Steady-State Mean Vector for the Observed Variables in the State Space Model

The steady-state mean vector for the observed variables in the state space model \(\mathrm{Mean} \left( \mathbf{y} \right)\) is given by $$ \mathrm{Mean} \left( \mathbf{y} \right) = \boldsymbol{\nu} + \boldsymbol{\Lambda} \mathrm{Mean} \left( \boldsymbol{\eta} \right) $$ where \(\boldsymbol{\nu}\) is the vector of intercept values for the measurement model, \(\boldsymbol{\Lambda}\) is the matrix of factor loadings, and \(\mathrm{Mean} \left( \boldsymbol{\eta} \right)\) is the steady-state mean vector for the latent variables.

Usage

SSMMeanY(nu, lambda, mean_eta)

Arguments

nu

Numeric vector. Vector of intercept values for the measurement model (\(\boldsymbol{\nu}\)).

lambda

Numeric matrix. Factor loading matrix linking the latent variables to the observed variables (\(\boldsymbol{\Lambda}\)).

mean_eta

Numeric vector. Steady-state mean vector of the latent variables \(\mathrm{Mean} \left( \boldsymbol{\eta} \right)\).

See also

Other Simulation of State Space Models Data Functions: LinSDE2SSM(), LinSDECovEta(), LinSDECovY(), LinSDEMeanEta(), LinSDEMeanY(), ProjectToHurwitz(), ProjectToStability(), SSMCovEta(), SSMCovY(), SSMMeanEta(), SimAlphaN(), SimBetaN(), SimBetaN2(), SimCovDiagN(), SimCovN(), SimIotaN(), SimNuN(), SimPhiN(), SimPhiN2(), SimSSMFixed(), SimSSMIVary(), SimSSMLinGrowth(), SimSSMLinGrowthIVary(), SimSSMLinSDEFixed(), SimSSMLinSDEIVary(), SimSSMOUFixed(), SimSSMOUIVary(), SimSSMVARFixed(), SimSSMVARIVary(), SpectralRadius(), TestPhi(), TestPhiHurwitz(), TestStability(), TestStationarity()

Author

Ivan Jacob Agaloos Pesigan

Examples

beta <- matrix(
  data = c(
    0.7, 0.5, -0.1,
    0.0, 0.6, 0.4,
    0.0, 0.0, 0.5
  ),
  nrow = 3
)
alpha <- rep(x = 1, times = 3)
lambda <- diag(3)
nu <- rep(x = 1, times = 3)
mean_eta <- SSMMeanEta(
  beta = beta,
  alpha = alpha
)
SSMMeanY(
  nu = nu,
  lambda = lambda,
  mean_eta = mean_eta
)
#> [1] 4.333333 7.666667 7.666667