Year: 2011
Type: dissertation
Abstract: Hierarchical models are applicable to modeling data from complex \nsurveys or longitudinal data when a clustered or multistage sample \ndesign is employed. The focus of this thesis is to investigate \ninference for discrete hierarchical models in the presence of \nmissing data. This thesis is divided into two parts: in the first \npart, methods are developed to analyze the discrete and ordinal \nresponse data from hierarchical longitudinal studies. Several \napproximation methods have been developed to estimate the parameters \nfor the fixed and random effects in the context of generalized \nlinear models. The thesis focuses on two likelihood-based \nestimation procedures, the pseudo likelihood (PL) method and the adaptive \nGaussian quadrature (AGQ) method. \n \nThe simulation results suggest that AGQ \nis preferable to PL when the \ngoal is to estimate the variance of the random intercept in a \ncomplex hierarchical model. AGQ provides smaller biases \nfor the estimate of the variance of the random intercept. \nFurthermore, it permits greater \nflexibility in accommodating user-defined likelihood functions. \n \nIn the second part, simulated data are used to develop a method for \nmodeling longitudinal binary data when non-response depends on \nunobserved responses. This simulation study modeled three-level \ndiscrete hierarchical data with 30% and 40% missing data \nusing a missing not at random (MNAR) missing-data mechanism. It \nfocused on a monotone missing data-pattern. The imputation methods \nused in this thesis are: complete case analysis (CCA), last \nobservation carried forward (LOCF), available case missing value \n(ACMVPM) restriction, complete case missing value (CCMVPM) \nrestriction, neighboring case missing value (NCMVPM) restriction, \nselection model with predictive mean matching method (SMPM), and \nBayesian pattern mixture model. All three restriction methods and \nthe selection model used the predictive mean matching method to \nimpute missing data. Multiple imputation is used to impute the \nmissing values. These m imputed values for each missing data \nproduce m complete datasets. Each dataset is analyzed and the \nparameters are estimated. The results from the m analyses are then \ncombined using the method of Rubin(1987), and inferences are \nmade from these results. Our results suggest that restriction \nmethods provide results that are superior to those of other methods. \nThe selection model provides smaller biases than the LOCF methods \nbut as the proportion of missing data increases the selection model \nis not better than LOCF. Among the three restriction methods the \nACMVPM method performs best. The proposed method provides an \nalternative to standard selection and pattern-mixture modeling \nframeworks when data are not missing at random. This method is \napplied to data from the third Waterloo Smoking Project, a \nseven-year smoking prevention study having substantial non-response \ndue to loss-to-follow-up.
Source: UWSpace (University of Waterloo)
Author: Muhammad Rashid Ahmed
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2158661795