Observation oriented modeling revised from a statistical point of view
Observation Oriented Modeling was proposed to overcome some of the problems in the application of statistical inference methods in the behavioral sciences. In this paper, we refine one part of this approach and show how it is connected to methods that are well known in statistical learning. Specifically, we argue that the Moore-Penrose pseudo inverse is superior to the initial solution from a statistical point of view. With this we also show that Observation Oriented Modeling can indeed be appropriate for some tasks in the analysis of observed data. To provide a practical example, we demonstrate the revised method by analyzing the effect of mindfulness training on attentional processes.
KeywordsStatistical inference Statistical modeling Observation oriented modeling Mindfulness
Karsten Luebke developed the mathematical framework of this paper. He also wrote substantial parts of this paper. Without his efforts, this work would not have appeared. Unfortunately, limited time ressources did not allow him to finalize the work on this paper; so he decided that he would not appear as author. I am deeply thankful for his contribution. I thankfully acknowledge Jana Lemke who collected the data. Christian Roever and Jane Zagorski provided helpful comments on an earlier draft of the manuscript. I also thank the editor and the reviewers for their constructive comments.
- Agresti, A. (2003). Categorical data analysis, 2nd Edn. Hoboken, NJ: John Wiley & Sons, Inc.Google Scholar
- Analytics, R. (2015). Checkpoint: Install packages from snapshots on the checkpoint server for reproducibility. Retrieved from https://CRAN.R-project.org/package=checkpoint.
- Aronson, E., Wilson, T.D., & Sommers, S.R. (2015). Social psychology. New York City: Pearson.Google Scholar
- Auguie, B. (2015). GridExtra: Miscellaneous functions for grid graphics. Retrieved from https://CRAN.R-project.org/package=gridExtra.
- Aust, F., & Barth, M. (2016). Papaja: Create apa manuscripts with rmarkdown. Retrieved from https://github.com/crsh/papaja.
- Ben-Israel, A., & Greville, T.N. (2003). Generalized inverses: Theory and applications (Second.) New York: Springer.Google Scholar
- Craig, D.P.A., Varnon, C.A., Sokolowski, M.B.C., Wells, H., & Abramson, C.I. (2014). An assessment of fixed interval timing in free-flying honey bees: An analysis of individual performance. PLoS ONE, 9, e101262. Retrieved from https://doi.org/10.1371%2Fjournal.pone.0101262.CrossRefPubMedPubMedCentralGoogle Scholar
- Dahl, D.B. (2014). Xtable: Export tables to latex or html. Retrieved from https://CRAN.R-project.org/package=xtable.
- Dinges, C.W., Avalos, A., Abramson, C.I., Craig, D.P.A., Austin, Z.M., Varnon, C.A., & Wells, H. (2013). Aversive conditioning in honey bees (apis mellifera anatolica): A comparison of drones and workers. Journal of Experimental Biology, 216(21), 4124–4134. https://doi.org/10.1242/jeb.090100.CrossRefPubMedGoogle Scholar
- Dougherty, J., Kohavi, R., & Sahami, M. (1995). Supervised and unsupervised discretization of continuous features. In Machine learning: Proceedings of the twelfth international conference, (Vol. 12 pp. 194–202).Google Scholar
- Edgington, E., & Onghena, P. (2007). Randomization tests. Boca Raton, FL: CRC Press.Google Scholar
- Efron, B., & Gong, G. (1983). A leisurely look at the bootstrap, the jackknife, and cross-validation. The American Statistician, 37(1), 36–48.Google Scholar
- Fisher, R.A. (1935). The design of experiments. Oliver & Boyd: Edinburgh.Google Scholar
- Fox, J., & Weisberg, S. (2015). Car: Companion to applied regression. Retrieved from https://CRAN.R-project.org/package=car.
- Grice, J.W. (2011). Observation oriented modeling: Analysis of cause in the behavioral sciences. Cambridge, MA: Academic Press.Google Scholar
- Grice, J.W. (2015). From means and variances to persons and patterns. Frontiers in Psychology, 6. https://doi.org/10.3389/fpsyg.2015.01007.
- Grice, J.W., Craig, D.P.A., & Abramson, C.I. (2015b). A simple and transparent alternative to repeated measures anova. SAGE Open, 5(3). https://doi.org/10.1177/2158244015604192.
- Grice, J.W., Yepez, M., Wilson, N.L., & Shoda, Y. (2016). Observation-oriented modeling going beyond; is it all a matter of chance?. Educational and Psychological Measurement, 0013164416667985.Google Scholar
- Gu, J., Strauss, C., Bond, R., & Cavanagh, K. (2015). How do Mindfulness-Based Cognitive Therapy and Mindfulness-Based Stress Reduction Improve Mental Health and Wellbeing? A Systematic Review and Meta-Analysis of Mediation Studies. Clinical Psychology Review, 37, 1–12. https://doi.org/10.1016/j.cpr.2015.01.006.CrossRefPubMedGoogle Scholar
- Kabat-Zinn, J. (2003). Mindfulness-Based Interventions in context: past, Present, and Future. Clinical Psychology: Science & Practice, 10(2), 144–156.Google Scholar
- Labatut, V., & Cherifi, H. (2012). Accuracy measures for the comparison of classifiers. CoRR, abs/1207.3790. Retrieved from arXiv:1207.3790.
- Levine, M., Cassidy, C., Brazier, G., & Reicher, S. (2002). Self-categorization and Bystander Non-intervention: Two Experimental Studies1. Journal of Applied Social Psychology, 32 (7), 1452–1463. https://doi.org/10.1111/j.1559-1816.2002.tb01446.x.CrossRefGoogle Scholar
- Michell, J. (1997). Quantitative science and the definition of measurement in psychology. British Journal of Psychology, 88(3), 355–383. https://doi.org/10.1111/j.2044-8295.1997.tb02641.x.CrossRefGoogle Scholar
- Neyman, J., & Pearson, E.S. (1966). Joint statistical papers. Berkeley: Univ of California Press.Google Scholar
- Piet, J., & Hougaard, E. (2011). The effect of mindfulness-based cognitive therapy for prevention of relapse in recurrent major depressive disorder: a systematic review and meta-analysis. Clinical Psychology Review, 31(6), 1032–40. https://doi.org/10.1016/j.cpr.2011.05.002.CrossRefPubMedGoogle Scholar
- R Core Team (2015). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from http://www.r-project.org/.
- Sauer, S., & Luebke, K. (2017a). Data for paper? Observation oriented modeling revised from a statistical point of view? Open Science Framework. https://doi.org/10.17605/OSF.IO/SGZYD.
- Sauer, S., & Luebke, K. (2017b). R-code for paper? Observation oriented modeling revised from a statistical point of view? Open Science Framework. https://doi.org/10.17605/OSF.IO/U3NQ9.
- Simpson, E.H. (1951). The interpretation of interaction in contingency tables. Journal of the Royal Statistical Society. Series B (Methodological), 13(2), 238–241.Google Scholar
- Stemmler, M. (2014). Person-centered methods. Springer International Publishing. https://doi.org/10.1007/978-3-319-05536-7.
- Szepannek, G., Luebke, K., & Weihs, C. (2005). Understanding patterns with different subspace classification. In Machine learning and data mining in pattern recognition (pp. 110–119). New York City: Springer.Google Scholar
- Venables, W.N., & Ripley, B.D. (2013). Modern Applied Statistics with S-PLUS. New York City: Springer. Retrieved from https://books.google.de/books?id=tovgBwAAQBAJ.
- Wassenhove, V., van Wittmann, M., Craig, D.P.A., & Paulus, M.P. (2011). Psychological and neural mechanisms of subjective time dilation. Frontiers in Neuroscience, 5.Google Scholar
- Wickham, H. (2015). Tidyr: Easily tidy data with ‘spread()‘ and ‘gather()‘ functions. Retrieved from https://CRAN.R-project.org/package=tidyr.
- Wickham, H., & Chang, W. (2015). Ggplot2: An implementation of the grammar of graphics. Retrieved from https://CRAN.R-project.org/package=ggplot2.
- Wickham, H., & Francois, R. (2015). Dplyr: A grammar of data manipulation. Retrieved from https://CRAN.R-project.org/package=dplyr.
- Ziliak, S.T., & McCloskey, D.N. (2008). The cult of statistical significance: How the standard error costs us jobs, justice and lives. Ann Arbor, MI: University of Michigan Press.Google Scholar