×

Robust fitting of mixtures of GLMs by weighted likelihood. (English) Zbl 1484.62097

Summary: Finite mixtures of generalized linear models are commonly fitted by maximum likelihood and the EM algorithm. The estimation process and subsequent inferential and classification procedures can be badly affected by the occurrence of outliers. Actually, contamination in the sample at hand may lead to severely biased fitted components and poor classification accuracy. In order to take into account the potential presence of outliers, a robust fitting strategy is proposed that is based on the weighted likelihood methodology. The technique exhibits a satisfactory behavior in terms of both fitting and classification accuracy, as confirmed by some numerical studies and real data examples.

MSC:

62J12 Generalized linear models (logistic models)
62F35 Robustness and adaptive procedures (parametric inference)
62G35 Nonparametric robustness
62H25 Factor analysis and principal components; correspondence analysis
62H30 Classification and discrimination; cluster analysis (statistical aspects)

Software:

TCLUST; flexmix
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Agostinelli, C., Robust model selection in regression via weighted likelihood methodology, Stat. Prob. Lett., 56, 3, 289-300 (2002) · Zbl 0998.62034
[2] Agostinelli, C.; Greco, L., A weighted strategy to handle likelihood uncertainty in Bayesian inference, Comput. Stat., 28, 1, 319-339 (2013) · Zbl 1305.65018
[3] Agostinelli, C.; Greco, L., Discussion on: the power of monitoring: how to make the most of a contaminated sample, Stat. Methods Appl., 27, 4, 609-619 (2018) · Zbl 1428.62215
[4] Agostinelli, C.; Greco, L., Weighted likelihood estimation of multivariate location and scatter, Test, 28, 3, 756-784 (2019) · Zbl 1420.62128
[5] Agostinelli, C.; Markatou, M., Test of hypotheses based on the weighted likelihood methodology, Stat. Sin., 11, 499-514 (2001) · Zbl 0980.62012
[6] Alqallaf, F.; Agostinelli, C., Robust inference in generalized linear models, Commun. Stat. Simul. Comput., 45, 9, 3053-3073 (2016) · Zbl 1348.62094
[7] Bai, X.; Yao, W.; Boyer, JE, Robust fitting of mixture regression models, Comput. Stat. Data Anal., 56, 7, 2347-2359 (2012) · Zbl 1252.62011
[8] Bashir, S.; Carter, E., Robust mixture of linear regression models, Commun. Stat. Theory Methods, 41, 18, 3371-3388 (2012) · Zbl 1296.62111
[9] Basu, A.; Lindsay, B., Minimum disparity estimation for continuous models: efficiency, distributions and robustness, Ann. Inst. Stat. Math., 46, 4, 683-705 (1994) · Zbl 0821.62018
[10] Celeux, G.; Govaert, G., Comparison of the mixture and the classification maximum likelihood in cluster analysis, J. Stat. Comput. Simul., 47, 3-4, 127-146 (1993)
[11] Cerioli, A.; Farcomeni, A., Error rates for multivariate outlier detection, Comput. Stat. Data Anal., 55, 1, 544-553 (2011) · Zbl 1247.62192
[12] Dempster, A.; Laird, NM; Rubin, DB, Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc. Ser. B (Methodol.), 39, 1-38 (1977) · Zbl 0364.62022
[13] Dotto, F.; Farcomeni, A., Robust inference for parsimonious model-based clustering, J. Stat. Comput. Simul., 89, 3, 414-442 (2019) · Zbl 07193731
[14] Dotto, F.; Farcomeni, A.; García-Escudero, L.; Mayo-Iscar, A., A reweighting approach to robust clustering, Stat. Comput., 28, 2, 477-493 (2018) · Zbl 1384.62193
[15] Elashoff, M.; Ryan, L., An EM algorithm for estimating equations, J. Comput. Graph. Stat., 13, 1, 48-65 (2004)
[16] Farcomeni, A.; Greco, L., Robust Methods for Data Reduction (2015), Boca Raton: CRC Press, Boca Raton · Zbl 1311.62006
[17] Farcomeni, A.; Greco, L., S-estimation of hidden Markov models, Comput. Stat., 30, 1, 57-80 (2015) · Zbl 1342.65032
[18] Fritz, H.; Garcia-Escudero, L.; Mayo-Iscar, A., A fast algorithm for robust constrained clustering, Comput. Stat. Data Anal., 61, 124-136 (2013) · Zbl 1349.62264
[19] García-Escudero, LA; Gordaliza, A.; Matrán, C.; Mayo-Iscar, A., A general trimming approach to robust cluster analysis, Ann. Stat., 36, 3, 1324-1345 (2008) · Zbl 1360.62328
[20] García-Escudero, L.; Gordaliza, A.; San Martin, R.; Van Aelst, S.; Zamar, R., Robust linear clustering, J. R. Stat. Soc. Ser. B (Stat. Methodol.), 71, 1, 301-318 (2009) · Zbl 1231.62112
[21] García-Escudero, LA; Gordaliza, A.; Mayo-Iscar, A.; San Martín, R., Robust clusterwise linear regression through trimming, Comput. Stat. Data Anal., 54, 12, 3057-3069 (2010) · Zbl 1284.62198
[22] Greco, L.; Agostinelli, C., Weighted likelihood mixture modeling and model-based clustering, Stat. Comput., 30, 2, 255-277 (2020) · Zbl 1436.62255
[23] Greco, L.; Lucadamo, A.; Agostinelli, C., Weighted likelihood latent class linear regression, Stat. Methods Appl. (2020) · Zbl 1480.62144
[24] Grün, B.; Leisch, F., Fitting finite mixtures of generalized linear regressions in R, Comput. Stat. Data Anal., 51, 11, 5247-5252 (2007) · Zbl 1445.62192
[25] Grun, B.; Leisch, F., Flexmix version 2: finite mixtures with concomitant variables and varying and constant parameters, J. Stat. Softw., 28, 4, 1-35 (2008)
[26] Ilie, PC; Stefanescu, S.; Smith, L., The role of vitamin D in the prevention of coronavirus disease 2019 infection and mortality, Aging Clin. Exp. Res. (2020)
[27] Karlis, D.; Xekalaki, E., Robust inference for finite Poisson mixtures, J. Stat. Plan. Inference, 93, 1-2, 93-115 (2001) · Zbl 0997.62042
[28] Kuchibhotla, A.; Basu, A., A general set up for minimum disparity estimation, Stat. Prob. Lett., 96, 68-74 (2015) · Zbl 1314.62089
[29] Lu, Z.; Hui, Y.; Lee, A., Minimum hellinger distance estimation for finite mixtures of Poisson regression models and its applications, Biometrics, 59, 4, 1016-1026 (2003) · Zbl 1274.62171
[30] Markatou, M., Mixture models, robustness, and the weighted likelihood methodology, Biometrics, 56, 2, 483-486 (2000) · Zbl 1060.62511
[31] Markatou, M.; Basu, A.; Lindsay, BG, Weighted likelihood equations with bootstrap root search, J. Am. Stat. Assoc., 93, 442, 740-750 (1998) · Zbl 0918.62046
[32] Maronna, R.; Martin, RD; Yohai, V.; Salibian-Barrera, M., Robust Statistics: Theory and Methods (with R) (2019), Hoboken: Wiley, Hoboken · Zbl 1409.62009
[33] Maruotti, A.; Belloc, F.; Nicita, A., Comments on: The role of vitamin d in the prevention of coronavirus disease 2019 infection and mortality, Aging Clin. Exp. Res., 32, 8, 1621-1623 (2020)
[34] McLachlan, G.; Peel, D., Finite Mixture Models (2004), Hoboken: Wiley, Hoboken · Zbl 0963.62061
[35] Neykov, N.M., Müller, C.H.: Breakdown point and computation of trimmed likelihood estimators in generalized linear models. In: Developments in Robust Statistics, pp 277-286. Springer (2003) · Zbl 05280058
[36] Neykov, N.; Filzmoser, P.; Dimova, R.; Neytchev, P., Robust fitting of mixtures using the trimmed likelihood estimator, Comput. Stat. Data Anal., 52, 1, 299-308 (2007) · Zbl 1328.62033
[37] Park, C.; Basu, A.; Lindsay, B., The residual adjustment function and weighted likelihood: a graphical interpretation of robustness of minimum disparity estimators, Comput. Stat. Data Anal., 39, 1, 21-33 (2002) · Zbl 1119.62302
[38] Torti, F.; Perrotta, D.; Riani, M.; Cerioli, A., Assessing trimming methodologies for clustering linear regression data, Adv. Data Anal. Classif., 13, 1, 227-257 (2019) · Zbl 1459.62010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.