Matching Items (5)
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- Creators: Kao, Ming-Hung
- All Subjects: Complete class
- All Subjects: generalized method of moments
Description
When analyzing longitudinal data it is essential to account both for the correlation inherent from the repeated measures of the responses as well as the correlation realized on account of the feedback created between the responses at a particular time and the predictors at other times. A generalized method of moments (GMM) for estimating the coefficients in longitudinal data is presented. The appropriate and valid estimating equations associated with the time-dependent covariates are identified, thus providing substantial gains in efficiency over generalized estimating equations (GEE) with the independent working correlation. Identifying the estimating equations for computation is of utmost importance. This paper provides a technique for identifying the relevant estimating equations through a general method of moments. I develop an approach that makes use of all the valid estimating equations necessary with each time-dependent and time-independent covariate. Moreover, my approach does not assume that feedback is always present over time, or present at the same degree. I fit the GMM correlated logistic regression model in SAS with PROC IML. I examine two datasets for illustrative purposes. I look at rehospitalization in a Medicare database. I revisit data regarding the relationship between the body mass index and future morbidity among children in the Philippines. These datasets allow us to compare my results with some earlier methods of analyses.
ContributorsYin, Jianqiong (Author) / Wilson, Jeffrey Wilson (Thesis advisor) / Reiser, Mark R. (Committee member) / Kao, Ming-Hung (Committee member) / Arizona State University (Publisher)
Created2012
Description
Statistical model selection using the Akaike Information Criterion (AIC) and similar criteria is a useful tool for comparing multiple and non-nested models without the specification of a null model, which has made it increasingly popular in the natural and social sciences. De- spite their common usage, model selection methods are not driven by a notion of statistical confidence, so their results entail an unknown de- gree of uncertainty. This paper introduces a general framework which extends notions of Type-I and Type-II error to model selection. A theo- retical method for controlling Type-I error using Difference of Goodness of Fit (DGOF) distributions is given, along with a bootstrap approach that approximates the procedure. Results are presented for simulated experiments using normal distributions, random walk models, nested linear regression, and nonnested regression including nonlinear mod- els. Tests are performed using an R package developed by the author which will be made publicly available on journal publication of research results.
ContributorsCullan, Michael J (Author) / Sterner, Beckett (Thesis advisor) / Fricks, John (Committee member) / Kao, Ming-Hung (Committee member) / Arizona State University (Publisher)
Created2018
Description
Bivariate responses that comprise mixtures of binary and continuous variables are common in medical, engineering, and other scientific fields. There exist many works concerning the analysis of such mixed data. However, the research on optimal designs for this type of experiments is still scarce. The joint mixed responses model that is considered here involves a mixture of ordinary linear models for the continuous response and a generalized linear model for the binary response. Using the complete class approach, tighter upper bounds on the number of support points required for finding locally optimal designs are derived for the mixed responses models studied in this work.
In the first part of this dissertation, a theoretical result was developed to facilitate the search of locally symmetric optimal designs for mixed responses models with one continuous covariate. Then, the study was extended to mixed responses models that include group effects. Two types of mixed responses models with group effects were investigated. The first type includes models having no common parameters across subject group, and the second type of models allows some common parameters (e.g., a common slope) across groups. In addition to complete class results, an efficient algorithm (PSO-FM) was proposed to search for the A- and D-optimal designs. Finally, the first-order mixed responses model is extended to a type of a quadratic mixed responses model with a quadratic polynomial predictor placed in its linear model.
In the first part of this dissertation, a theoretical result was developed to facilitate the search of locally symmetric optimal designs for mixed responses models with one continuous covariate. Then, the study was extended to mixed responses models that include group effects. Two types of mixed responses models with group effects were investigated. The first type includes models having no common parameters across subject group, and the second type of models allows some common parameters (e.g., a common slope) across groups. In addition to complete class results, an efficient algorithm (PSO-FM) was proposed to search for the A- and D-optimal designs. Finally, the first-order mixed responses model is extended to a type of a quadratic mixed responses model with a quadratic polynomial predictor placed in its linear model.
ContributorsKhogeer, Hazar Abdulrahman (Author) / Kao, Ming-Hung (Thesis advisor) / Stufken, John (Committee member) / Reiser, Mark R. (Committee member) / Zheng, Yi (Committee member) / Cheng, Dan (Committee member) / Arizona State University (Publisher)
Created2020
Description
Correlation is common in many types of data, including those collected through longitudinal studies or in a hierarchical structure. In the case of clustering, or repeated measurements, there is inherent correlation between observations within the same group, or between observations obtained on the same subject. Longitudinal studies also introduce association between the covariates and the outcomes across time. When multiple outcomes are of interest, association may exist between the various models. These correlations can lead to issues in model fitting and inference if not properly accounted for. This dissertation presents three papers discussing appropriate methods to properly consider different types of association. The first paper introduces an ANOVA based measure of intraclass correlation for three level hierarchical data with binary outcomes, and corresponding properties. This measure is useful for evaluating when the correlation due to clustering warrants a more complex model. This measure is used to investigate AIDS knowledge in a clustered study conducted in Bangladesh. The second paper develops the Partitioned generalized method of moments (Partitioned GMM) model for longitudinal studies. This model utilizes valid moment conditions to separately estimate the varying effects of each time-dependent covariate on the outcome over time using multiple coefficients. The model is fit to data from the National Longitudinal Study of Adolescent to Adult Health (Add Health) to investigate risk factors of childhood obesity. In the third paper, the Partitioned GMM model is extended to jointly estimate regression models for multiple outcomes of interest. Thus, this approach takes into account both the correlation between the multivariate outcomes, as well as the correlation due to time-dependency in longitudinal studies. The model utilizes an expanded weight matrix and objective function composed of valid moment conditions to simultaneously estimate optimal regression coefficients. This approach is applied to Add Health data to simultaneously study drivers of outcomes including smoking, social alcohol usage, and obesity in children.
ContributorsIrimata, Kyle (Author) / Wilson, Jeffrey R (Thesis advisor) / Broatch, Jennifer (Committee member) / Kamarianakis, Ioannis (Committee member) / Kao, Ming-Hung (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2018
Description
This study concerns optimal designs for experiments where responses consist of both binary and continuous variables. Many experiments in engineering, medical studies, and other fields have such mixed responses. Although in recent decades several statistical methods have been developed for jointly modeling both types of response variables, an effective way to design such experiments remains unclear. To address this void, some useful results are developed to guide the selection of optimal experimental designs in such studies. The results are mainly built upon a powerful tool called the complete class approach and a nonlinear optimization algorithm. The complete class approach was originally developed for a univariate response, but it is extended to the case of bivariate responses of mixed variable types. Consequently, the number of candidate designs are significantly reduced. An optimization algorithm is then applied to efficiently search the small class of candidate designs for the D- and A-optimal designs. Furthermore, the optimality of the obtained designs is verified by the general equivalence theorem. In the first part of the study, the focus is on a simple, first-order model. The study is expanded to a model with a quadratic polynomial predictor. The obtained designs can help to render a precise statistical inference in practice or serve as a benchmark for evaluating the quality of other designs.
ContributorsKim, Soohyun (Author) / Kao, Ming-Hung (Thesis advisor) / Dueck, Amylou (Committee member) / Pan, Rong (Committee member) / Reiser, Mark R. (Committee member) / Stufken, John (Committee member) / Arizona State University (Publisher)
Created2017