Skip to main content
SpringerLink
Log in

Bayesian reduced rank multigroup regression analysis: a new model for multigroup data with hybrid parameter sharing

  • Invited Paper
  • Published:
Behaviormetrika Aims and scope Submit manuscript

Abstract

In this paper, we develop a new multiple regression analysis method for multigroup data. The model enforces some rank conditions on the matrix with regression coefficient vectors, and thus enables a parsimonious representation of group characteristics. The technique used can be considered as a hybrid approach to soft and hard parameter sharing in multi-task learning.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Braun HI, Jones DH, Rubin DB, Thayer DT (1983) Empirical Bayes estimation of coefficients in the general linear model from data of deficient rank. Psychometrika 48(2):171–181

    Article  Google Scholar 

  • Davies PT (1982) Procedures for reduced-rank regression. Appl Stat 31:244–255

    Article  MathSciNet  Google Scholar 

  • Goh G, Dey DK, Chen K (2017) Bayesian sparse reduced rank multivariate regression. J Multivar Anal 157:14–28

    Article  MathSciNet  MATH  Google Scholar 

  • Izenman AJ (1975) Reduced-rank regression for the multivariate linear model. J Multivar Anal 5:248–264

    Article  MathSciNet  MATH  Google Scholar 

  • Kruskal JB (1981) Multilinear models for data analysis. Behaviormetrika 10:1–20

    Article  Google Scholar 

  • Lindley DV (1970) A Bayesian solution for some educational prediction problems, III. ETS Res Bull Ser 1970:1–14

    Google Scholar 

  • Lindley DV, Novick MR (1981) The role of exchangeability in inference. Ann Stat 9:45–58

    Article  MathSciNet  MATH  Google Scholar 

  • Lindley DV, Smith AF (1972) Bayes estimates for the linear model. J R Stat Soc Ser B (Methodological) 34:1–18

    MathSciNet  MATH  Google Scholar 

  • Marsh LC, Cormier DR (2001) Spline regression models. SAGE Publications Inc, New York

    Google Scholar 

  • Novick MR, Jackson PH, Thayer DT, Cole NS (1972) Estimating multiple regressions in \(M\) groups: a cross-validation study. Br J Math Stat Psychol 25:33–50

    Article  MATH  Google Scholar 

  • Okada K, Mayekawa S (2018) Post-processing of Markov chain Monte Carlo output in Bayesian latent variable models with application to multidimensional scaling. Comput Stat 33:1457–1473

    Article  MathSciNet  MATH  Google Scholar 

  • Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464

    Article  MathSciNet  MATH  Google Scholar 

  • Sener O, Koltun V (2018) Multi-task learning as multi-objective optimization. Adv Neural Inf Process Syst 527–538

  • Shigemasu K, Mayekawa SI (1996) A Bayesian hierarchical linear model with educational applications. J Jpn Stat Soc 26:1–23

    Article  MATH  Google Scholar 

  • Stein C (1956) Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. Stanford University, Stanford

  • Van den Wollenberg AL (1977) Redundancy analysis: an alternative for canonical correlation analysis. Psychometrika 42:207–219

    Article  MATH  Google Scholar 

  • Watanabe S (2013) A widely applicable Bayesian information criterion. J Mach Learn Res 14:867–897

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Center for University Entrance Examinations, 2-19-23 Komaba, Meguro, Tokyo, Japan

    Shin-ichi Mayekawa

  2. Graduate School of Human Sciences, Osaka University, 1-2 Yamada-oka, Suita, Osaka, Japan

    Naoto Yamashita

Authors
  1. Shin-ichi Mayekawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Naoto Yamashita
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shin-ichi Mayekawa.

Additional information

Communicated by Wim J. van der Linden.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mayekawa, Si., Yamashita, N. Bayesian reduced rank multigroup regression analysis: a new model for multigroup data with hybrid parameter sharing. Behaviormetrika 47, 411–426 (2020). https://doi.org/10.1007/s41237-020-00112-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41237-020-00112-w

Keywords

Search

Navigation