gqz {npmlreg}

Gauss-Hermite integration points

Description

Calculate Gaussian Quadrature points for the Normal distribution using the abscissas and weights for Hermite integration.

Usage

gqz(numnodes=20, minweight=0.000001)

Arguments

numnodes

theoretical number of quadrature points.

minweight

locations with weights that are less than this value will be omitted.

Details

The conversion of the locations and weights is given in Lindsey (1992, page 169:3) and Skrondal & Rabe-Hesketh (2004, page 165:1). The argument numnodes is the theoretical number of quadrature points, locations with weights that are less than the argument minweight will be omitted. The default value of minweight=0.000001 returns 14 masspoints for the default numnodes=20 as in Aitkin, Francis & Hinde (2005).

Value

A list with two vectors:

location

locations of mass points

weight

masses

Author(s)

Nick Sofroniou (2005)

References

Aitkin, M., Francis, B. and Hinde, J. (2005). Statistical Modelling in GLIM 4. Second Edition, Oxford Statistical Science Series, Oxford, UK.

Lindsey, J. K. (1992). The Analysis of Stochastic Processes using GLIM. Berlin: Springer-Verlag.

Skrondal, A. and Rabe-Hesketh, S. (2004). Generalized latent variable modelling. Boca Raton: Chapman and Hall/CRC.

See Also

alldist, allvc

Examples

gqz(20, minweight=1e-14)
  # gives k=20 GH integration points. These are used in alldist  
  # and allvc as fixed mass point locations when working with 
  # option random.distribution='gq', and serve as EM starting points 
  # otherwise.