Sage Journals: Discover world-class research

Abstract

The cluster-weighted model (CWM) is a member of the family of mixtures of regression models and is also known as a mixture of regressions with random covariates. CWMs refer to the framework of model-based clustering and naturally apply when the research interest requires modeling the relationship between a response variable and a set of covariates using a regression-based approach such as a generalized linear model with the sample being suspected of comprising heterogeneous latent classes. A command for fitting these models is not yet available in Stata, so the aim of this article is to introduce the package cwmglm, which fits CWMs based on the most common generalized linear models with random covariates. Moreover, cwmglm allows the estimation of parsimonious models of Gaussian distributions, with the parameterization of the variance–covariance matrix based on the eigenvalue decomposition. These features are completely new for Stata users. The cwmglm package features goodness-of-fit, bootstrapping, and model-selection tools. We illustrate the use of cwmglm with real and simulated datasets.

Keywords

st0762 cwmglm cluster-weighted model finite mixtures of regressions with random covariates model-based clustering saturated mixture regression model Gaussian parsimonious models postestimation

Get full access to this article

View all access options for this article.

References

Aitken

A. C

. 1927. XXV.—On Bernoulli’s numerical solution of algebraic equations. Proceedings of the Royal Society of Edinburgh 46: 289–305. 10.1017/S0370164600022070.

Banfield

J. D.

Raftery

A. E.

. 1993. Model-based Gaussian and non-Gaussian clustering. Biometrics 49: 803–821. 10.2307/2532201.

Berta

Ingrassia

Punzo

Vittadini

. 2016. Multilevel cluster-weighted models for the evaluation of hospitals. METRON 74: 275–292. 10.1007/s40300-016-0098-3.

Berta

Ingrassia

Vittadini

Spinelli

. 2024. Latent heterogeneity in COVID-19 hospitalisations: A cluster-weighted approach to analyse mortality. Australian and New Zealand Journal of Statistics 66: 1–20. 10.1111/anzs.12407.

Berta

Vinciotti

. 2019. Multilevel logistic cluster-weighted model for outcome evaluation in health care. Statistical Analysis and Data Mining: The ASA Data Science Journal 12: 434–443. 10.1002/sam.11421.

Brilleman

2011. devr2: Stata module to compute Cameron and Windmeijer’s deviance based R-squared measure. Statistical Software Components S457340, Department of Economics, Boston College. https://ideas.repec.org/c/boc/bocode/s457340.html.

Browne

R. P.

McNicholas

P. D.

. 2014. Estimating common principal components in high dimensions. Advances in Data Analysis and Classification 8: 217–226. 10.1007/s11634-013-0139-1.

Cameron

A. C.

Windmeijer

F. A. G.

. 1996. R-squared measures for count data regression models with applications to health-care utilization. Journal of Business and Economic Statistics 14: 209–220. 10.2307/1392433.

–––. 1997. An R-squared measure of goodness of fit for some common nonlinear regression models. Journal of Econometrics 77: 329–342. 10.1016/S0304-4076(96)01818-0.

10.

Celeux

Govaert

. 1995. Gaussian parsimonious clustering models. Pattern Recognition 28: 781–793. 10.1016/0031-3203(94)00125-6.

11.

Dayton

C. M.

Macready

G. B.

. 1988. Concomitant-variable latent-class models. Journal of the American Statistical Association 83: 173–178. 10.2307/2288938.

12.

Dempster

A. P.

Laird

N. M.

Rubin

D. B.

. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, B ser., 39: 1–22. 10.1111/j.2517-6161.1977.tb01600.x.

13.

Di Mari

Ingrassia

Punzo

. 2023. Local and overall deviance R-squared measures for mixtures of generalized linear models. Journal of Classification 40: 233–266. 10.1007/s00357-023-09432-4.

14.

Diani

Galimberti

Soffritti

. 2022. Multivariate cluster-weighted models based on seemingly unrelated linear regression. Computational Statistics and Data Analysis 171: art. 107451. 10.1016/j.csda.2022.107451.

15.

Fabbian

De Giorgi

Maietti

Gallerani

Pala

Cappadona

Manfredini

Fedeli

. 2017. A modified Elixhauser score for predicting in-hospital mortality in internal medicine admissions. European Journal of Internal Medicine 40: 37–42. 10.1016/j.ejim.2017.02.002.

16.

Früwirth-Schnatter

. 2006. Finite Mixture and Markov Switching Models. New York: Springer. 10.1007/978-0-387-35768-3.

17.

Gershenfeld

. 1997. Nonlinear inference and cluster-weighted modeling. Annals of the New York Academy of Sciences 808: 18–24. 10.1111/j.1749-6632.1997.tb51651.x.

18.

–––. 1999. The Nature of Mathematical Modelling. Cambridge: Cambridge University Press.

19.

Gershenfeld

Schöner

Metois

. 1999. Cluster-weighted modelling for time-series analysis. Nature 397: 329–332. 10.1038/16873.

20.

Gray

L. A.

Hernández Alava

. 2018. A command for fitting mixture regression models for bounded dependent variables using the beta distribution. Stata Journal 18: 51–75. 10.1177/1536867X1801800105.

21.

Hennig

. 2000. Identifiab[i]lity of models for clusterwise linear regression. Journal of Classification 17: 273–296. 10.1007/s003570000022.

22.

Hernández Alava

Wailoo

. 2015. Fitting adjusted limited dependent variable mixture models to EQ-5D. Stata Journal 15: 737–750. 10.1177/1536867X1501500307.

23.

Huismans

Nijenhuis

J. W.

Sirchenko

. 2022. A mixture of ordered probit models with endogenous switching between two latent classes. Stata Journal 22: 557–596. 10.1177/1536867X221124516.

24.

Ingrassia

Minotti

S. C.

Vittadini

. 2012. Local statistical modeling via a cluster-weighted approach with elliptical distributions. Journal of Classification 29: 363–401. 10.1007/s00357-012-9114-3.

25.

Ingrassia

Punzo

. 2020. Cluster validation for mixtures of regressions via the total sum of squares decomposition. Journal of Classification 37: 526–547. 10.1007/s00357-019-09326-4.

26.

Ingrassia

Punzo

Vittadini

Minotti

S. C.

. 2015. The generalized linear mixed cluster-weighted model. Journal of Classification 32: 85–113. 10.1007/s00357-015-9175-1.

27.

Jenkins

S. P.

Rios-Avila

. 2023. Finite mixture models for linked survey and administrative data: Estimation and postestimation. Stata Journal 23: 53–85. 10.1177/1536867X231161976.

28.

Mazza

Punzo

Ingrassia

. 2018. flexCWM: A flexible framework for cluster-weighted models. Journal of Statistical Software 86: art. 2. 10.18637/jss.v086.i02.

29.

McCullagh

Nelder

J. A.

. 1989. Generalized Linear Models. 2nd ed. London: Chapman and Hall/CRC. 10.1201/9780203753736.

30.

McLachlan

G. J.

Peel

. 2000. Finite Mixture Models. New York: Wiley.

31.

McNicholas

P. D.

2016. Model-based clustering. Journal of Classification 33: 331–373. 10.1007/s00357-016-9211-9.

32.

Punzo

. 2014. Flexible mixture modelling with the polynomial Gaussian cluster-weighted model. Statistical Modelling 14: 257–291. 10.1177/1471082X13503455.

33.

Sarkar

Zhu

Melnykov

Ingrassia

. 2020. On parsimonious models for modeling matrix data. Computational Statistics and Data Analysis 142: art. 106822. 10.1016/j.csda.2019.106822.

34.

Schöner

2000. Probabilistic characterization and synthesis of complex data driven systems. PhD thesis, School of Architecture and Planning, Program in Media Arts and Sciences, Massachusetts Institute of Technology. https://hdl.handle.net/1721.1/62352 .

35.

Soffritti

. 2021. Estimating the covariance matrix of the maximum likelihood estimator under linear cluster-weighted models. Journal of Classification 38: 594–625. 10.1007/s00357-021-09390-9.

36.

Subedi

Punzo

Ingrassia

McNicholas

P. D.

. 2013. Clustering and classification via cluster-weighted factor analyzers. Advances in Data Analysis and Classification 7: 5–4. 10.1007/s11634-013-0124-8.

37.

Wedel

. 2002. Concomitant variables in finite mixture models. Statistica Nederlandica 56: 362–375. 10.1111/1467-9574.t01-1-00072.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.46 MB

Cluster-weighted models using Stata

Abstract

Keywords

Get full access to this article

References

Supplementary Material