Constrained statistical inference: Sample-size tables for ANOVA and regression

Frontiers in Psychology

Volumn 5, Issue OCT, 2014, Pages

  Vanbrabant, Leonard ^a,b   Van De Schoot, Rens ^b,c   Rosseel, Yves ^a  

^a GHENT UNIVERSITY   (Belgium)

^b UTRECHT UNIVERSITY   (Netherlands)

^c NORTH WEST UNIVERSITY   (South Africa)

Author keywords

F bar test statistic; Inequality order constraints; Linear model; Power; Sample size tables

Indexed keywords

EID: 84926653588     PISSN: None     EISSN: 16641078     Source Type: Journal    
DOI: 10.3389/fpsyg.2014.01565     Document Type: Article

References (33)

1. Barlow, R. E., Bartholomew, D. J., Bremner, H. M., and Brunk, H. D. (1972). Statistical Inference Under Order Restrictions. New York, NY: Wiley.
2. Bartholomew, D. (1959a). A test of homogeneity for ordered alternatives. Biometrika 46, 36-48.
3. Bartholomew, D. (1959b). A test of homogeneity for ordered alternatives. II. Biometrika 46, 328-335.
4. Bartholomew, D. (1961a). Ordered tests in the analysis of variance. Biometrika 48, 325-332.
5. Bartholomew, D. (1961b). A test of homogeneity of means under restricted alternatives. J. R. Stat. Soc. B 23, 239-281.
6. Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences, 2nd Edn. Hillsdale, NJ: Erlbaum.
7. Davis, K. (2012). Constrained statistical inference: a hybrid of statistical theory, projective geometry and applied optimization techniques. Prog. Appl. Math. 4, 167-181.
8. Gouriéroux, C., Holly, A., and Monfort, A. (1982). Likelihood ratio test, wald test, and kuhn-tucker test in linear models with inequality constraints on the regression parameters. Econometrica 50, 63-80.
9. Grömping, U. (2010). Inference with linear equality and inequality constraints using R: the package ic.infer. J. Stat. Softw. 33, 1-31.
10. Hoijtink, H. (2012). Informative Hypotheses: Theory and Practice for Behavioral and Social Scientists. Boca Raton, FL: Taylor & Francis.
11. Kim, D., and Taylor, J. (1995). The restricted EM algorithm for maximum likelihood estimation under linear restrictions on the parameters. J. Am. Stat. Assoc. 90, 708-716.
12. Kudô, A. (1963). A multivariate analogue of the one-sided test. Biometrika 50, 403-418.
13. Kudô, A., and Choi, J. (1975). A generalized multivariate analogue of the one sided test. Mem. Facul. Sci. 29, 303-328. doi: 10.2206/kyushumfs.29.303.
14. Kuiper, R., and Hoijtink, H. (2010). Comparisons of means using exploratory and confirmatory approaches. Psychol. Methods 15, 69-86. doi: 10.1037/a0018720.
15. Kuiper, R., Klugkist, I., and Hoijtink, H. (2010). A Fortran 90 program for confirmatory analysis of variance. J. Stat. Softw. 34, 1-31.
16. Kuiper, R., Nederhoff, T., and Klugkist, I. (2011). Performance and Robustness of Confirmatory Approaches. Available online at: http://vkc.library.uu.nl/vkc/ms/SiteCollectionDocuments/Herbert/book%20unpublished/Kuiper, %20Nederhoff%20and%20Klugkist.pdf.
17. Nüesch, P. (1966). On the problem of testing location in multivariate populations for restricted alternatives. Ann. Math. Stat. 37, 113-119.
18. Perlman, M. (1969). One-sided testing problems in multivariate analysis. Ann. Math. Stat. 40, 549-567.
19. R Development Core Team (2012). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing.
20. Robertson, T., Wright, F. T., and Dykstra, R. L. (1988). Order Restricted Statistical Inference. New York, NY: Wiley.
21. SAS Institute Inc. (2012). SAS/STAT® 12.1 User's Guide. Cary, NC: SAS Institute Inc.
22. Shi, N., Zheng, S., and Guo, J. (2005). The restricted EM algorithm under inequality restrictions on the parameters. J. Multivariate Anal. 92, 53-76. doi: 10.1016/S0047-259X(03)00134-9.
23. Silvapulle, M., and Sen, P. (2005). Constrained Statistical Inference: Order, Inequality, and Shape Constraints. Hoboken, NJ: Wiley.
24. Silvapulle, M. (1992a). Robust tests of inequality constraints and one-sided hypotheses in the linear model. Biometrika 79, 621-630.
25. Silvapulle, M. (1992b). Robust wald-type tests of one-sided hypotheses in the linear model. J. Am. Stat. Assoc. 87, 156-161.
26. Silvapulle, M. (1996). On an F-type statistic for testing one-sided hypotheses and computation of chi-bar-squared weights. Stat. Probab. Lett. 28, 137-141.
27. Turlach, B., and Weingessel, A. (2013). Quadprog: Functions to Solve Quadratic Programming Problems (version 1.5-5). Available online at: http://cran.r-project.org/web/packages/quadprog/quadprog.pdf.
28. Van De Schoot, R., and Strohmeier, D. (2011). Testing informative hypotheses in SEM increases power: an illustration contrasting classical hypothesis testing with a parametric bootstrap approach. Int. J. Behav. Dev. 35, 180-190. doi: 10.1177/0165025410397432.
29. Van De Schoot, R., Hoijtink, H., and Dekovic, M. (2010). Testing inequality constrained hypotheses in SEM models. Struct. Equ. Model. 17, 443-463. doi: 10.1080/10705511.2010.489010.
30. Wolak, F. (1987). An exact test for multiple inequality and equality constraints in the linear regression model. J. Am. Stat. Assoc. 82, 782-793.
31. Wolak, F. (1989). Testing inequality constraints in linear econometric models. J. Econom. 41, 205-235.
32. Yancey, T., Judge, G., and Bock, M. (1981). Testing multiple equality and inequality hypothesis is economics. Econ. Lett. 7, 249-255.
33. Zheng, S., Shi, N., and Guo, J. (2005). The restricted EM algorithm under linear inequalities in a linear model with missing data. Sci. China Ser. A 48, 819-828. doi: 10.1360/03ys0275.