qmc.nodes: Calculation of Quasi Monte Carlo Integration Points

In alexanderrobitzsch/sirt: Supplementary Item Response Theory Models

Calculation of Quasi Monte Carlo Integration Points

Description

This function calculates integration nodes based on the multivariate normal distribution with zero mean vector and identity covariance matrix. See Pan and Thompson (2007) and Gonzales et al. (2006) for details.

Usage

qmc.nodes(snodes, ndim)

Arguments

snodes	Number of integration nodes
ndim	Number of dimensions

Value

theta

A matrix of integration points

Note

This function uses the sfsmisc::QUnif function from the sfsmisc package.

References

Gonzalez, J., Tuerlinckx, F., De Boeck, P., & Cools, R. (2006). Numerical integration in logistic-normal models. Computational Statistics & Data Analysis, 51, 1535-1548.

Pan, J., & Thompson, R. (2007). Quasi-Monte Carlo estimation in generalized linear mixed models. Computational Statistics & Data Analysis, 51, 5765-5775.

Examples

## some toy examples

# 5 nodes on one dimension
qmc.nodes( snodes=5, ndim=1 )
  ##            [,1]
  ## [1,]  0.0000000
  ## [2,] -0.3863753
  ## [3,]  0.8409238
  ## [4,] -0.8426682
  ## [5,]  0.3850568

# 7 nodes on two dimensions
qmc.nodes( snodes=7, ndim=2 )
  ##             [,1]        [,2]
  ## [1,]  0.00000000 -0.43072730
  ## [2,] -0.38637529  0.79736332
  ## [3,]  0.84092380 -1.73230641
  ## [4,] -0.84266815 -0.03840544
  ## [5,]  0.38505683  1.51466109
  ## [6,] -0.00122394 -0.86704605
  ## [7,]  1.35539115  0.33491073

alexanderrobitzsch/sirt documentation built on Sept. 8, 2024, 2:45 a.m.