Matching Items (3)
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
Some topics concerning the singular value decomposition and generalized singular value decomposition
Description
This dissertation involves three problems that are all related by the use of the singular value decomposition (SVD) or generalized singular value decomposition (GSVD). The specific problems are (i) derivation of a generalized singular value expansion (GSVE), (ii) analysis of the properties of the chi-squared method for regularization parameter selection in the case of nonnormal data and (iii) formulation of a partial canonical correlation concept for continuous time stochastic processes. The finite dimensional SVD has an infinite dimensional generalization to compact operators. However, the form of the finite dimensional GSVD developed in, e.g., Van Loan does not extend directly to infinite dimensions as a result of a key step in the proof that is specific to the matrix case. Thus, the first problem of interest is to find an infinite dimensional version of the GSVD. One such GSVE for compact operators on separable Hilbert spaces is developed. The second problem concerns regularization parameter estimation. The chi-squared method for nonnormal data is considered. A form of the optimized regularization criterion that pertains to measured data or signals with nonnormal noise is derived. Large sample theory for phi-mixing processes is used to derive a central limit theorem for the chi-squared criterion that holds under certain conditions. Departures from normality are seen to manifest in the need for a possibly different scale factor in normalization rather than what would be used under the assumption of normality. The consequences of our large sample work are illustrated by empirical experiments. For the third problem, a new approach is examined for studying the relationships between a collection of functional random variables. The idea is based on the work of Sunder that provides mappings to connect the elements of algebraic and orthogonal direct sums of subspaces in a Hilbert space. When combined with a key isometry associated with a particular Hilbert space indexed stochastic process, this leads to a useful formulation for situations that involve the study of several second order processes. In particular, using our approach with two processes provides an independent derivation of the functional canonical correlation analysis (CCA) results of Eubank and Hsing. For more than two processes, a rigorous derivation of the functional partial canonical correlation analysis (PCCA) concept that applies to both finite and infinite dimensional settings is obtained.
ContributorsHuang, Qing (Author) / Eubank, Randall (Thesis advisor) / Renaut, Rosemary (Thesis advisor) / Cochran, Douglas (Committee member) / Gelb, Anne (Committee member) / Young, Dennis (Committee member) / Arizona State University (Publisher)
Created2012
Description
A simulation study was conducted to explore the robustness of general factor mean difference estimation in bifactor ordered-categorical data. In the No Differential Item Functioning (DIF) conditions, the data generation conditions varied were sample size, the number of categories per item, effect size of the general factor mean difference, and the size of specific factor loadings; in data analysis, misspecification conditions were introduced in which the generated bifactor data were fit using a unidimensional model, and/or ordered-categorical data were treated as continuous data. In the DIF conditions, the data generation conditions varied were sample size, the number of categories per item, effect size of latent mean difference for the general factor, the type of item parameters that had DIF, and the magnitude of DIF; the data analysis conditions varied in whether or not setting equality constraints on the noninvariant item parameters.
Results showed that falsely fitting bifactor data using unidimensional models or failing to account for DIF in item parameters resulted in estimation bias in the general factor mean difference, while treating ordinal data as continuous had little influence on the estimation bias as long as there was no severe model misspecification. The extent of estimation bias produced by misspecification of bifactor datasets with unidimensional models was mainly determined by the degree of unidimensionality (i.e., size of specific factor loadings) and the general factor mean difference size. When the DIF was present, the estimation accuracy of the general factor mean difference was completely robust to ignoring noninvariance in specific factor loadings while it was very sensitive to failing to account for DIF in threshold parameters. With respect to ignoring the DIF in general factor loadings, the estimation bias of the general factor mean difference was substantial when the DIF was -0.15, and it can be negligible for smaller sizes of DIF. Despite the impact of model misspecification on estimation accuracy, the power to detect the general factor mean difference was mainly influenced by the sample size and effect size. Serious Type I error rate inflation only occurred when the DIF was present in threshold parameters.
Results showed that falsely fitting bifactor data using unidimensional models or failing to account for DIF in item parameters resulted in estimation bias in the general factor mean difference, while treating ordinal data as continuous had little influence on the estimation bias as long as there was no severe model misspecification. The extent of estimation bias produced by misspecification of bifactor datasets with unidimensional models was mainly determined by the degree of unidimensionality (i.e., size of specific factor loadings) and the general factor mean difference size. When the DIF was present, the estimation accuracy of the general factor mean difference was completely robust to ignoring noninvariance in specific factor loadings while it was very sensitive to failing to account for DIF in threshold parameters. With respect to ignoring the DIF in general factor loadings, the estimation bias of the general factor mean difference was substantial when the DIF was -0.15, and it can be negligible for smaller sizes of DIF. Despite the impact of model misspecification on estimation accuracy, the power to detect the general factor mean difference was mainly influenced by the sample size and effect size. Serious Type I error rate inflation only occurred when the DIF was present in threshold parameters.
ContributorsLiu, Yixing (Author) / Thompson, Marilyn (Thesis advisor) / Levy, Roy (Committee member) / O’Rourke, Holly (Committee member) / Arizona State University (Publisher)
Created2019