The C-S method in computation of the logistic normal integral

In logistic regression models with measurement error involved, the likelihood function is often taking the form as the logistic normal integral. The method proposed by E. Crouch and D. Spiegelman (1990) (C-S) and programmed in FORTRAN performs a good candidate from the computational perspective. We investigate this method by calling the FORTRAN code into R, and compare its performance with the classic Gaussian Quadrature method. The simulation results show that the C-S approach is much faster than the classic Gaussian Quadrature algorithm without losing any precision of the estimates, especially when the sample size is large. Hopefully the result can help researchers efficiently use logistic normal integral during their works.