covFun function

(Co)variance parameter transformations.

Converts lists of (co)variance parameters either between list and vector format or between the theta and nu scales.

stTrans(x)

conTrans(Gcon, Rcon)

start2theta(Gstart, Rstart, name = NULL)

matlist2vech(theta)

vech2matlist(vech, skeleton)

theta2nu_trans(theta)

nu2theta_trans(nu)

theta2nu_lambda(theta, thetaG, thetaR)

nu2theta_lambda(nu, sigma2e, thetaG, thetaR)

nuVar2thetaVar_lambda(object)

nuAI2thetaAIinv_lambda(object)

nu2theta_noTrans(nu, thetaG, thetaR)

Arguments

• x, theta, nu: A list of matrices containing the (co)variance parameters of the model.
• Gcon, Rcon: A list of starting (co)variance constraints for the G-structure (random effects terms) or R-structure (residual).
• Gstart, Rstart: A list of starting (co)variance values for the G-structure (random effects terms) or R-structure (residual).
• name: An (optional) character vector containing the (co)variance component names.
• vech: A vector of (co)variance parameters.
• skeleton: An example structure to map vech onto.
• thetaG, thetaR: A vector indexing the G-structure or R-structure components, respectively.
• sigma2e: A numeric estimate of the factored out residual variance from the mixed model equations (i.e., the lambda scale) $\sigma^{2}_{e}$.
• object: An object of class gremlin .

Returns

Functions are specified to mostly return either a list of matrices (structure as defined by the skel attribute or in the skeleton object) or a vector containing the (co)variance parameters of the model. Additional list elements returned can be:

• thetaG: A vector indexing the G-structure components.
• thetaR: A vector indexing the R-structure components.

Alternatively, nuVar2thetaVar_lambda and nuAI2thetaAIinv_lambda

return a vector and matrix, respectively, holding the sampling (co)variances of the model (co)variance parameters both on the theta

scale. These are elements of the inverse Average Information matrix.

Details

• stTrans: Transform start parameters into lower triangle matrices of class dsCMatrix.

• conTrans: Transformation of starting constraints to correct format.

• start2theta: Converts lists of starting values for (co)variance parameters to a theta object used to structure the (co)variance components within gremlin.

• matlist2vech: Converts a list of (co)variance parameter matrices to a vector with a skel attribute.

• vech2matlist: Converts a vector of (co)variance parameters to a list of covariance matrices.

• theta2nu_trans: Transforms theta to nu scale by taking the Cholesky factor of each covariance matrix and then replacing the diagonals with their (natural) logarithms. Done to ensure matrices are positive definite.

• nu2theta_trans: Back transformation from theta2nu_trans: exponentiates the diagonal elements of each matrix then calculates the cross-product.

• theta2nu_lambda: Transformation that factors out a residual variance so that nu contains the lambda parameterization: ratios of variance parameters with the residual variance.

• nu2theta_lambda: Back transformation from theta2nu_lambda.

• nuVar2thetaVar_lambda: Transformation of Sampling Variances from lambda Scale for theta.

• nuAI2thetaAIinv_lambda: Transform AI matrix from lambda

   Scale to AI-inverse of `theta`.
  

• nu2theta_noTrans: Structures theta when not transformed.

Examples

# User-specified starting parameters
  thetaOut <- start2theta(Gstart = list(matrix(1), matrix(2)),
    Rstart = matrix(3))
  ## convert to a vector and then back into a matrix list
  thetav <- matlist2vech(thetaOut$theta)
  theta <- vech2matlist(thetav, attr(thetav, "skel"))
    identical(thetaOut$theta, theta)  #<-- should be TRUE
  # lambda parameterization transformation
  nu <- theta2nu_lambda(theta, thetaOut$thetaG, thetaOut$thetaR)
  # back-transform from (lambda scale) nu to theta
  ## For example, when the sigma2e estimate=0.5
  theta2 <- nu2theta_lambda(nu, sigma2e = 0.5, thetaOut$thetaG, thetaOut$thetaR)

Author(s)

matthewwolak@gmail.com