Research project
Robust nonlinear and semiparametric mixed models
Estimation and monitoring methods for mixed models that remain reliable when observations are aberrant or the parametric model is misspecified.
Research problem
In data well modelled by a nonlinear mixed model, a single aberrant observation within a cluster, or an entire aberrant cluster, can greatly distort parameter estimates and their standard errors, so that inferences about the parameters become misleading [1].
In profile monitoring, most earlier work modelled linear or nonlinear profiles with fixed and random effects under the assumption that the parametric model is correctly specified [2], including logistic regression models for binary responses [3]; this assumption is often uncertain in practice [3].
Methodology
An outlier-robust method based on linearization estimates the fixed-effects parameters and the variance components of the nonlinear mixed model [1].
A semiparametric procedure, mixed model robust profile monitoring (MMRPM), combines parametric and nonparametric profile fits, accounts for autocorrelation within profiles and treats the profiles as a random sample from a common population; Hotelling’s T² statistics based on the estimated random effects are used for Phase I analysis [2].
For profiles from the exponential family, nonparametric penalized-spline and semiparametric model-robust mixed-model methods are combined with Hotelling’s T² charts for binary responses with replicates [3].
Main contribution
An outlier-robust estimation method for the nonlinear mixed model [1]; the MMRPM approach to Phase I profile monitoring [2]; and its extension to the generalized linear mixed model [3].
Findings
Robust and non-robust estimates were compared for a four-parameter logistic model fitted to bioassay data [1].
In simulations, MMRPM performed well in identifying outlying profiles compared with a misspecified parametric model or nonparametric regression, and remained competitive with a correctly specified parametric model; applied to automobile engine data, the nonparametric and MMRPM methods indicated signals that the parametric approach did not [2].
Evaluated by mean squared error and probability of signal, the proposed charts for the generalized linear mixed model showed satisfactory performance [3].
Applications
Bioassay data [1], automobile engine data [2], and industrial, medical and biological processes with binary responses [3].
Research outputs
- PublishedOutlier robust nonlinear mixed model estimationJames D. Williams, Jeffrey B. Birch, Abdel-Salam G. Abdel-Salam · Statistics in Medicine · 2015
- PublishedA Semiparametric Mixed Model Approach to Phase I Profile MonitoringAbdel-Salam G. Abdel-Salam, Jeffrey B. Birch, Willis A. Jensen · Quality and Reliability Engineering International · 2013
- PublishedModel robust profile monitoring for the generalized linear mixed model for Phase I analysisKeerthi Bandara, Abdel-Salam G. Abdel-Salam, Jeffrey B. Birch · Applied Stochastic Models in Business and Industry · 2020
- PublishedA semiparametric nonlinear mixed model approach to phase I profile monitoringAbdel-Salam Gomaa, Jeffrey B. Birch · Communications in Statistics - Simulation and Computation · 2019
- PublishedAn ANOVA-based test for random effects in a nonlinear mixed model using a Monte Carlo permutation procedureYahia S. El-Horbaty, Abdel-Salam G. Abdel-Salam · Journal of Statistical Computation and Simulation · 2024
- PublishedSeveral nonparametric and semiparametric approaches to linear mixed model regressionMegan J. Waterman, Jeffrey B. Birch, Abdel-Salam G. Abdel-Salam · Journal of Statistical Computation and Simulation · 2015
Sources for this summary
- [1] Williams, Birch and Abdel-Salam (2015). Outlier robust nonlinear mixed model estimation. Statistics in Medicine. Summary based on the published abstract (Crossref).
- [2] Abdel-Salam, Birch and Jensen (2013). A Semiparametric Mixed Model Approach to Phase I Profile Monitoring. Quality and Reliability Engineering International. Summary based on the published abstract (Crossref).
- [3] Bandara, Abdel-Salam and Birch (2020). Model robust profile monitoring for the generalized linear mixed model for Phase I analysis. Applied Stochastic Models in Business and Industry. Summary based on the published abstract (Crossref).
Every statement above summarises the published abstracts of the papers listed; numbers in brackets refer to these sources. No unpublished or ongoing work is included.