Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Modified partial least squares method implementing mixed-effect model

  • Kyunga Kim (Biomedical Statistics Center, Research Institute for Future Medicine, Samsung Medical Center) ;
  • Shin-Jae Lee (Seoul National University School of Dentistry & Dental Research Institute) ;
  • Soo-Heang Eo (GreenLabs Inc.) ;
  • HyungJun Cho (Department of Statistics, Korea University) ;
  • Jae Won Lee (Department of Statistics, Korea University)
  • Received : 2022.04.21
  • Accepted : 2022.09.25
  • Published : 2023.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

Contemporary biomedical data often involve an ill-posed problem owing to small sample size and large number of multi-collinear variables. Partial least squares (PLS) method could be a plausible alternative to an ill-conditioned ordinary least squares. However, in the case of a PLS model that includes a random-effect, how to deal with a random-effect or mixed effects remains a widely open question worth further investigation. In the present study, we propose a modified multivariate PLS method implementing mixed-effect model (PLSM). The advantage of PLSM is its versatility in handling serial longitudinal data or its ability for taking a randomeffect into account. We conduct simulations to investigate statistical properties of PLSM, and showcase its real clinical application to predict treatment outcome of esthetic surgical procedures of human faces. The proposed PLSM seemed to be particularly beneficial 1) when random-effect is conspicuous; 2) the number of predictors is relatively large compared to the sample size; 3) the multicollinearity is weak or moderate; and/or 4) the random error is considerable.

Keywords

Acknowledgement

The data presented in the present study were part of a doctoral dissertation (SJL).

References

  1. Azzalini A, Genz A, Miller A, Wichura MJ, Hill GW, and Ge Y (2021). Mnormt: The multivariate normal and t-distributions, and their truncated versions, Available from: http://CRAN.Rproject.org/package=mnormt
  2. Chun H and Keles S (2010). Sparse partial least squares regression for simultaneous dimension reduction and variable selection, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 72, 3-25. https://doi.org/10.1111/j.1467-9868.2009.00723.x
  3. Dai JJ, Lieu L, and Rocke D (2006). Dimension reduction for classification with gene expression microarray data, Statistical Applications in Genetics and Molecular Biology, 5, 6.
  4. Donatelli RE and Lee SJ (2013). How to report reliability in orthodontic research. Part 2, American Journal of Orthodontics and Dentofacial Orthopedics, 144, 315-318. https://doi.org/10.1016/j.ajodo.2013.03.023
  5. Fordellone M and Vichi M (2020). Finding groups in structural equation modeling through the partial least squares algorithm, Computational Statistics & Data Analysis, 147, 106957.
  6. Garthwaite PH (1994). An interpretation of partial least-squares, Journal of the American Statistical Association, 89, 122-127. https://doi.org/10.1080/01621459.1994.10476452
  7. Hastie T, Tibshirani R, and Friedman J (2009). The Elements of Statistical Learning. Data Mining, Inference, and Prediction (2nd ed), Springer Verlag, New York.
  8. Hwang HW, Moon JH, Kim MG, Donatelli RE and Lee SJ (2021). Evaluation of automated cephalometric analysis based on the latest deep learning method, The Angle Orthodontist, 91, 329-335. https://doi.org/10.2319/021220-100.1
  9. Johnson RA and Wichern DW (2007). Applied Multivariate Statistical Analysis, Pearson Prentice Hall, New Jersey.
  10. Krishnan A, Williams LJ, McIntosh AR, and Abdi H (2011). Partial least squares (PLS) methods for neuroimaging: A tutorial and review, Neuroimage, 56, 455-475. https://doi.org/10.1016/j.neuroimage.2010.07.034
  11. Laird NM and Ware JH (1982). Random-effects models for longitudinal data, Biometrics, 38, 963-974. https://doi.org/10.2307/2529876
  12. Lee D, Lee W, Lee Y, and Pawitan Y (2010). Super-sparse principal component analyses for highthroughput genomic data, BMC Bioinformatics, 11, 1-10. https://doi.org/10.1186/1471-2105-11-1
  13. Lee YS, Suh HY, Lee SJ, and Donatelli RE (2014). A more accurate soft-tissue prediction model for Class III 2-jaw surgeries, American Journal of Orthodontics and Dentofacial Orthopedics, 146, 724-733. https://doi.org/10.1016/j.ajodo.2014.08.010
  14. Liland KH, Mevik BH, Wehrens R, and Hiemstra P (2021). PLS: partial least squares and principal component regression. R package version 2.8-0, Available from: http://CRAN.R-project.org/pack age=pls
  15. Martins JPA, Teofilo RF, and Ferreira MMC (2010). Computational performance and cross-validation error precision of five PLS algorithms using designed and real data sets, Journal of Chemometrics, 24, 320-332. https://doi.org/10.1002/cem.1309
  16. Mevik BH and Wehrens R (2007). The pls package: Principal component and partial least squares regression in R, Journal of Statistical Software, 18, 1-24. https://doi.org/10.1360/jos180001
  17. R Development Core Team (2021). R: A language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna.
  18. Suh HY, Lee SJ, Lee YS, Donatelli RE, Wheeler TT, Kim SH, Eo SH, and Seo BM (2012). A more accurate method of predicting soft-tissue changes after mandibular setback surgery, Journal of Oral and Maxillofacial Surgery, 70, e553-e562. https://doi.org/10.1016/j.joms.2012.06.187
  19. Suh HY, Lee HJ, Lee YS, Eo SH, Donatelli RE, and Lee SJ (2019). Predicting soft-tissue changes after orthognathic surgery: The sparse partial least squares method, The Angle Orthodontist, 89, 910-916. https://doi.org/10.2319/120518-851.1
  20. Wehrens R (2011). Chemometric with R: Multivariate Data Analysis in the Natural Sciences and Life Sciences (1st ed), Springer, Heidelberg.
  21. Zhou XF, Shao Q, Coburn RA, and Morris ME (2005). Quantitative structure-activity relationship and quantitative structure-pharmacokinetics relationship of 1,4-dihydropyridines and pyridines as multidrug resistance modulators, Pharmaceutical Research, 22, 1989-1996.  https://doi.org/10.1007/s11095-005-8112-0