Test whether terminated estimation criteria for a given model passes
the second order test by checking the positive definiteness of the resulting
Hessian matrix. This function, which accepts the symmetric Hessian/information
matrix as the input, returns TRUE if the matrix is positive definite
and FALSE otherwise.
Arguments
- mat
symmetric matrix to test for positive definiteness (typically the Hessian at the highest point of model estimator, such as MLE or MAP)
- ...
arguments passed to either
eigen,chol, or'det'for the positiveness of the eigen values, positiveness of leading minors via the Cholesky decomposition, or evaluation of whether the determinant is greater than 0- method
method to use to test positive definiteness. Default is
'eigen'
References
Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. doi:10.18637/jss.v048.i06
Author
Phil Chalmers rphilip.chalmers@gmail.com
Examples
if (FALSE) { # \dontrun{
# PD matrix
mod <- mirt(Science, 1, SE=TRUE)
info <- solve(vcov(mod)) ## observed information
secondOrderTest(info)
secondOrderTest(info, method = 'chol')
secondOrderTest(info, method = 'det')
# non-PD matrix
mat <- matrix(c(1,0,0,0,1,1,0,1,1), ncol=3)
mat
secondOrderTest(mat)
secondOrderTest(mat, method = 'chol')
secondOrderTest(mat, method = 'det')
} # }