checkAdequation: Function to Check the Adequation of the Second Derivatives

In irtProb: Utilities and Probability Distributions Related to Multidimensional Person Item Response Models

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.

Author(s)

Gilles Raiche, Universite du Quebec a Montreal (UQAM),

Departement d'education et pedagogie

[e-mail], http://www.er.uqam.ca/nobel/r17165/

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
## ..........................................................

irtProb documentation built on May 2, 2019, 1:30 p.m.