Influence diagnostics in nonlinear mixed-effects elliptical models

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.