Fit a state-space MAR model using the MARSS package.

Uses a fitted MAR object from the function run.mar and an aggregated data.frame from the function transform.data to fit a state-space MAR model. The bestfit model in the MAR object is used to determine where the 0s are in the B and C matrices. Users can specify the form of the observation error variance-covariance matrix (R) and process error variance-covariance matrix (Q).

Usage

ss.mar1(aggregated.data, MAR.obj=NULL, model=list(), control=list(), silent=FALSE)

Arguments

aggregated.data: Data frame with continuous time-block variable in first column, ordered by dates in second column, followed by columns of taxa abundance time-series. This type of data frame is output by the function transform.data.
MAR.obj: A fitted MAR.obj as output by the function run.mar.
model: An optional list with elements B, C, Q, or R that specify the form of those matrices. For Q and R, a numeric matrix can be used in which case Q or R will be fixed to those values. The text string ``unconstrained'' can be used for Q to specify that all elements are estimated (the default). The text string ``diagonal and equal'' can be used for Q or R to specify that the variance-covariance matrix is diagonal with one variance on the diagonal. The text string ``diagonal and unequal'' can be used for Q or R to specify that the variance-covariance matrix is diagonal but the variances on the diagonal are unconstrained. The text strings ``zero'' and ``identity'' can also be used for R or Q to specify those matrix forms. B and Q can be passed into the model list in order to use a B or C matrix other than the bestfit B and C in MAR.obj. In this case B and C must be a numeric matrix with 0s in the elements that will be fixed at 0. All non-zero values will be estimated. See ?MARSS (after installing the MARSS package) for a discussion of the model argument.
control: A list of control elements for the MARSS package functions. The most useful may be minit to set a minimum number of iterations and maxit to set a maximum number of iterations.
silent: If FALSE, the output from the MARSS fitting function is suppressed.

Details

The functions fits a simple observation model where each species in the B matrix is assumed to be observed with independent observation error. The covariates are assumed to be observed with no error. Missing variates and covariates are allowed.

The B and C matrices are constrained by default by the bestfit model in the MLE.obj. ss.mar1 will use the 0 locations in the bestfit model and constrain those B and C elements to be 0. Other B or C matrices can be passed in via the model argument and will override this behavior.

References

The MARSS User Guide: Holmes, E. E., E. J. Ward, and M. D. Scheuerell (2012) Analysis of multivariate time-series using the MARSS package. NOAA Fisheries, Northwest Fisheries Science Center, 2725 Montlake Blvd E., Seattle, WA 98112. Available at https://CRAN.R-project.org/package=MARSS.

Author

Eli Holmes

Value

A list with the elements

ssfit: A marssMLE object output from MARSS().
A: The estimated A matrix
B: The estimated B matrix
C: The estimated C matrix
process.errors: The process errors
observation.errors: The observation errors
AIC: AIC
AIC: AICc
log.likelihood: log likelihood

Examples

if (FALSE) {
## These examples take 1-2 minutes to run

## construct a MAR model using 'run.mar' arguments to set variables and restrictions ##

data(L4.mar)

myvar <- c(0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 2, 2, 2) # 8 variates, 3 covariates
myres <- matrix(0.5,
  nrow = length(which(myvar == 1)),
  ncol = length(which(myvar != 0))
) # no restrictions (all 0.5)

run1 <- run.mar(L4.mar, variables = myvar, restrictions = myres, search = "exhaustive")

# control can be passed in to limit the number of iterations run.
ss.fit <- ss.mar1(L4.mar, run1, control = list(maxit = 50))

# compare to best fit model
ss.fit$B
run1$bestfit$B

# Use a known observation error
R <- diag(0.2, 8)
ss.fit <- ss.mar1(L4.mar, run1, model = list(R = R), control = list(maxit = 50))
}