R/modelImpliedEq.R

In stim: Incorporating Stability Information into Cross-Sectional Estimates

#' Get the model implied symbolic equations for the auto-regressive effects and
#' the covariances between the phantom variables
#'
#' @param S Sample covariance matrix
#' @param blueprint A character matrix that specifies which effects to estimate and
#'                  which effects to constrain to a non-zero value
#' @param stability A named object that contains stability information for each
#'                  variable in the model.
#' @param residualcov A list with both the lavaan syntax for the residual covariance
#'                    and a dataframe with the variable names
#'
#' @return A list of 1) A character vector with the model implied equations for the autoregressive
#'         effects and the phantom variable covariances, and 2) the symbolic psi and covariance
#'         matrices that were used to get the model implied equations.
#' @keywords internal
#'


modelImpliedEq <- function(S, blueprint, stability, residualcov){

  # Get symbolic covariance and psi matrices. Both symbolic matrices will
  # be used to get model implied equations
  SymbolicMats <- symbMatrix(blueprint, residualcov)

  SymbolicCovMat <- SymbolicMats$SymbCov

  # Matrix algebra with symbolic matrices to get model implied
  # stability equations

  Psi <- Ryacas::ysym(SymbolicMats$Psi)
  B <- Ryacas::ysym(blueprint)
  Cov1 <- Ryacas::ysym(SymbolicCovMat)
  Cov2 <- symbMultiplication(t(B), Cov1)


  StNames <- apply(as.matrix(colnames(blueprint)), 1, function(x){paste0("Cov", x, "0", x, "1")})

  ArEquations <- rep(0, length(StNames))

  # We actually want the autoregressive equations which we can get by reorganizing
  # the stability equations.
  # We also need to input the user-specified stability values into these equations
  for(i in 1:length(StNames)){

    StEquations <- paste0(StNames[i], "==", Ryacas::diag(Cov2)[i])
    ArEquations[i] <- as.character(solve(Ryacas::ysym(StEquations), Ryacas::diag(blueprint)[i]))

    ArEquations[i] <- gsub(StNames[i], stability[, i], ArEquations[i])

  }


  ArEquations <- gsub('{', "", ArEquations, fixed = TRUE)
  ArEquations <- gsub('}', "", ArEquations, fixed = TRUE)

  # Matrix algebra with symbolic matrices to get model implied
  # phantom variable covariance equations

  Cov3 <- symbMultiplication(Cov2, B) + Psi

  Covariances <- SymbolicCovMat[upper.tri(SymbolicCovMat)]

  for( i in 1:length(Covariances) ){

    location <- which(SymbolicCovMat == Covariances[i], arr.ind = TRUE)[1,]
    ArEquations <- c(ArEquations, paste0(Covariances[i], '==',
                                         as.character(Cov3[location[1], location[2]])))

  }

  return(list(modelImpliedEquations = ArEquations, SymbolicMatrices = SymbolicMats))
}