goodwin.f77 Implementing Crouch EAC, Spiegelman D. The evaluation of integrals of the form f(t)exp{-t2}dt: Application to logistic-normal models. Journal of the American Statistical Association 1990; 85: 464-469. Logistic-normal distributions and related functions arise in a variety of statistical applications of current interest, including binary measurement-error models and the analysis of teratogenicity experiments. Analytic intractability has led to the development of numerous approximations to the desired forms, often with consequences that have not been well studied. A method is developed to compute these forms to arbitrary accuracy, and comparative calculations are made that show when the common numerical alternative, 20-point Gaussian quadrature, begins to fail. By using a simple matrix transformation, this method can be used with multiple covariate regression models of the logistic-normal form. We conducted a simulation study that compares the ability of 20-point Gaussian quadrature and our new method to obtain the maximum likelihood estimator of relative risk in the logistic-normal measurement-error model. Using standard subroutines to maximize the likelihood equations, 27 of 50 trials failed to converge with 20-point Gaussian quadrature, whereas the new method allowed convergence in all but one case.

References in zbMATH (referenced in 22 articles )

Showing results 1 to 20 of 22.
Sorted by year (citations)

1 2 next

  1. Zhang, Tonglin: General Gaussian estimation (2019)
  2. Wang, Zhanfeng; Chen, Zhuojian; Chen, Zimu: H-relative error estimation for multiplicative regression model with random effect (2018)
  3. Pirjol, Dan: Hogan-Weintraub singularity and explosive behaviour in the Black-Derman-Toy model (2015)
  4. Russo, Jorge G.; Silva, Guillermo A.; Tierz, Miguel: Supersymmetric (U(N)) Chern-Simons-matter theory and phase transitions (2015)
  5. Alazah, Mohammad; Chandler-Wilde, Simon N.; La Porte, Scott: Computing Fresnel integrals via modified trapezium rules (2014)
  6. Feddag, M.-L.: Pairwise marginal likelihood for the Bradley-Terry model (2013)
  7. Geyer, Charles J.; Ridley, Caroline E.; Latta, Robert G.; Etterson, Julie R.; Shaw, Ruth G.: Local adaptation and genetic effects on fitness: calculations for exponential family models with random effects (2013)
  8. Lyles, Robert H.; Kupper, Lawrence L.: Approximate and pseudo-likelihood analysis for logistic regression using external validation data to model log exposure (2013)
  9. Balanzario, Eugenio P.; Sánchez-Ortiz, Jorge: Riemann-Siegel integral formula for the Lerch zeta function (2012)
  10. Shklyar, S. V.: Logistic regression with homoscedastic errors -- a Berkson model (2012)
  11. Qiu, Weiliang; Rosner, Bernard: Measurement error correction for the cumulative average model in the survival analysis of nutritional data: application to nurses’ health study (2010)
  12. Feddag, M.-L.; Bacci, S.: Pairwise likelihood for the longitudinal mixed Rasch model (2009)
  13. Glickman, Mark E.: Bayesian locally optimal design of knockout tournaments (2008)
  14. Sciandra, Mariangela; Muggeo, Vito M. R.; Lovison, Gianfranco: Subject-specific odds ratios in binomial GLMMs with continuous response (2008)
  15. Crowder, Martin; Hand, David J.; Krzanowski, Wojtek: On optimal intervention for customer lifetime value (2007)
  16. González, Jorge; Tuerlinckx, Francis; De Boeck, Paul; Cools, Ronald: Numerical integration in logistic-normal models (2006)
  17. Jiang, Jiming; Lahiri, P.: Mixed model prediction and small area estimation. (With comments of P. Hall, D. Morales, C. N. Morris, J. N. K. Rao, and J. L. Eltinge) (2006)
  18. Roy, Surupa; Banerjee, Tathagata: A flexible model for generalized linear regression with measurement error (2006)
  19. Ünlü, Ali: Estimation of careless error and lucky guess probabilities for dichotomous test items: a psychometric application of a biometric latent class model with random effects (2006)
  20. Demidenko, Eugene; Spiegelman, Donna: A paradox: More measurement error can lead to more efficient estimates (1997)

1 2 next