irtProb (version 1.0)

checkAdequation: Function to Check the Adequation of the Second Derivatives

Description

Check the adequation of the second derivatives (hessian) for computation of variance and covariance. Use inside the function m4plEstimateMore to assure that computations can be applied to this second derivative. Problems encountered can be of not positive definitetess, singular matrix, diagonal not complitely positive. In these cases inversion of the matrix is not posssible or variances cannot be computed from the inverse of the diagonal.

Usage

checkAdequation(x)

Arguments

x

matrix: second derivative (hessian).

Value

• isNumbers
  logical: check if the elements of the x matrix are all numerics.
• correctClass
  logical: check if the the x matrix is of class matrix.
• squareMatrix
  logical: check if the the x matrix is square.
• diagPositive
  logical: check if the elements of the x matrix are all positive and > 0.
• positiveDefinite
  logical: check if the the x matrix is positiveDefinite.
• nonSingular
  logical: check if the the x matrix is nonSingular.

References

Seber, G. E. A. F. (2008). A matrix handbook for statisticians. New York, New Jersey: Wiley.

See Also

eigen, det, diag

Examples

## Complete adequation of the matrix
## ..........................................................
 x <- matrix(c(4.867054, 16.66902, 16.669023, 107.36390), ncol=2)
 checkAdequation(x)
 all(checkAdequation(x))
 eigen(x)$values
 det(x)
 diag(x)
## ..........................................................

## Not positiveDefinite matrix
## ..........................................................
 x <- matrix(1:4, ncol=2)
 checkAdequation(x)
 all(checkAdequation(x))
 eigen(x)$values
 det(x)
 diag(x)
## ..........................................................

## More problems
## ..........................................................
 x <- matrix(c("Inf",2,5,10), ncol=2)
 checkAdequation(x)
 all(checkAdequation(x))
 det(x)
 diag(x)
# eigen(x)$values
 x <- matrix(c("NaN",2,5,10), ncol=2)
 checkAdequation(x)
 all(checkAdequation(x))
 det(x)
 diag(x)
# eigen(x)$values
## ..........................................................