Testing log-linear models with inequality constraints: A comparison of asymptotic, bootstrap, and posterior predictive p-values

Statistica Neerlandica

Volumn 59, Issue 1, 2005, Pages 82-94

  Galindo Garre, Francisca ^a   Vermunt, Jeroen K ^b  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b TILBURG UNIVERSITY   (Netherlands)

Author keywords

Inequality constraints; Order restricted inference; Parametric bootstrap; Posterior predictive p values

Indexed keywords

EID: 15544376784     PISSN: 00390402     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9574.2005.00281.x     Document Type: Article

References (22)

1. AGRESTI, A. (2002), Categorical data analysis, New York: Wiley.
2. ANDREWS, D. W. K. (2000), Inconsistency of the bootstrap when a parameter is on the boundary of the parameter space, Econometrica 68, 399-405.
3. 2 within binary variables, The Annals of Statistics 28, 1206-1218.
4. BAYARRI, M. J. and O. BERGER (2000), p-values for composite null models, Journal of the Americal Statistical Association 95, 1127-1142.
5. BERKHOF, J., I. VAN MECHELEN and H. HOIJTINK (2000), Posterior predictive checks: principles and discussion, Computational Statistics 15, 337-354.
6. CHERNOFF, H. (1954), On the distribution of the likelihood ratio, Annals of Mathematical Statistics 25, 573-578.
7. DARDANONI, V. and A. FORCINA (1998), A unified approach to likelihood inference on stochastic ordering in a nonparametric context. Journal of the American Statistical Association 93, 1112-1123.
8. GALINDO, F. and J. K. VERMUNT (2004), The order-restricted association model: Two estimation algorithms and issues in testing, Psychometrika, in press.
9. GALINDO, F., J. K. VERMUNT and M. A. CROON (2002), Likelihood-ratio tests for order-restricted log-linear models: a comparison of asymptotic and bootstrap methods, Metodologia de las Ciencias del Comportamiento 4, 325-337.
10. GELFAND, A. E., A. F. SMITH and T. M. LEE (1992), Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling, Journal of the American Statistical Association 87, 523-532.
11. GELMAN, A., X. MENG and H. STERN (1996), Posterior predictive assessment of model fitness via realized discrepancies, Statistica Sinica 6, 733-807.
12. GELMAN, A., J. B. CARLIN, H. S. STERN and D. B. RUBIN (2003), Bayesian data analysis. Chapman & Hall, London.
13. GILL, P. E. and W. MURRAY (1974), Numerical methods for constrained optimization. Academic Press Inc., London.
14. HOIJTINK, H. and I. W. MOLENAAR (1997), A multidimensional item response model: constrained latent class analysis using the Gibbs sampler and posterior predictive checks, Psychometrika 62, 171-190.
15. MENG, X. (1994), Posterior predictive p-values, The Annals of Statistics 22, 1142-1160.
16. RITOV, Y. and Z. GILULA (1993), Analysis of contingency tables by correspondence models subject to order constraints, Journal of the American Statistical Association 88, 1380-1387.
17. RUBIN, D. B. (1984), Bayesianly justifiable and relevant frequency calculations for the applied statistician, The Annals of Statistics 12, 1151-1172.
18. RUBIN, D. B. and H. S. STERN (1994), Testing in latent class models using a posterior predictive check distribution, in: A. VON EYE and C. CLOGG (eds), Latent variable analysis: applications for developmental research, Sage, California, 420-430.
19. SHAPIRO, A. (1985), Asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints, Biometrika 72, 133-144.
20. VAN ONNA, M. (2002), Bayesian estimation and model selection in ordered latent class models for polytomous IRT models, Psychometrika 67, 519-538.
21. VERMUNT, J. K. (1999), Nonparametric models for ordinal data, Sociological Methodology 29, 187-223.
22. VERMUNT, J. K. (2001), The use of restricted latent class models for defining and testing nonparametric and parametric item response theory models, Applied Psychological Measurement 25, 283-294.