MARSS (version 3.9)

MARSSparamCIs: Standard Errors, Confidence Intervals and Bias for MARSS Parameters

Description

Computes standard errors, confidence intervals and bias for the maximum-likelihood estimates of MARSS model parameters. If you what confidence intervals on the estimated hidden states, see print.marssMLE and look for "states.cis".

Usage

MARSSparamCIs(MLEobj, method = "hessian", alpha = 0.05, nboot=1000)

Arguments

MLEobj

An object of class marssMLE. Must have a $par element containing the MLE parameter estimates.

method

Method for calculating the standard errors: "hessian", "parametric", and "innovations" implemented currently.

alpha

alpha level for the 1-alpha confidence intervals.

nboot

Number of bootstraps to use for "parametric" and "innovations" methods.

Value

MARSSparamCIs returns the marssMLE object passed in, with additional components par.se, par.upCI, par.lowCI, par.CI.alpha, par.CI.method, par.CI.nboot and par.bias (if method is "parametric" or "innovations").

Details

Approximate confidence intervals (CIs) on the model parameters may be calculated from the Hessian matrix (the matrix of partial 2nd derivatives of the parameter estimates) or parametric or non-parametric (innovations) bootstrapping using nboot bootstraps. The Hessian CIs are based on the asymptotic normality of MLE parameters under a large-sample approximation. The Hessian computation for variance-covariance matrices is done on these matrices in their equivalent Cholesky decomposition form (see MARSShessian. Bootstrap estimates of parameter bias are reported if method "parametric" or "innovations" is specified.

Note, these are added to the par (etc) elements of a marssMLE object but are in marss form not marxss form. Thus the MLEobj$par.upCI and related elements that are added to the marssMLE object may not look familiar to the user. Instead the user should extract these elements using print(MLEobj) and passing in the argument what set to "par.se","par.bias","par.lowCIs", or "par.upCIs". See print.marssMLE.

References

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 Type RShowDoc("UserGuide",package="MARSS") to open a copy.

See Also

MARSSboot MARSSinnovationsboot MARSShessian

Examples

# NOT RUN {
  dat = t(harborSealWA)
  dat = dat[2:4,]
  kem = MARSS(dat, model=list(Z=matrix(1,3,1), 
     R="diagonal and unequal"))
  kem.with.CIs.from.hessian = MARSSparamCIs(kem)
  kem.with.CIs.from.hessian
# }