IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v86y2021i2d10.1007_s11336-021-09769-y.html
   My bibliography  Save this article

Bayesian Analysis of ANOVA and Mixed Models on the Log-Transformed Response Variable

Author

Listed:
  • Aldo Gardini

    (Università di Bologna)

  • Carlo Trivisano

    (Università di Bologna)

  • Enrico Fabrizi

    (Università Cattolica del S. Cuore)

Abstract

The analysis of variance, and mixed models in general, are popular tools for analyzing experimental data in psychology. Bayesian inference for these models is gaining popularity as it allows to easily handle complex experimental designs and data dependence structures. When working on the log of the response variable, the use of standard priors for the variance parameters can create inferential problems and namely the non-existence of posterior moments of parameters and predictive distributions in the original scale of the data. The use of the generalized inverse Gaussian distributions with a careful choice of the hyper-parameters is proposed as a general purpose option for priors on variance parameters. Theoretical and simulations results motivate the proposal. A software package that implements the analysis is also discussed. As the log-transformation of the response variable is often applied when modelling response times, an empirical data analysis in this field is reported.

Suggested Citation

  • Aldo Gardini & Carlo Trivisano & Enrico Fabrizi, 2021. "Bayesian Analysis of ANOVA and Mixed Models on the Log-Transformed Response Variable," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 619-641, June.
  • Handle: RePEc:spr:psycho:v:86:y:2021:i:2:d:10.1007_s11336-021-09769-y
    DOI: 10.1007/s11336-021-09769-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-021-09769-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11336-021-09769-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Enrico Fabrizi & Maria Rosaria Ferrante & Carlo Trivisano, 2018. "Bayesian small area estimation for skewed business survey variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(4), pages 861-879, August.
    2. Enrico Fabrizi & Carlo Trivisano, 2016. "Bayesian Conditional Mean Estimation in Log-Normal Linear Regression Models with Finite Quadratic Expected Loss," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1064-1077, December.
    3. Crainiceanu, Ciprian M. & Ruppert, David & Wand, Matthew P., 2005. "Bayesian Analysis for Penalized Spline Regression Using WinBUGS," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i14).
    4. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    5. Charness, Gary & Gneezy, Uri & Kuhn, Michael A., 2012. "Experimental methods: Between-subject and within-subject design," Journal of Economic Behavior & Organization, Elsevier, vol. 81(1), pages 1-8.
    6. Enrico Fabrizi & Carlo Trivisano, 2011. "Bayes estimators of log-normal means with finite quadratic expected loss," Quaderni di Dipartimento 6, Department of Statistics, University of Bologna.
    7. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "On the stick–breaking representation of normalized inverse Gaussian priors," DEM Working Papers Series 008, University of Pavia, Department of Economics and Management.
    8. Gerard Breukelen, 2005. "Psychometric Modeling of response speed and accuracy with mixed and conditional regression," Psychometrika, Springer;The Psychometric Society, vol. 70(2), pages 359-376, June.
    9. Jeffrey Rouder & Jordan Province & Richard Morey & Pablo Gomez & Andrew Heathcote, 2015. "The Lognormal Race: A Cognitive-Process Model of Choice and Latency with Desirable Psychometric Properties," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 491-513, June.
    10. S. Favaro & A. Lijoi & I. Prünster, 2012. "On the stick-breaking representation of normalized inverse Gaussian priors," Biometrika, Biometrika Trust, vol. 99(3), pages 663-674.
    11. T. Loeys & Y. Rosseel & K. Baten, 2011. "A Joint Modeling Approach for Reaction Time and Accuracy in Psycholinguistic Experiments," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 487-503, July.
    12. repec:dau:papers:123456789/1908 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Aldo Gardini & Enrico Fabrizi & Carlo Trivisano, 2022. "Poverty and inequality mapping based on a unit‐level log‐normal mixture model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 2073-2096, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Maria Bolsinova & Paul Boeck & Jesper Tijmstra, 2017. "Modelling Conditional Dependence Between Response Time and Accuracy," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1126-1148, December.
    2. Gabriel Riutort-Mayol & Virgilio Gómez-Rubio & José Luis Lerma & Julio M. del Hoyo-Meléndez, 2020. "Correlated Functional Models with Derivative Information for Modeling Microfading Spectrometry Data on Rock Art Paintings," Mathematics, MDPI, vol. 8(12), pages 1-25, December.
    3. Aldo Gardini & Enrico Fabrizi & Carlo Trivisano, 2022. "Poverty and inequality mapping based on a unit‐level log‐normal mixture model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 2073-2096, October.
    4. Fang Liu & Xiaojing Wang & Roeland Hancock & Ming-Hui Chen, 2022. "Bayesian Model Assessment for Jointly Modeling Multidimensional Response Data with Application to Computerized Testing," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1290-1317, December.
    5. Ederer, Florian & Stremitzer, Alexander, 2017. "Promises and expectations," Games and Economic Behavior, Elsevier, vol. 106(C), pages 161-178.
    6. Kazi Iqbal & Asad Islam & John List & Vy Nguyen, 2021. "Myopic Loss Aversion and Investment Decisions: From the Laboratory to the Field," Framed Field Experiments 000730, The Field Experiments Website.
    7. Francis,David C. & Kubinec ,Robert, 2022. "Beyond Political Connections : A Measurement Model Approach to Estimating Firm-levelPolitical Influence in 41 Economies," Policy Research Working Paper Series 10119, The World Bank.
    8. Martinovici, A., 2019. "Revealing attention - how eye movements predict brand choice and moment of choice," Other publications TiSEM 7dca38a5-9f78-4aee-bd81-c, Tilburg University, School of Economics and Management.
    9. Yongping Bao & Ludwig Danwitz & Fabian Dvorak & Sebastian Fehrler & Lars Hornuf & Hsuan Yu Lin & Bettina von Helversen, 2022. "Similarity and Consistency in Algorithm-Guided Exploration," CESifo Working Paper Series 10188, CESifo.
    10. Heinrich, Torsten & Yang, Jangho & Dai, Shuanping, 2020. "Growth, development, and structural change at the firm-level: The example of the PR China," MPRA Paper 105011, University Library of Munich, Germany.
    11. Alexandre Rodrigues & Peter Diggle & Renato Assuncao, 2010. "Semiparametric approach to point source modelling in epidemiology and criminology," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(3), pages 533-542, May.
    12. van Kesteren Erik-Jan & Bergkamp Tom, 2023. "Bayesian analysis of Formula One race results: disentangling driver skill and constructor advantage," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 19(4), pages 273-293, December.
    13. Jonas Schmidt & Tammo H. A. Bijmolt, 2020. "Accurately measuring willingness to pay for consumer goods: a meta-analysis of the hypothetical bias," Journal of the Academy of Marketing Science, Springer, vol. 48(3), pages 499-518, May.
    14. Xin Xu & Yang Lu & Yupeng Zhou & Zhiguo Fu & Yanjie Fu & Minghao Yin, 2021. "An Information-Explainable Random Walk Based Unsupervised Network Representation Learning Framework on Node Classification Tasks," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    15. Jie, Yun, 2020. "Responding to requests for help: Effects of payoff schemes with small monetary units," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 88(C).
    16. Erin E. Gabriel & Michael J. Daniels & M. Elizabeth Halloran, 2016. "Comparing biomarkers as trial level general surrogates," Biometrics, The International Biometric Society, vol. 72(4), pages 1046-1054, December.
    17. Aksoy, Billur & Chadd, Ian & Koh, Boon Han, 2023. "Sexual identity, gender, and anticipated discrimination in prosocial behavior," European Economic Review, Elsevier, vol. 154(C).
    18. Sarah Brown & Pulak Ghosh & Bhuvanesh Pareek & Karl Taylor, 2017. "Financial Hardship and Saving Behaviour: Bayesian Analysis of British Panel Data," Working Papers 2017011, The University of Sheffield, Department of Economics.
    19. Xiaoyue Xi & Simon E. F. Spencer & Matthew Hall & M. Kate Grabowski & Joseph Kagaayi & Oliver Ratmann & Rakai Health Sciences Program and PANGEA‐HIV, 2022. "Inferring the sources of HIV infection in Africa from deep‐sequence data with semi‐parametric Bayesian Poisson flow models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(3), pages 517-540, June.
    20. Kuschnig, Nikolas, 2021. "Bayesian Spatial Econometrics and the Need for Software," Department of Economics Working Paper Series 318, WU Vienna University of Economics and Business.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:86:y:2021:i:2:d:10.1007_s11336-021-09769-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.