MARSS (version 3.8)

MARSShatyt: Compute Expected Value of Y,YY, and YX

Description

Computes the expected value of random variables involving Y for the EM algorithm. This function is not exported. Users should use print( MLEobj, what="Ey") to access this output. See print.marssMLE.

Usage

MARSShatyt( MLEobj )

Arguments

MLEobj

A marssMLE object with the par element of estimated parameters, model element with the model description and data.

Value

• A list with the following components (n is the number of state processes). Following the notation in Holmes (2012), y(1) is the observed data (for t=1:TT) while y(2) is the unobserved data. y(1,1:t) is the observed data from time 1 to t.
• ytT
  Estimates E[Y(t) | Y(1,1:TT)=y(1,1:TT)] (n x T matrix).
• ytt1
  Estimates E[Y(t) | Y(1,1:t-1)=y(1,1:t-1)] (n x T matrix).
• OtT
  Estimates E[Y(t) t(Y(t) | Y(1)=y(1)] (n x n x T array).
• yxtT
  Estimates E[Y(t) t(X(t) | Y(1)=y(1)] (n x m x T array).
• yxt1T
  Estimates E[Y(t) t(X(t-1) | Y(1)=y(1)] (n x m x T array).
• errors
  Any error messages due to ill-conditioned matrices.
• ok
  (T/F) Whether errors were generated.

Details

For state space models, MARSShatyt() computes the expectations involving Y. If Y is completely observed, this entails simply replacing Y with the observed y. When Y is only partially observed, the expectation involves the conditional expectation of a multivariate normal.

References

Holmes, E. E. (2012) Derivation of the EM algorithm for constrained and unconstrained multivariate autoregressive state-space (MARSS) models. Technical report. arXiv:1302.3919 [stat.ME] Type RShowDoc("EMDerivation",package="MARSS") to open a copy.

See Also

MARSS marssMODEL MARSSkem