Sandwich SE estimation for (explanatory) LCA

[seonghobae]

Hi Phil,

I having a trouble fitting an LCA model with sandwich SE estimation.

Here is a test case.

> mdirt(Science[,1:3], 1, SE = T, SE.type = 'sandwich', method = 'EM', covdata = data.frame(Science[4]), formula = ~Benefit)
Iteration: 2, Log-Lik: -1229.960, Max-Change: 0.00000

Calculating information matrix...
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
No hessian defined for lca class
Error in solve.default(-Ihess - IgradP + Igrad) : 
  Lapack routine dgesv: system is exactly singular: U[1,1] = 0

Seongho

[philchalmers]

The fix for this is straightforward but takes time. The hessian for the internal lca type has to be defined using C++ code like many of the other optimised itemtypes.

For now, you could compute the crossprod and Oakes estimates and combine this yourself to make the sandwich ACOV estimate.

mod <- mirt(Science, 1, SE=T)
modcp <- mirt(Science, 1, SE=T, SE.type = 'crossprod')
vcov(modcp) %*% solve(vcov(mod)) %*% vcov(modcp)

I'll likely add a SE.type = 'Oakes.sandwich' sometime because computing the robust ACOV this way can be much faster.