MVN(0,R)

vec(R) = f_r(t)+D_r(t)r

x(0) ~ MVN(f_p+D_p p, V0) or x(1) ~ MVN(f_p+D_p p, V0

vec(V0) = f_l+D_l l

In the marssMODEL(form=marss) object, f(t) + D(t)m, is the vec of a matrix M(t), so f_b(t)+D_b(t)b would be vec(B(t)). The estimated parameters are in the column vectors: b, u, q, z, a, r, p, and l. Each matrix M(t) is f(t)+D(t)m so is the sum of a fixed part f(t) and the linear combination, D(t), of the free (or estimated) part m.

The vec form of the MARSS model is specified by 3D matrices for each f and D for each parameter: B, U, Q, Z, A, R, x0, V0. The number of columns in the D matrix for a parameter determines the number of estimated values for that parameter. The first dimension for f (fixed) and D (free) must be:

Z

n x m

B, Q, and V0

m x m

U and x0

m x 1

A

n x 1

R

n x n

The third dimension of f (fixed) and D (free) is either 1 (if not time-varying) or T (if time-varying). The second dimension of f (fixed) is always 1, while the second dimension of D (free) depends on how many values are being estimated for a matrix. It can be 0 (if the matrix is fixed) or up to the size of the matrix (if all elements are being estimated).

See Also

MARSS(), MARSS.marxss(), marssMODEL