SimSSMVARIVary {simStateSpace}

Simulate Data from the Vector Autoregressive Model (Individual-Varying Parameters)

Description

This function simulates data from the vector autoregressive model using a state space model parameterization. It assumes that the parameters can vary across individuals.

Usage

SimSSMVARIVary(
  n,
  time,
  mu0,
  sigma0_l,
  alpha,
  beta,
  psi_l,
  type = 0,
  x = NULL,
  gamma = NULL
)

Arguments

n

Positive integer. Number of individuals.

time

Positive integer. Number of time points.

mu0

List of numeric vectors. Each element of the list is the mean of initial latent variable values (\boldsymbol{\mu}_{\boldsymbol{\eta} \mid 0}).

sigma0_l

List of numeric matrices. Each element of the list is the Cholesky factorization (t(chol(sigma0))) of the covariance matrix of initial latent variable values (\boldsymbol{\Sigma}_{\boldsymbol{\eta} \mid 0}).

alpha

List of numeric vectors. Each element of the list is the vector of constant values for the dynamic model (\boldsymbol{\alpha}).

beta

List of numeric matrices. Each element of the list is the transition matrix relating the values of the latent variables at the previous to the current time point (\boldsymbol{\beta}).

psi_l

List of numeric matrices. Each element of the list is the Cholesky factorization (t(chol(psi))) of the covariance matrix of the process noise (\boldsymbol{\Psi}).

type

Integer. State space model type. See Details in SimSSMVARFixed() for more information.

x

List. Each element of the list is a matrix of covariates for each individual i in n. The number of columns in each matrix should be equal to time.

gamma

List of numeric matrices. Each element of the list is the matrix linking the covariates to the latent variables at current time point (\boldsymbol{\Gamma}).

Details

Parameters can vary across individuals by providing a list of parameter values. If the length of any of the parameters (mu0, sigma0_l, alpha, beta, psi_l, gamma, or kappa) is less the n, the function will cycle through the available values.

Value

Returns an object of class simstatespace which is a list with the following elements:

• call: Function call.

• args: Function arguments.

• data: Generated data which is a list of length n. Each element of data is a list with the following elements:

  • id: A vector of ID numbers with length l, where l is the value of the function argument time.

  • time: A vector time points of length l.

  • y: A l by k matrix of values for the manifest variables.

  • eta: A l by p matrix of values for the latent variables.

  • x: A l by j matrix of values for the covariates (when covariates are included).

• fun: Function used.

Author(s)

Ivan Jacob Agaloos Pesigan

References

Chow, S.-M., Ho, M. R., Hamaker, E. L., & Dolan, C. V. (2010). Equivalence and differences between structural equation modeling and state-space modeling techniques. Structural Equation Modeling: A Multidisciplinary Journal, 17(2), 303–332. doi:10.1080/10705511003661553

See Also

Other Simulation of State Space Models Data Functions: LinSDE2SSM(), SimBetaN(), SimPhiN(), SimSSMFixed(), SimSSMIVary(), SimSSMLinGrowth(), SimSSMLinGrowthIVary(), SimSSMLinSDEFixed(), SimSSMLinSDEIVary(), SimSSMOUFixed(), SimSSMOUIVary(), SimSSMVARFixed(), TestPhi(), TestStability(), TestStationarity()

Examples

# prepare parameters
# In this example, beta varies across individuals.
set.seed(42)
## number of individuals
n <- 5
## time points
time <- 50
## dynamic structure
p <- 3
mu0 <- list(
  rep(x = 0, times = p)
)
sigma0 <- 0.001 * diag(p)
sigma0_l <- list(
  t(chol(sigma0))
)
alpha <- list(
  rep(x = 0, times = p)
)
beta <- list(
  0.1 * diag(p),
  0.2 * diag(p),
  0.3 * diag(p),
  0.4 * diag(p),
  0.5 * diag(p)
)
psi <- 0.001 * diag(p)
psi_l <- list(
  t(chol(psi))
)
## covariates
j <- 2
x <- lapply(
  X = seq_len(n),
  FUN = function(i) {
    matrix(
      data = stats::rnorm(n = time * j),
      nrow = j,
      ncol = time
    )
  }
)
gamma <- list(
  diag(x = 0.10, nrow = p, ncol = j)
)

# Type 0
ssm <- SimSSMVARIVary(
  n = n,
  time = time,
  mu0 = mu0,
  sigma0_l = sigma0_l,
  alpha = alpha,
  beta = beta,
  psi_l = psi_l,
  type = 0
)

plot(ssm)

# Type 1
ssm <- SimSSMVARIVary(
  n = n,
  time = time,
  mu0 = mu0,
  sigma0_l = sigma0_l,
  alpha = alpha,
  beta = beta,
  psi_l = psi_l,
  type = 1,
  x = x,
  gamma = gamma
)

plot(ssm)