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Browsing Department of Statistics by Author "Abdel-Salam, Abdel-Salam Gomaa"
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- Model robust profile monitoring for the generalized linear mixed model for Phase I analysisBandara, Keerthi; Abdel-Salam, Abdel-Salam Gomaa; Birch, Jeffrey B. (2020-11-02)The generalized linear mixed model (GLMM) becomes very popular in profile monitoring, especially when the production processes follow nonnormal distribution. In most of the real-life applications in industry, medicine, biology horizontal ellipsis and so on researchers assume that the response variable follows a Bernoulli or Binomial distribution. The majority of previous studies in profile monitoring focused on parametric modeling using the logistic regression model, with both fixed or random effects, under the assumption of correct model specification. This research considers those cases where the parametric logistic regression model for the family of profiles is unknown or at least uncertain. Consequently, we propose two mixed model methods to monitor profiles from the exponential family: a nonparametric (NP) regression method based on the penalized spline regression technique and a semiparametric method (model robust profile monitoring for the generalized linear mixed model) which combines the advantages of both the parametric and NP methods. Several Hotelling T2 charts that have been studied for a binary response variable with replicates for Phase I profile monitoring. The performance of the proposed method is evaluated by using mean squares of errors and probability of signals criteria. The results showed satisfactory performance of the proposed control charts.
- Nonparametric and Semiparametric Linear Mixed ModelsWaterman, Megan J.; Birch, Jeffrey B.; Abdel-Salam, Abdel-Salam Gomaa (Virginia Tech, 2012)Mixed models are powerful tools for the analysis of clustered data and many extensions of the classical linear mixed model with normally distributed response have been established. As with all parametric models, correctness of the assumed model is critical for the validity of the ensuing inference. An incorrectly specified parametric means model may be improved by using a local, or nonparametric, model. Two local models are proposed by a pointwise weighting of the marginal and conditional variance-covariance matrices. However, nonparametric models tend to fit to irregularities in the data and may provide fits with high variance. Model robust regression techniques estimate mean response as a convex combination of a parametric and a nonparametric model fit to the data. It is a semiparametric method by which incomplete or incorrectly specified parametric models can be improved by adding an appropriate amount of the nonparametric fit. We compare the approximate integrated mean square error of the parametric, nonparametric, and mixed model robust methods via a simulation study and apply these methods to two real data sets: the monthly wind speed data from counties in Ireland and the engine speed data.
- Nonparametric and Semiparametric Mixed Model Methods for Phase I Profile MonitoringAbdel-Salam, Abdel-Salam Gomaa; Birch, Jeffrey B.; Jensen, Willis A. (Virginia Tech, 2010)Profile monitoring is an approach in quality control best used where the process data follow a profile (or curve). The majority of previous studies in profile monitoring focused on the parametric modeling of either linear or nonlinear profiles, with both fixed and random-effects, under the assumption of correct model specification. Our work considers those cases where the parametric model for the family of profiles is unknown or, at least uncertain. Consequently, we consider monitoring profiles via two methods, a nonparametric (NP) method and a semiparametric procedure that combines both parametric and NP profile fits. We refer to our semiparametric procedure as mixed model robust profile monitoring (MMRPM). Also, we incorporate a mixed model approach to both the parametric and NP model fits to account for the autocorrelation within profiles and to deal with the collection of profiles as a random sample from a common population. For each case, we propose two Hotelling’s T² statistics for use in Phase I analysis to determine unusual profiles, one based on the estimated random effects and one based on the fitted values and obtain the corresponding control limits. Our simulation results show that our methods are robust to the common problem of model misspecification of the user’s proposed parametric model. We also found that both the NP and the semiparametric methods result in charts with good abilities to detect changes in Phase I data, and in charts with easily calculated control limits. The proposed methods provide greater flexibility and efficiency when compared to parametric methods commonly used in profile monitoring for Phase I that rely on correct model specification, an unrealistic situation in many practical problems in industrial applications. An example using our techniques is also presented.
- Outlier Robust Nonlinear Mixed Model EstimationWilliams, James D.; Birch, Jeffrey B.; Abdel-Salam, Abdel-Salam Gomaa (Virginia Tech, 2014)In standard analyses of data well-modeled by a nonlinear mixed model (NLMM), an aberrant observation, either within a cluster, or an entire cluster itself, can greatly distort parameter estimates and subsequent standard errors. Consequently, inferences about the parameters are misleading. This paper proposes an outlier robust method based on linearization to estimate fixed effects parameters and variance components in the NLMM. An example is given using the 4-parameter logistic model and bioassay data, comparing the robust parameter estimates to the nonrobust estimates given by SASR®.