Diagnostics for mixed-model analysis of variance
Technometrics
Assessment of local influence in elliptical linear models with longitudinal structure
Computational Statistics & Data Analysis
Case deletion diagnostics in multilevel models
Journal of Multivariate Analysis
Deletion measures for generalized linear mixed effects models
Computational Statistics & Data Analysis
Influence analyses of skew-normal/independent linear mixed models
Computational Statistics & Data Analysis
Short communication: A note on influence diagnostics in nonlinear mixed-effects elliptical models
Computational Statistics & Data Analysis
Estimation in nonlinear mixed-effects models using heavy-tailed distributions
Statistics and Computing
Influence diagnostics in linear and nonlinear mixed-effects models with censored data
Computational Statistics & Data Analysis
Bayesian inference in nonlinear mixed-effects models using normal independent distributions
Computational Statistics & Data Analysis
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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.