# R/hess_ram.R In regsem: Regularized Structural Equation Modeling

#### Defines functions hess_ram

```hess_ram = function(par,ImpCov,SampCov,Areg,Sreg,A,S,F){

#?sfClusterApplyLB
#sfClusterApplyLB(index, simulationIteration, n, rho, g, h, pv, het=F)

hess.out <- matrix(0,length(par),length(par))
h <- 0.00001

B = solve(diag(nrow(A)) - Areg)
C = diag(nrow(ImpCov)) - solve(ImpCov) %*% SampCov
E = B %*% Sreg %*% t(B)

#if(type=="none"){

# not symmetric

for(i in 1:nrow(hess.out)){
for(j in 1:ncol(hess.out)){

Ai <- (A == i)*1
Aj <- (A == j)*1
Aij <- matrix(0,nrow(A),ncol(A))
Aij[Ai==T & Aj ==T] <- 1

Si <- (S == i)*1;
Sj <- (S == j)*1;
Sij <- matrix(0,nrow(S),ncol(S))
Sij[Si==T & Sj==T] <- 1

deriv15_I <- F %*% B %*% Ai %*% E %*% t(F) + F %*% B %*% Si %*% t(B) %*% t(F)
deriv15_J <- F %*% B %*% Aj %*% E %*% t(F) + F %*% B %*% Sj %*% t(B) %*% t(F)

# this is cause of asymmetry
deriv15_IJ <- F %*% B %*% Ai %*% B %*% Aj %*% E %*% t(F) +
F %*% B %*% Aj %*% B %*% Ai %*% E %*% t(F) +
F %*% B %*% Ai %*% B %*% Sj %*% t(B) %*% t(F) +
F %*% B %*% Ai %*% E %*% t(Aj) %*% t(B) %*% t(F) +
F %*% B %*% Aj %*% B %*% Si %*% t(B) %*% t(F)

# left out mean part
hess.out[i,j]  <- trace(solve(ImpCov) %*% deriv15_IJ %*% C - solve(ImpCov) %*%
deriv15_I %*% solve(ImpCov) %*% deriv15_J %*% C +
solve(ImpCov) %*% deriv15_J %*% solve(ImpCov) %*% deriv15_I %*%
solve(ImpCov) %*% SampCov)

}
}

hess.out

}
```

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regsem documentation built on March 18, 2018, 2:12 p.m.