Skip to main content

Automatic Discovery of Common and Idiosyncratic Latent Effects in Multilevel Regression

  • Conference paper
  • First Online:
Advances in Knowledge Discovery and Data Mining (PAKDD 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10234))

Included in the following conference series:

  • 3837 Accesses

Abstract

We present a flexible non-parametric generative model for multilevel regression that strikes an automatic balance between identifying common effects across groups while respecting their idiosyncrasies. The model is built using techniques that are now considered standard in the statistical parameter estimation literature, namely, Hierarchical Dirichlet processes (HDP) and Hierarchical Generalized Linear Models (HGLM), and therefore, we name it “Infinite Mixtures of Hierarchical Generalized Linear Models” (iHGLM). We demonstrate how the use of a HDP prior in local, groupwise GLM modeling of response-covariate densities allows iHGLM to capture latent similarities and differences within and across groups. We demonstrate iHGLM’s superior accuracy in comparison to well known competing methods like Generalized Linear Mixed Model (GLMM), Regression Tree, Least Square Regression, Bayesian Linear Regression, Ordinary Dirichlet Process Regression, and several other regression models on several synthetic and real world datasets.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Antoniak, C.: Mixtures of dirichlet processes with applications to Bayesian nonparametric problems. Ann. Stat. 2(6), 1152–1174 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  2. Blackwell, D., MacQueen, J.B.: Ferguson distributions via polya urn schemes. Ann. Stat. 1(2), 353–355 (1973)

    Article  MATH  Google Scholar 

  3. Breslow, N.E., Clayton, D.G.: Approximate inference in generalized linear mixed models. J. Am. Stat. Assoc. 88(421), 9–25 (1993)

    MATH  Google Scholar 

  4. Ferguson, T.: A Bayesian analysis of some nonparametric problems. Ann. Stat. 1, 209–230 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hastie, T., Tibshirani, R.: Varying-coefficient models. J. R. Stat. Soc. Ser. B (Methodological) 55(4), 757–796 (1993)

    MathSciNet  MATH  Google Scholar 

  6. http://www.ibm.com/support/knowledgecenter/SSLVMB_21.0.0/com.ibm.spss.statistics.cs/glmm_anticonvulsant_intro.htm. (2012)

  7. Jordan, M., Jacobs, R.: Hierarchical mixtures of experts and the EM algorithm. International Joint Conference on Neural Networks (1993)

    Google Scholar 

  8. Lee, Y., Nelder, J.A.: Hierarchical generalized linear models. J. R. Stat. Soc. Ser. B (Methodological) 58(4), 619–678 (1996)

    MathSciNet  MATH  Google Scholar 

  9. Lee, Y., Nelder, J.A.: Hierarchical generalised linear models: a synthesis of generalised linear models, random-effect models and structured dispersions. Biometrika 88(4), 987–1006 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lee, Y., Nelder, J.A.: Modelling and analysing correlated non-normal data. Stat. Model. 1(1), 3–16 (2001)

    Article  MATH  Google Scholar 

  11. Lee, Y., Nelder, J.A.: Double hierarchical generalized linear models (with discussion). J. R. Stat. Soc.: Ser. C (Appl. Stat.) 55(2), 139–185 (2006)

    Article  MATH  Google Scholar 

  12. Neal, R.M.: Markov chain sampling methods for dirichlet process mixture models. J. Comput. Graph. Stat. 9(2), 249–265 (2000)

    MathSciNet  Google Scholar 

  13. Nelder, J.A., Wedderburn, R.W.M.: Generalized linear models. J. R. Stat. Soc. Ser. A (Gen.) 135(3), 370–384 (1972)

    Article  Google Scholar 

  14. Rasmussen, C., Williams, C.: Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning). MIT Press, Cambridge (2005)

    Google Scholar 

  15. Robinson, A.P., Wykoff, W.R.: Imputing missing height measures using a mixed-effects modeling strategy. Can. J. For. Res. 34, 2492–2500 (2004)

    Article  Google Scholar 

  16. Sethuraman, J.: A constructive definition of Dirichlet priors. Stat. Sin. 4, 639–650 (1994)

    MathSciNet  MATH  Google Scholar 

  17. Teh, Y.W., Jordan, M.I., Beal, M., Blei, D.: Hierarchical Dirichlet processes. J. Am. Stat. Assoc. 101, 1566–1581 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Viele, K., Tong, B.: Modeling with mixtures of linear regressions. Stat. Comput. 12(4), 315–330 (2002)

    Article  MathSciNet  Google Scholar 

  19. http://en.wikipedia.org/wiki/Atom_%28measure_theory%29

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sk Minhazul Islam .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Islam, S.M., Banerjee, A. (2017). Automatic Discovery of Common and Idiosyncratic Latent Effects in Multilevel Regression. In: Kim, J., Shim, K., Cao, L., Lee, JG., Lin, X., Moon, YS. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2017. Lecture Notes in Computer Science(), vol 10234. Springer, Cham. https://doi.org/10.1007/978-3-319-57454-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-57454-7_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57453-0

  • Online ISBN: 978-3-319-57454-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics