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Influence diagnostics in nonlinear mixed-effects elliptical models

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  • Russo, Cibele M.
  • Paula, Gilberto A.
  • Aoki, Reiko

Abstract

In this work we propose and analyze nonlinear elliptical models for longitudinal data, which represent an alternative to gaussian models in the cases of heavy tails, for instance. The elliptical distributions may help to control the influence of the observations in the parameter estimates by naturally attributing different weights for each case. We consider random effects to introduce the within-group correlation and work with the marginal model without requiring numerical integration. An iterative algorithm to obtain maximum likelihood estimates for the parameters is presented, as well as diagnostic results based on residual distances and local influence [Cook, D., 1986. Assessment of local influence. Journal of the Royal Statistical Society - Series B 48 (2), 133-169; Cook D., 1987. Influence assessment. Journal of Applied Statistics 14 (2), 117-131; Escobar, L.A., Meeker, W.Q., 1992, Assessing influence in regression analysis with censored data, Biometrics 48, 507-528]. As numerical illustration, we apply the obtained results to a kinetics longitudinal data set presented in [Vonesh, E.F., Carter, R.L., 1992. Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1-17], which was analyzed under the assumption of normality.

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  • Russo, Cibele M. & Paula, Gilberto A. & Aoki, Reiko, 2009. "Influence diagnostics in nonlinear mixed-effects elliptical models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4143-4156, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4143-4156
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    Cited by:

    1. Huihui Sun, 2017. "Testing of homogeneity of variance and autocorrelation coefficients of nonlinear mixed models with AR(1) errors based on M-estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(2), pages 362-375, January.
    2. Zeller, Camila B. & Labra, Filidor V. & Lachos, Victor H. & Balakrishnan, N., 2010. "Influence analyses of skew-normal/independent linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1266-1280, May.
    3. Victor H. Lachos & Celso R.B. Cabral & Carlos A. Abanto-Valle, 2012. "A non-iterative sampling Bayesian method for linear mixed models with normal independent distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(3), pages 531-549, July.
    4. Reiko Aoki & Juan P. M. Bustamante & Gilberto A. Paula, 2022. "Local influence diagnostics with forward search in regression analysis," Statistical Papers, Springer, vol. 63(5), pages 1477-1497, October.
    5. Cibele M. Russo & Gilberto A. Paula & Francisco Jos� A. Cysneiros & Reiko Aoki, 2012. "Influence diagnostics in heteroscedastic and/or autoregressive nonlinear elliptical models for correlated data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1049-1067, October.
    6. Patriota, Alexandre G., 2011. "A note on influence diagnostics in nonlinear mixed-effects elliptical models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 218-225, January.
    7. Matos, Larissa A. & Lachos, Victor H. & Balakrishnan, N. & Labra, Filidor V., 2013. "Influence diagnostics in linear and nonlinear mixed-effects models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 450-464.
    8. Matos, Larissa A. & Bandyopadhyay, Dipankar & Castro, Luis M. & Lachos, Victor H., 2015. "Influence assessment in censored mixed-effects models using the multivariate Student’s-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 104-117.
    9. Lachos, Victor H. & Castro, Luis M. & Dey, Dipak K., 2013. "Bayesian inference in nonlinear mixed-effects models using normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 237-252.
    10. Cibele Russo & Reiko Aoki & Gilberto Paula, 2012. "Assessment of variance components in nonlinear mixed-effects elliptical models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 519-545, September.
    11. Joelmir A. Borssoi & Gilberto A. Paula & Manuel Galea, 2020. "Elliptical linear mixed models with a covariate subject to measurement error," Statistical Papers, Springer, vol. 61(1), pages 31-69, February.
    12. Victor H. Lachos & Dipankar Bandyopadhyay & Dipak K. Dey, 2011. "Linear and Nonlinear Mixed-Effects Models for Censored HIV Viral Loads Using Normal/Independent Distributions," Biometrics, The International Biometric Society, vol. 67(4), pages 1594-1604, December.

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