Cluster-weighted modeling with measurement error in covariates

References

• Byrd, R. H., P. Lu, J. Nocedal, and C. Zhu. 1995. A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing 16 (5):1190–208. doi:10.1137/0916069.
   Web of Science ®Google Scholar
• Dempster, A. P., N. M. Laird, and D. B. Rubin. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological) 39 (1):1–22. doi:10.1111/j.2517-6161.1977.tb01600.x.
   Web of Science ®Google Scholar
• DeSarbo, W. S., and W. L. Cron. 1988. A maximum likelihood methodology for clusterwise linear regression. Journal of Classification 5 (2):249–82. doi:10.1007/BF01897167.
   Web of Science ®Google Scholar
• Di Mari, R., Z. Bakk, and A. Punzo. 2020. A random-covariate approach for distal outcome prediction with latent class analysis. Structural Equation Modeling: A Multidisciplinary Journal 27 (3):351–68. doi:10.1080/10705511.2019.1648186.
   Web of Science ®Google Scholar
• Di Mari, R., S. Ingrassia, and A. Punzo. 2023. Local and overall deviance R-squared measures for mixtures of generalized linear models. Journal of Classification 40:233–66.
   Web of Science ®Google Scholar
• Dunn, J. C. 1974. Well-separated clusters and optimal fuzzy partitions. Journal of Cybernetics 4 (1):95–104.
   Google Scholar
• Frühwirth-Schnatter, S. 2006. Finite mixture and Markov switching models. New York: Springer Science & Business Media.
   Google Scholar
• Fuller, W. 1987. Measurement error models. New York: John Wiley & Sons.
   Google Scholar
• Gallaugher, M. P. B., S. D. Tomarchio, P. D. McNicholas, and A. Punzo. 2022a. Multivariate cluster weighted models using skewed distributions. Advances in Data Analysis and Classification 16 (1):93–124. doi:10.1007/s11634-021-00480-5.
   Web of Science ®Google Scholar
• Gallaugher, M. P., S. D. Tomarchio, P. D. McNicholas, and A. Punzo. 2022b. Model-based clustering via skewed matrix-variate cluster-weighted models. Journal of Statistical Computation and Simulation 92 (13):2645–66. doi:10.1080/00949655.2022.2084093.
   Web of Science ®Google Scholar
• Gershenfeld, N. 1997. Nonlinear inference and cluster-weighted modeling. Annals of the New York Academy of Sciences 808 (1):18–24. doi:10.1111/j.1749-6632.1997.tb51651.x.
   Google Scholar
• Harrison, D., and D. L. Rubinfeld. 1978. Hedonic housing prices and the demand for clean air. Journal of Environmental Economics and Management 5 (1):81–102. doi:10.1016/0095-0696(78)90006-2.
   Web of Science ®Google Scholar
• Hennig, C. 2000. Identifiablity of models for clusterwise linear regression. Journal of Classification 17 (2):273–96. doi:10.1007/s003570000022.
   Web of Science ®Google Scholar
• Hubert, L., and P. Arabie. 1985. Comparing partitions. Journal of Classification 2 (1):193–218. doi:10.1007/BF01908075.
   Web of Science ®Google Scholar
• Ingrassia, S., and A. Punzo. 2016. Decision boundaries for mixtures of regressions. Journal of the Korean Statistical Society 45 (2):295–306. doi:10.1016/j.jkss.2015.11.005.
   Web of Science ®Google Scholar
• Ingrassia, S., S. C. Minotti, and A. Punzo. 2014. Model-based clustering via linear cluster-weighted models. Computational Statistics & Data Analysis 71:159–82. doi:10.1016/j.csda.2013.02.012.
   Web of Science ®Google Scholar
• Ingrassia, S., S. C. Minotti, and G. Vittadini. 2012. Local statistical modeling via a cluster-weighted approach with elliptical distributions. Journal of Classification 29 (3):363–401. doi:10.1007/s00357-012-9114-3.
   Web of Science ®Google Scholar
• Punzo, A. 2014. Flexible mixture modelling with the polynomial Gaussian cluster-weighted model. Statistical Modelling 14 (3):257–91. doi:10.1177/1471082X13503455.
   Web of Science ®Google Scholar
• Punzo, A., and P. D. McNicholas. 2016. Parsimonious mixtures of multivariate contaminated normal distributions. Biometrical Journal. Biometrische Zeitschrift 58 (6):1506–37. doi:10.1002/bimj.201500144. 27510372.
   PubMed Web of Science ®Google Scholar
• Rousseeuw, P. J. 1987. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics 20:53–65. doi:10.1016/0377-0427(87)90125-7.
   Web of Science ®Google Scholar
• Schwarz, G. 1978. Estimating the dimension of a model. The Annals of Statistics, 6:461–4.
   Google Scholar
• Tomarchio, S. D., P. D. McNicholas, and A. Punzo. 2021. Matrix normal cluster-weighted models. Journal of Classification 38 (3):556–75. doi:10.1007/s00357-021-09389-2.
   Web of Science ®Google Scholar
• Yao, W., and W. Song. 2015. Mixtures of linear regression with measurement errors. Communications in Statistics- Theory and Methods 44 (8):1602–14. doi:10.1080/03610926.2013.781638.
   Web of Science ®Google Scholar
• Zarei, S., A. Mohammadpour, S. Ingrassia, and A. Punzo. 2019. On the use of the sub-Gaussian α-stable distribution in the cluster-weighted model. Iranian Journal of Science and Technology, Transactions A: Science 43 (3):1059–69. doi:10.1007/s40995-018-0526-8.
   Google Scholar
• Zhang, W., and Y. Di. 2020. Model-based clustering with measurement or estimation errors. Genes 11 (2):185. doi:10.3390/genes11020185.
   PubMed Web of Science ®Google Scholar