Title from PDF of title page (University of Missouri--Columbia, viewed on March 10, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Thesis advisor: Dr. Steve Osterlind. Includes bibliographical references.

This simulation study was designed to assess the impact of three ad hoc procedures for handling missing level two (here, school) identifiers in multilevel modeling. A multiple membership data structure was generated and both conventional hierarchical linear modeling (HLM) and multiple membership random effects modeling (MMREM) were employed. HLM models purely hierarchical data structures while MMREM appropriately models multiple membership data structures. Two of the ad hoc procedures investigated involved removing different subsamples of students from the analysis (HLM-Delete and MMREM-Delete) while the other procedure retained all subjects and involved creating a pseudo-identifier for the missing level two identifier (MMREM-Unique). Relative parameter and standard error (SE) bias were calculated for each parameter estimated to assess parameter recovery. Across the conditions and parameters investigated, each procedure had some level of substantial bias. MMREM-Unique and MMREM-Delete resulted in the least amount of relative parameter bias while HLM-Delete resulted in the least amount of relative SE bias. Results and implications for applied researchers are discussed. / text

Mediational analysis quantifies proposed causal mechanisms through which treatments act on outcomes. In the presence of clustered data, conventional multiple regression mediational methods break down, requiring the use of hierarchical linear modeling techniques. As an additional consideration, nonlinear relationships in multilevel mediation models require unique specifications that are ignored if modeled linearly. Improper specification of nonlinear relationships can lead to a consistently overestimated mediated effect. This has direct implications for inferences regarding intervention causality and efficacy. The current investigation examined a specific nonlinear multilevel mediation model parameterization to account for nonlinear relationships in clustered data. A simulation study was conducted to compare linear and nonlinear model specifications in the presence of truly nonlinear data. MacKinnon et al.’s (2007a) empirical-M based PRODCLIN method for estimating the confidence interval surrounding the instantaneous indirect effect was used to compare confidence interval coverage rates surrounding both the linear and nonlinear models’ estimates. Overall, the nonlinear model’s estimates were less biased, more efficient, and produced higher coverage rates than the linear model specification. For conditions containing a true value of zero for the instantaneous indirect effect, bias, efficiency, and coverage rate values were similar for the linear and nonlinear estimators. For conditions with a non-zero value for the instantaneous indirect effect, both the linear and nonlinear models were substantially biased. However, the nonlinear model was always less biased and always produced higher coverage rates than the linear model. The nonlinear model was more efficient than the linear model for all but two design conditions. / text

This thesis consists of results relating to the theoretical and computational advances in modeling the Normal-Normal hierarchical model. / Statistics

Symmetrical multilevel diversity coding (SMDC) is a classical model for coding over distributed storage. In this setting, a simple separate encoding strategy known as superposition coding was shown to be optimal in terms of achieving the minimum sum rate and the entire admissible rate region of the problem in the literature. The proofs utilized carefully constructed induction arguments, for which the classical subset entropy inequality of Han played a key role. This thesis includes two parts. In the first part the existing optimality proofs for classical SMDC are revisited, with a focus on their connections to subset entropy inequalities. First, a new sliding-window subset entropy inequality is introduced and then used to establish the optimality of superposition coding for achieving the minimum sum rate under a weaker source-reconstruction requirement. Second, a subset entropy inequality recently proved by Madiman and Tetali is used to develop a new structural understanding to the proof of Yeung and Zhang on the optimality of superposition coding for achieving the entire admissible rate region. Building on the connections between classical SMDC and the subset entropy inequalities developed in the first part, in the second part the optimality of superposition coding is further extended to the cases where there is an additional all-access encoder, an additional secrecy constraint or an encoder hierarchy.

The advantages of Multilevel Item Response Theory (MLIRT) model have been studied by several researchers, and even the impact of ignoring a higher level of data structure in multilevel analysis has been studied and discussed. However, due to the technical complexity of modeling and the shortage in function of dealing with multilevel data in traditional IRT packages (e.g., BILOG and PARSCALE), researchers may not be able to analyze the multilevel IRT data accurately. The impact of this type of misspecification, especially for MLIRT models, has not yet been thoughtfully examined. This dissertation consists of two studies: one is a Monte Carlo study that investigates the impact of this type of misspecification and the other one is a study with real-world data to validate the results obtaining from the simulation study. In Study One (the simulation study), we investigate the potential impact of several factors, including: intra-class correlation (ICC), sample size, cluster size and test length, on the parameter estimates and corresponding test of significance under two situations: when the higher level nesting structure is appropriately modeled (i.e., true model condition) versus inappropriately modeled (i.e., misspecified model condition). Three-level straightly hierarchical data (i.e., items are nested within students who are further nested within schools) were generated. Two person-related and school-related covariates were added at the second level (i.e., person-level) and the third level (i.e., school-level), respectively. The results of simulation studies showed that both parameter estimates and their corresponding standard errors would be biased if the higher level nesting structure was ignored. In Study Two, a real data from the Programme for International Student Assessment with purely hierarchical structure were analyzed by comparing parameter estimates when inappropriate versus appropriate IRT models are specified. The findings mirrored the results obtained from the first study. The implication of this dissertation to researchers is that it is important to model the multilevel data structure even in item response theory models. Researchers should interpret their results in caution when ignoring a higher level nesting structure in MLIRT models. What's more, the findings may help researchers determine when MLIRT should be used to get an unbiased result. Limitations concerning about some of the constraints of the simulation study could be relaxed. For instance, although this study used only dichotomous items, the MLIRT could also be used with polytomous items. The test length could be longer and more variability could be introduced into the item parameters’ values.

ABSTRACT The TDR measures soil water content by measuring the travel time of an electromagnetic step pulse through a wave guide embedded in the soil. Damage during insertion and retrieval of the probe makes it unsuitable for repeated use. A multilevel-TDR probe with adequate protection for cable was designed and tested to overcome this problem. Each section of the multilevel-TDR probe was constructed by embedding a 60 mm centre rod and a 63 mm outer loop in grooves on the outer wall of a 200 mm section of PVC pipe. Fifteen such probes were tested in the laboratory and the field by comparing it with the weighing method. Regression analysis between TDR-ϴv and weighing method-ϴv showed good correlation with an R2 of 0.97 and 0.98 during two laboratory experiments and 0.51 during the field experiment. This multilevel probe is cost effective, reusable and can measure soil water content at different depths.

ABSTRACT The TDR measures soil water content by measuring the travel time of an electromagnetic step pulse through a wave guide embedded in the soil. Damage during insertion and retrieval of the probe makes it unsuitable for repeated use. A multilevel-TDR probe with adequate protection for cable was designed and tested to overcome this problem. Each section of the multilevel-TDR probe was constructed by embedding a 60 mm centre rod and a 63 mm outer loop in grooves on the outer wall of a 200 mm section of PVC pipe. Fifteen such probes were tested in the laboratory and the field by comparing it with the weighing method. Regression analysis between TDR-ϴv and weighing method-ϴv showed good correlation with an R2 of 0.97 and 0.98 during two laboratory experiments and 0.51 during the field experiment. This multilevel probe is cost effective, reusable and can measure soil water content at different depths.

Hierarchical models are applicable to modeling data from complex surveys or longitudinal data when a clustered or multistage sample design is employed. The focus of this thesis is to investigate inference for discrete hierarchical models in the presence of missing data. This thesis is divided into two parts: in the first part, methods are developed to analyze the discrete and ordinal response data from hierarchical longitudinal studies. Several approximation methods have been developed to estimate the parameters for the fixed and random effects in the context of generalized linear models. The thesis focuses on two likelihood-based estimation procedures, the pseudo likelihood (PL) method and the adaptive Gaussian quadrature (AGQ) method. The simulation results suggest that AGQ is preferable to PL when the goal is to estimate the variance of the random intercept in a complex hierarchical model. AGQ provides smaller biases for the estimate of the variance of the random intercept. Furthermore, it permits greater flexibility in accommodating user-defined likelihood functions. In the second part, simulated data are used to develop a method for modeling longitudinal binary data when non-response depends on unobserved responses. This simulation study modeled three-level discrete hierarchical data with 30% and 40% missing data using a missing not at random (MNAR) missing-data mechanism. It focused on a monotone missing data-pattern. The imputation methods used in this thesis are: complete case analysis (CCA), last observation carried forward (LOCF), available case missing value (ACMVPM) restriction, complete case missing value (CCMVPM) restriction, neighboring case missing value (NCMVPM) restriction, selection model with predictive mean matching method (SMPM), and Bayesian pattern mixture model. All three restriction methods and the selection model used the predictive mean matching method to impute missing data. Multiple imputation is used to impute the missing values. These m imputed values for each missing data produce m complete datasets. Each dataset is analyzed and the parameters are estimated. The results from the m analyses are then combined using the method of Rubin(1987), and inferences are made from these results. Our results suggest that restriction methods provide results that are superior to those of other methods. The selection model provides smaller biases than the LOCF methods but as the proportion of missing data increases the selection model is not better than LOCF. Among the three restriction methods the ACMVPM method performs best. The proposed method provides an alternative to standard selection and pattern-mixture modeling frameworks when data are not missing at random. This method is applied to data from the third Waterloo Smoking Project, a seven-year smoking prevention study having substantial non-response due to loss-to-follow-up.

Thesis (M.A.)--University of Toronto, 2005.