Flexible regression modeling for censored data

• Grant number: 15/20922-5
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Duration: July 01, 2016 - June 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Víctor Hugo Lachos Dávila
• Grantee: Víctor Hugo Lachos Dávila
• Visiting researcher: Celso Romulo Barbosa Cabral
• Visiting researcher institution: Universidade Federal do Amazonas (UFAM). Instituto de Ciências Exatas, Brazil
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this project, we consider the linear regression model with censored responses. Econometrics is an area example where censored responses frequently occurs. Other examples can be found in survival analysis, where partially observed survival times can occur due to the ending of an assay. In the analysis of regression models with censored responses, in general, the normality assumption for the errors is assumed. However, it is well known that in several practical situations there are serious departures from this assumption, like heavy tails, skewness and multiple modes. Thus, clearly there is a need for extensions of the existing Gaussian methods, which is the main objective of this project. An important issue is the study of the relationship between variables from several latent homogeneous groups. In this case, the assumption that the regression coefficient is fixed over all possible realizations of the response is inadequate, and models where the regression coefficient changes are of great practical importance. One way to capture such changes in the parameter of a regression model is to use finite mixtures of regression models. However, the existing proposals that deal simultaneously with censored data and latent heterogeneity only take into account the case where the errors are normally distributed, an assumption that is not satisfactory when discrepant observations are present. In this project, we propose models with heavier tails than the normal model, allowing the accommodation of outliers. Another relevant issue is when the covariate cannot be observed directly, that is, it is measured with an error. This case is known as the error in variables model. In general, the normality assumption for the latent covariate is made. In this project, we propose a more flexible modeling, where the errors and the latent covariate are modeled by a scale mixture of normal distributions. Finally, we also consider the existence of missing data in a longitudinal linear censored regression model with heavy tails. (AU)

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

LACHOS, VICTOR H.; LOPEZ MORENO, EDGAR J.; CHEN, KUN; BARBOSA CABRAL, CELSO ROMULO. Finite mixture modeling of censored data using the multivariate Student-t distribution. JOURNAL OF MULTIVARIATE ANALYSIS, v. 159, p. 151-167, JUL 2017. (14/02938-9, 15/20922-5)

ORDONEZ, JOSE A.; BANDYOPADHYAY, DIPANKAR; LACHOS, VICTOR H.; CABRAL, CELSO R. B.. Geostatistical estimation and prediction for censored responses. SPATIAL STATISTICS, v. 23, p. 109-123, MAR 2018. (15/20922-5)

MATOS, LARISSA A.; CASTRO, LUIS M.; CABRAL, CELSO R. B.; LACHOS, VICTOR H.. Multivariate measurement error models based on Student-t distribution under censored responses. STATISTICS, v. 52, n. 6, p. 1395-1416, 2018. (15/20922-5, 18/05013-7, 15/05385-3, 11/22063-9)

LACHOS, VICTOR H.; CABRAL, CELSO R. B.; PRATES, MARCOS O.; DEY, DIPAK K.. Flexible regression modeling for censored data based on mixtures of student-t distributions. Computational Statistics, v. 34, n. 1, p. 123-152, MAR 2019. (15/20922-5, 18/05013-7)

LACHOS, VICTOR H.; GARAY, ALDO M.; CABRAL, CELSO R. B.. Moments of truncated scale mixtures of skew-normal distributions. BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, v. 34, n. 3, p. 478-494, AUG 2020. (15/20922-5)