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Model-based SIR for dimension reduction

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  • Scrucca, Luca

Abstract

A new dimension reduction method based on Gaussian finite mixtures is proposed as an extension to sliced inverse regression (SIR). The model-based SIR (MSIR)1 approach allows the main limitation of SIR to be overcome, i.e., failure in the presence of regression symmetric relationships, without the need to impose further assumptions. Extensive numerical studies are presented to compare the new method with some of the most popular dimension reduction methods, such as SIR, sliced average variance estimation, principal Hessian direction, and directional regression. MSIR appears sufficiently flexible to accommodate various regression functions, and its performance is comparable with or better, particularly as sample size grows, than other available methods. Lastly, MSIR is illustrated with two real data examples about ozone concentration regression, and hand-written digit classification.

Suggested Citation

  • Scrucca, Luca, 2011. "Model-based SIR for dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3010-3026, November.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:11:p:3010-3026
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    References listed on IDEAS

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    1. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard & Langrognet, Florent, 2006. "Model-based cluster and discriminant analysis with the MIXMOD software," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 587-600, November.
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    Cited by:

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    2. Coudret, R. & Girard, S. & Saracco, J., 2014. "A new sliced inverse regression method for multivariate response," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 285-299.
    3. Milad Mokhtaridoost & Jordan J. Chalmers & Marzieh Soleimanpoor & Brandon J. McMurray & Daniella F. Lato & Son C. Nguyen & Viktoria Musienko & Joshua O. Nash & Sergio Espeso-Gil & Sameen Ahmed & Kate , 2024. "Inter-chromosomal contacts demarcate genome topology along a spatial gradient," Nature Communications, Nature, vol. 15(1), pages 1-17, December.
    4. Hino, Hideitsu & Wakayama, Keigo & Murata, Noboru, 2013. "Entropy-based sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 105-114.
    5. Szretter Noste, María Eugenia, 2019. "Using DAGs to identify the sufficient dimension reduction in the Principal Fitted Components model," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 317-320.

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