Informative Hypotheses

Tutorial papers

The papers listed here can serve as tutorials for researchers who want to learn about the use of informative hypotheses evaluation without diving too deep in all technical details. In most of these papers illustrative data, mainly from the social or behavioural sciences, play an important role.

How to Use the R package/JASP module bain

  • Hoijtink, H., Mulder, J., van Lissa, C., and Gu, X. (2019). A tutorial on testing hypotheses using the Bayes factor. Psychological Methods, 24, 539-556. DOI: 10.1037/met0000201 CLICK HERE to obtain BFTutorial.pdf, BFTutorial.R (using the named-object input to bain which shows some of its inner workings), EasyBFTutorial.R (using the lm-object input to bain which is easy to use)  and corresponding data sets. Also consult the vignette included with the R package bain for further instructions and examples.

    Teacher’s Corner: Evaluating Informative Hypotheses Using the Bayes Factor in Structural Equation Models. CLICK HERE to download Van Lissa, C., Gu, X., Mulder, J., Rosseel, Y., van Zundert, C. and Hoijtink, H. (2020), Structural Equation Modelling, 28, 292-301. The examples discussed in this tutorial are contained in the vignette included with the R package bain.

How to Use the R function goric() in the restriktor package / in JASP



  • Rebecca Kuiper (2022). AIC-type Theory-Based Model Selection for Structural Equation Models, Structural Equation Modeling: A Multidisciplinary Journal, 29(1), 151-158, DOI: 10.1080/10705511.2020.1836967


  • Rebecca Kuiper (2021). Evaluating Causal Dominance of CTmeta-Analyzed Lagged Regression Estimates, Structural Equation Modeling: A Multidisciplinary Journal, 28(6), 951-963, DOI: 10.1080/10705511.2020.1823228
  • Altınısık, Y., Van Lissa, C. J., Hoijtink, H., Oldehinkel, A. J., and Kuiper, R. M. (2021). Evaluation of inequality constrained hypotheses using a generalization of the AIC. Psychological Methods, 26(5), 599-621. doi: 10.1037/met0000406


  • Vanbrabant, L., Van Loey, N., & Kuiper, R. M. (2020). Evaluating a Theory-Based Hypothesis Against Its Complement Using an AIC-Type Information Criterion With an Application to Facial Burn Injury. Psychological Methods25(2), 129-142.


  • Vanbrabant, L., Van de Schoot, R., Van Loey, N., & Rosseel, Y. (2017). A General Procedure for Testing Inequality Constrained Hypotheses in SEM. Methodology, 13(2), doi: 10.1027/1614-2241/a000123
  • Zondervan-Zwijnenburg, M. A. J., Van de Schoot, R., Johnson, A. R. (2017). Computing complexity for the Bayes Factor in inequality constrained hypotheses. doi: 10.17605/OSF.IO/5YT3J


  • Braeken, J., Mulder, J., & Wood, S. (2015). Relative effects at work: Bayes factors for order hypotheses. Journal of Management, 41, 511-573. doi:10.1177/0149206314525206

  • Konijn, E.A., Van de Schoot, R., Winter, S.D., & Ferguson, C.J. (2015). Possible solution to publication bias through Bayesian statistics, including proper null hypothesis testing. Communication Methods and Measures, 9(4), 280-302. doi: 10.1080/19312458.2015.1096332

  • Vanbrabant, L., Van de Schoot, R., & Rosseel, Y. (2015). Constrained statistical inference: Sample-size tables for ANOVA and regression. Frontiers in Psychology, 5(1565), 1-8. doi: 10.3389/fpsyg.2014.01565 (open access)


  • Van de Schoot, R., & Meeus W. (2014). Various positions on testing Inequality constrained hypotheses for LTA results. [Link] (open access)


  • Kuiper, R. M., & Hoijtink, H. (2013). A Fortran 90 program for the generalization of the order-restricted information criterion. Journal of Statistical Software54, 1-19.
  • Van de Schoot, R., Verhoeven, M., & Hoijtink, H. (2013). Bayesian evaluation of informative hypotheses in SEM using Mplus: A black bear story. European Journal of Developmental Psychology, 10, 81-98. doi: 10.1080/17405629.2012.732719[Link]


  • Baayen, C., Klugkist, I., Mechsner, F. (2012). A test of order constrained hypotheses for circular data with applications to human movement science. Journal of Motor Behavior, 44, 351-363 doi: 10.1080/00222895.2012.709549[Link]
  • Béland, S., Klugkist, I., Raîche, G., Magis, D. (2012). A short introduction into Bayesian evaluation of informative hypotheses as an alternative to exploratory comparisons of multiple group means. Tutorials in Quantitative Methods for Psychology, 8, 122-126. [Link]
  • Kluytmans, A., Van de Schoot, R., Mulder, J., & Hoijtink, H. (2012). Illustrating Bayesian evaluation of informative hypotheses for regression models. Frontiers in Psychology, 3(2). doi: 10.3389/fpsyg.2012.00002 (open access)[Link]


  • Finch, W. H., & Bronk, K. C. (2011). Conducting confirmatory latent class analysis using Mplus. Structural Equation Modeling: A Multidisciplinary Journal, 18, 132-151. doi: 10.1080/10705511.2011.532732.
  • Klugkist, I., Van wesel, F., Bullens, J. (2011). Do we know what we test and do we test what we want to know? International Journal of Behavioral Development, 35, 550-560. doi: 10.1177/0165025411425873[Link]
  • Van de Schoot, R., Mulder, J., Hoijtink, H., van Aken, M.A.G. , Dubas, J.S., de Castro, B. O., Meeus, W. & Romeijn, J.-W. (2011). An Introduction to Bayesian model selection for evaluating informative hypotheses. European Journal of Developmental Psychology, 8 (6), 713–729. doi:10.1080/17405629.2011.621799 (open access)[File]
  • 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[Link]
  • Van de Schoot, R., Hoijtink, H., & Romeijn, J-W (2011). Moving beyond traditional null hypothesis testing: Evaluating expectations directly. Frontiers in Quantitative Psychology and Measurement, 2:24. doi: 10.3389/fpsyg.2011.00024 (open access)[Link]
  • Van de Schoot, R., Hoijtink, H., Mulder, J., Van Aken, M. A. G., Orobio de Castro, B., Meeus, W. & Romeijn, J.-W. (2011). Evaluating expectations about negative emotional states of aggressive boys using Bayesian model selection. Developmental Psychology, 47, 203-212. doi: 10.1037/a0020957
  • Van de Schoot, R. (2011). Rechtstreeks verwachtingen evalueren of de nul hypothese toetsen? Stator, 2,22-24. doi: 10.2139/ssrn.1919023 (open access)


  • Kuiper, R. M., Klugkist, I. G., & Hoijtink, H. J. A. (2010). A Fortran 90 Program for Confirmatory Analysis of Variance. Journal of Statistical Software34(8), 1-31.


  • Van de Schoot, R., Hoijtink, H. & Doosje, S. (2009). Rechtstreeks verwachtingen evalueren of de nul hypothese toetsen? Nul hypothese toetsing versus Bayesiaanse model selectie. [Directly evaluating expectations or testing the null hypothesis: Null hypothesis testing versus Bayesian model selection]. De Psycholoog 4, 196-203[Link] (open access)


  • Romeijn, J. W. & Van de Schoot, R. (2008). A philosopher’s view on Bayesian evaluation of informative hypotheses. In H. Hoijtink, I. Klugkist, & P. Boelen (ed.). Bayesian evaluation of informative hypotheses (pp. 329-358). New-York: Springer. [Link] (open access)
  • Van de Schoot, R., & Hoijtink, H. (2008). Tutorial for inequality constrained latent class modeling (LCM version 1.0). [Link] (open access)