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Informative Hypotheses

Methodological papers


  • Hoijtink, H., Gu, X., & Mulder, J. (2019). Bayesian evaluation of informative hypotheses for multiple populations. British Journal of Mathematical and Statistical Psychology72(2), 219-243. doi: 10.1111/bmsp.12145
  • Hoijtink, H., Gu, X., Mulder, J., & Rosseel, Y. (2019). Computing Bayes factors from data with missing values. Psychological Methods24(2), 253-268. doi: 10.1037/met0000187


  • Böing-Messing, F., & Mulder, J. (2018). Automatic Bayes factors for testing equality- and inequality-constrained hypotheses on variances. Psychometrika83(3), 586-617. doi: 10.1007/s11336-018-9615-z
  • Gu, X., Mulder, J., & Hoijtink, H. (2018). Approximated adjusted fractional Bayes factors: A general method for testing informative hypotheses. British Journal of Mathematical and Statistical Psychology71(2), 229-261. doi: 10.1111/bmsp.12110


  • Böing-Messing, F., van Assen, M. A. L. M., Hofman, A. D., Hoijtink, H., & Mulder, J. (2017). Bayesian evaluation of constrained hypotheses on variances of multiple independent groups. Psychological Methods22(2), 262-287. doi: 10.1037/met0000116


  • Gu. X.. Hoijtink, H., and Mulder, J. (2016). Error probabilities in default Bayesian hypothesis testing. Journal of Mathematical Psychology, 72, 130-143. doi:10.1016/j.jmp.2015.09.001 

  • Hoijtink, H. van Kooten, P., and Hulsker, K. (2016). Bayes factors have frequency properties. This should not be ignored. A rejoinder to Morey, Wagenmakers and Rouder. Multivariate Behavioral Research, 51, 20-22. doi: 10.1080/00273171.2015.1071705

  • Hoijtink, H., van Kooten, P., and Hulsker, K. (2016). Why Bayesian psychologists should change the way they use the Bayes factor. Multivariate Behavioral Research, 51, 2-10. doi: 10.1080/00273171.2014.969364


  • Böing-Messing, F. & Mulder J. (2016). Automatic Bayes Factors for Comparing Variances of Two Independent Normal Distributions. Journal of Mathematical Psychology, 72, 170. doi:10.1016/j.jmp.2015.08.001

  • Mulder, J. (2016). Bayes Factors for Testing Order-Constrained Hypotheses on Correlations. Journal of Mathematical Psychology, 72, 104-115. doi:10.1016/j.jmp.2014.09.004

  • Kuiper, R. M., Nederhoff, T., & Klugkist, I. (2015). Properties of hypothesis testing techniques and (Bayesian) model selection for exploration‐based and theory‐based (order‐restricted) hypotheses. British Journal of Mathematical and Statistical Psychology, 68(2), 220-245. doi: 10.1111/bmsp.12041
  • Okada, K. (2015). Bayesian meta-analysis of Cronbach’s coefficient alpha to evaluate informative hypotheses. Research Synthesis Methods. doi: 10.1002/jrsm.1155
  • Tijmstra, J., Hoijtink, H., and Sijtsma, K. (2015). Evaluating manifest monotonicity using Bayes factors. Psychometrika, 80, 880-896. doi: 10.1007/s11336-015-9475-8


  • Baayen, C., & Klugkist, I. (2014). Evaluating order-constrained hypotheses for circular data from a between-within subjects design. Psychological Methods,19(3), 398-408. doi: 10.1037/a0037414
  • Gu, X., Mulder, J., Dekovic, M., and Hoijtink, H. (2014). Bayesian evaluation of inequality constrained hypotheses. Psychological Methods, 19(4). doi: 10.1037/met0000017
  • Klugkist, I., Post, L., Haarhuis, F., & van Wesel, F. (2014). Confirmatory methods, or huge samples, are required to obtain power for the evaluation of theories. Open Journal of Statistics, 4, 710-725. doi: 10.4236/ojs.2014.49066 (open access)
  • Mulder, J. (2014). Bayes factors for testing inequality constrained hypotheses: Issues with prior specification. British Journal of Mathematical and Statistical Psychology, 67(1), 153-171. doi: 10.1111/bmsp.12013 (open access)
  • Mulder, J. (2014). Prior adjusted default Bayes factors for testing inequality constrained hypotheses. Computational Statistics and Data Analysis, 71, 448–463. doi: 10.1016/j.csda.2013.07.017


  • Hoijtink, H. (2013). Objective Bayes Factors for Inequality Constrained Hypotheses. International Statistical Review, 81, 207-229. doi: 10.1111/insr.12010
  • Hoijtink, H., Beland, S., & Vermeulen, J. (2013). Cognitive diagnostic assessment via Bayesian evaluation of informative diagnostic hypotheses. Psychological Methods. doi: 10.1037/a0034176
  • Kuiper, R. M., Gerhard, D., & Hothorn, L. A. (2013). Identification of the minimum effective dose for normally distributed endpoints using a model Selection approach. Statistics in Biopharmaceutical Research, 5. doi: 10.1080/19466315.2013.847384
  • Kuiper, R. M., & Hoijtink, H. (2013). A Fortran 90 program for the generalization of the order-restricted information criterion. Journal of Statistical Software, 54(8), 1-19. [File] (open access)
  • Kuiper, R. M., Buskens, V., Raub, W., & Hoijtink, H. (2013). Combining statistical evidence from several studies: Positive past effects on trust. Sociological Methods and Research, 42(1), 60-81. doi: 10.1177/0049124112464867
  • Mulder, J. & Fox, J.P. (2013). Bayesian tests for variance components in a compound symmetry covariance structure. Statistics and Computing, 23(1), 109-122. doi: 10.1007/s11222-011-9295-3 (open access)
  • Van Rossum, M., van de Schoot, R. & Hoijtink, H. (2013). `Is the hypothesis correct’ or `Is it not’? Bayesian evaluation of one informative hypothesis in ANOVA. Methodology, 9(1), 13-22. doi: 10.1027/1614-2241/a000050 (open access)
    The WinBugs syntax supplemental to this article can be downloaded here.


  • Klugkist, I., Bullens, J. & Postma, A. (2012). Evaluating order constrained hypotheses for circular data using permutation tests. British Journal of Mathematical and Statistical Psychology, 65, 222-236. doi: 10.1111/j.2044-8317.2011.02018.x
  • Kuiper, R. M., Hoijtink, H. and Silvapulle, M. J. (2012). Generalization of the order-restricted information criterion for multivariate normal linear models. Journal of Statistical Planning and Inference, 142, 2454-2463. doi: 10.1016/j.jspi.2012.03.007
  • Mulder, J., Hoijtink, H., & de Leeuw, C. (2012). BIEMS: A Fortran 90 program for calculating Bayes factors for inequality and equality constrained models. Journal of Statistical Software, 46(2). [File] (open access)
  • Van de Schoot, R., Hoijtink, H., Hallquist, M. N., & Boelen, P.A. (2012). Bayesian Evaluation of inequality-constrained Hypotheses in SEM Models using Mplus. Structural Equation Modeling,19:1–17, 2012. doi: 10.1080/10705511.2012.713267.


  • Kuiper, R. M., Hoijtink, H., & Silvapulle, M. J. (2011). An Akaike type information criterion for model selection under inequality constraints. Biometrika, 98, 495-501. doi:=10.1093/biomet/asr002
  • Van de Schoot, R., Hoijtink, H., Romeijn, J-W & Brugman, D. (2011). A prior predictive loss function for the evaluation of inequality constrained hypotheses. Journal of Mathematical  Psychology, 56, 13-23. doi:10.1016/j.jmp.2011.10.001
  • Van de Schoot, R. & Strohmeier, D. (2011). Testing informative hypotheses in SEM increases power: An illustration contrasting classical hypothesis testing with a parametric bootstrap approach. International Journal of Behavioral Development, 35: 180-190. doi:10.1177/0165025410397432


  • Kuiper, R. M., Klugkist, I. & Hoijtink, H. (2010). A Fortran 90 program for confirmatory analysis of variance. Journal of Statistical Software, 34 (8), 1-31. doi: 10.18637/jss.v034.i08
  • Kuiper, R. M., & Hoijtink, H. (2010). Comparisons of means using exploratory and confirmatory approaches. Psychological Methods, 15, 69-86. doi: 10.1037/a0018720
  • Klugkist, I., Laudy, O. & Hoijtink, H. (2010). Bayesian evaluation of inequality and equality constrained hypotheses for contingency tables. Psychological Methods, 15, 281-299doi: 10.1037/a0020137
  • Mulder, J., Hoijtink, H. & Klugkist, I. (2010). Equality and inequality constrained multivariate linear models: objective model selection using constrained posterior priors. Journal of Statistical Planning and Inference, 140, 887-906. doi: 10.1016/j.jspi.2009.09.022
  • Van de Schoot, R., Hoijtink, H., & Dekovic, M. (2010). Testing inequality constrained hypotheses in SEM models. Structural Equation Modeling, 17, 443–463. doi: 10.1080/10705511.2010.489010


  • Hoijtink, H. (2009). Bayesian Data Analysis. In R.E. Millsap and A. Maydeu-Olivares. The SAGE Handbook of Quantitave Methods in Psychology. London: Sage.
  • Mulder, J., Klugkist, I., van de Schoot, R., Meeus, W., Selfhout, M. & Hoijtink, H. (2009). Bayesian model selection of informative hypotheses for repeated measurements. Journal of Mathematical Psychology, 53,530-546. doi: 10.1016/j.jmp.2009.09.003
  • Van de Schoot, R., Hoijtink, H. & Doosje, S. (2009). Rechtstreeks verwachtingen evalueren of de nul hypothese toetsen? Nul hypothese toetsing versus Bayesiaanse model selectie. De Psycholoog 4, 196-203. [Link] (full text)
  • Van Deun, K., Hoijtink, H., Thorrez, L., van Lommel, L., Schuit, F., van Mechelen, I. (2009). Testing the hypothesis of tissue-selectivity: The Intersection-Union Test and a Bayesian approach. Bioinformatics, 25,2588-2594doi: 10.1093/bioinformatics/btp439 (open access)


  • Hoijtink, H. (2007). De analyse van empirische data met behulp van informatieve hypothesen. Stator, 8 (2), 4-7. [File] (open access)
  • Hoijtink, H.  & Klugkist, I. (2007). Comparison of hypothesis testing and Bayesian model selection. Quality and Quantity, 41, 73-91. doi: 10.1007/s11135-005-6224-6
  • Klugkist, I., & Hoijtink, H. (2007). The Bayes factor for inequality and about equality constrained models. Computational Statistics and Data Analysis, 51, 6367-6379. doi: 10.1016/j.csda.2007.01.024
  • Laudy, O.,  & Hoijtink, H. (2007). Bayesian methods for the analysis of inequality constrained contingency tables. Statistical Methods in Medical Research, 16, 123-138. doi: 10.1177/0962280206071925


  • Kato, B.S. and Hoijtink, H. (2006). A Bayesian approach to inequality constrained linear mixed models: estimation and model selection. Statistical Modelling, 6, 231-249. doi: 10.1191/1471082X06st119oa


  • Hoijtink, H. (2005). Beter een goed verhaal dan de hele waarheid. In: A.E. Bronner, P. Dekker, E. de Leeuw, K. de Ruyter, A. Smidts en J.E. Wieringa, Ontwikkelingen in het martkonderzoek, pp. 201-212. Haarlem, De Vrieseborch. [Link] (full text)
  • Klugkist, I., Laudy, O. and Hoijtink, H. (2005). Inequality constrained analysis of variance: A Bayesian approach. Psychological Methods, 10, 477-493. doi: 10.1037/1082-989X.10.4.477
  • Klugkist, I., Laudy, O. and Hoijtink, H. (2005). Bayesian eggs and Bayesian omelettes. Psychological Methods, 10, 500-503. doi: 10.1037/1082-989X.10.4.500
  • Klugkist, I., Kato, B. and Hoijtink, H. (2005). Bayesian model selection using encompassing priors. Statistica Neerlandica, 59, 57-69. [Link] (full text)


  • Laudy, O., Boom, J. and Hoijtink, H. (2004). Bayesian computational methods for inequality constrained latent class analysis. In: A. van der Ark, M. Croon and K. Sijtsma. New developments in categorical data analysis for the social and behavioral sciences. Mahwah, N.J.: Erlbaum. [LInk] (full text)


  • Hoijtink, H. (2001). Confirmatory latent class analysis: model selection using Bayes factors and (pseudo) likelihood ratio statistics. Multivariate Behavioral Research, 36, 563-588. doi: 10.1207/S15327906MBR3604_04 


  • Hoijtink, H. (1998). Constrained latent class analysis using the Gibbs sampler and posterior predictive p-values: Applications to educational testing. Statistica Sinica, 8, 691-712. [Link] (full text)


  • Hoijtink, H. and Molenaar I.W. (1997). A multidimensional item response model: Constrained latent class analysis using the Gibbs sampler and posterior predictive checks. Psychometrika, 62, 171-190. doi: 10.1007/BF02295273