Determining Predictor Importance in Multilevel Models for Longitudinal Data: An Extension of Dominance Analysis

Longitudinal models are used not only to analyze the change of an outcome over time but also to describe what person-level and time-varying factors might influence this trend. Whenever a researcher is interested in the factors or predictors impacting an outcome, a common follow-up question asked is that of the relative importance of such factors. Hence, this study aimed to extend and evaluate Dominance Analysis (DA), a method used to determine the relative importance of predictors in various linear models (Budescu, 1993; Azen & Budescu, 2003; Azen, 2013), for use with longitudinal multilevel models. A simulation study was conducted to investigate the effect of number of measurement occasions (level-1 units), number of subjects (level-2 units), different levels of model complexity (i.e., number of predictors at level-1 and level-2), size of predictor coefficients, predictor collinearity levels, misspecification of the covariance structure, and measures of model fit on DA results and provide recommendations to researchers who wish to determine the relative importance of predictors in longitudinal multilevel models. Results indicated that number of subjects was the most important factor influencing the accuracy of DA in rank-ordering the model predictors, and that more than 50 subjects are needed to obtain adequate power and confidence in the reproducibility of DA results. The McFadden pseudo R² is recommended as the standard measure of fit to use when performing DA in multilevel longitudinal models. Finally, asymptotic standard error and percentile confidence intervals constructed through bootstrapping can be used to determine if one predictor significantly dominates another but might not provide sufficient power unless there are at least 200 subjects in the sample or the magnitude of the general dominance difference measure is greater than 0.01 using McFadden’s R²

A review of agreement measure as a subset of association measure between raters

Agreement can be regarded as a special case of association and not the other way round. Virtually in all life or social science researches, subjects are being classified into categories by raters, interviewers or observers and both association and agreement measures can be obtained from the results of this researchers. The distinction between association and agreement for a given data is that, for two responses to be perfectly associated we require that we can predict the category of one response from the category of the other response, while for two response to agree, they must fall into the identical category. Which hence mean, once there is agreement between the two responses, association has already exist, however, strong association may exist between the two responses without any strong agreement. Many approaches have been proposed by various authors for measuring each of these measures. In this work, we present some up till date development on these measures statistics

Robust change-point detection and dependence modeling

This doctoral thesis consists of three parts: robust estimation of the autocorrelation function, the spatial sign correlation, and robust change-point detection in panel data. Albeit covering quite different statistical branches like time series analysis, multivariate analysis, and change-point detection, there is a common issue in all of the sections and this is robustness. Robustness is in the sense that the statistical analysis should stay reliable if there is a small fraction of observations which do not follow the chosen model. The first part of the thesis is a review study comparing different proposals for robust estimation of the autocorrelation function. Over the years many estimators have been proposed but thorough comparisons are missing, resulting in a lack of knowledge which estimator is preferable in which situation. We treat this problem, though we mainly concentrate on a special but nonetheless very popular case where the bulk of observations is generated from a linear Gaussian process. The second chapter deals with something congeneric, namely measuring dependence through the spatial sign correlation, a robust and within the elliptic model distribution-free estimator for the correlation based on the spatial sign covariance matrix. We derive its asymptotic distribution and robustness properties like influence function and gross error sensitivity. Furthermore we propose a two stage version which improves both efficiency under normality and robustness. The surprisingly simple formula of its asymptotic variance is used to construct a variance stabilizing transformation, which enables us to calculate very accurate confidence intervals, which are distribution-free within the elliptic model. We also propose a positive semi-definite multivariate spatial sign correlation, which is more efficient but less robust than its bivariate counterpart. The third chapter deals with a robust test for a location change in panel data under serial dependence. Robustness is achieved by using robust scores, which are calculated by applying psi-functions. The main focus here is to derive asymptotics under the null hypothesis of a stationary panel, if both the number of individuals and time points tend to infinity. We can show under some regularity assumptions that the limiting distribution does not depend on the underlying distribution of the panel as long as we have short range dependence in the time dimension and ndependence in the cross sectional dimension

Extensions to Canonical Correlation Analysis and Principal Components Analysis with Applicatoins to Survival and Brain Imaging Data

Canonical correlation analysis (CCA) is a method for finding a low dimension representation of the linear associations between two sets of variables. Likewise principal components analysis (PCA) is a tool for finding a low dimensional representation of a single set of variables. The solution to CCA is an eigendecomposition involving the joint covariance or correlation matrix of both sets of variables and the solution to PCA is an eigendecomposition involving the covariance or correlation matrix of the single set of variables. We extend CCA and PCA using robust or non-standard estimators of the covariance or correlation matrix. First we extend CCA using a robust correlation estimator based on transformations of Kendall's tau rank correlation coefficient. We show that the CCA estimates using this robust correlation estimator are consistent and asymptotically normal. We also define a bootstrap based testing procedure for identifying informative canonical directions. Simulations show that this robust estimator performs better than standard CCA for data from heavy tailed and skewed distributions. We apply this method to brain white matter structure data from diffusion tensor imaging (DTI) and executive function (EF) test scores in six-year-old children to show that lateralization of white matter brain structure is correlated with higher EF scores. Next we define PCA for the multivariate survival setting where failure time data can be right censored. We estimate the covariance and correlation matrices of the counting processes defined by the failure times and their associated martingales. We use eigendecomposition of these covariance and correlation matrix estimates to obtain principal direction estimates. These estimates are consistent and asymptotically normal. We apply this method to a data set from a clinical trial for patients with pancreatic cancer and are able to define medically relevant groupings of adverse events. Finally we extend robust CCA to the multi-set and high dimensional setting in which there are more than two sets of variables and one or more of the sets is high-dimensional. We use the same robust correlation estimate using transformations of Kendall's tau. We also use cross-validation for dimension reduction and testing procedures. Unlike existing methods this cross-validation testing procedure is valid when data come from a heavy tailed elliptical distribution. We extend our analysis of DTI and EF data to include brain gray matter volume data from 88 different brain regions to further investigate the association between brain structure and EF test scores.Doctor of Philosoph

Reliability Analysis And Optimal Maintenance Planning For Repairable Multi-Component Systems Subject To Dependent Competing Risks

Modern engineering systems generally consist of multiple components that interact in a complex manner. Reliability analysis of multi-component repairable systems plays a critical role for system safety and cost reduction. Establishing reliability models and scheduling optimal maintenance plans for multi-component repairable systems, however, is still a big challenge when considering the dependency of component failures. Existing models commonly make prior assumptions, without statistical verification, as to whether different component failures are independent or not. In this dissertation, data-driven systematic methodologies to characterize component failure dependency of complex systems are proposed. In CHAPTER 2, a parametric reliability model is proposed to capture the statistical dependency among different component failures under partially perfect repair assumption. Based on the proposed model, statistical hypothesis tests are developed to test the dependency of component failures. In CHAPTER 3, two reliability models for multi-component systems with dependent competing risks under imperfect assumptions are proposed, i.e., generalized dependent latent age model and copula-based trend-renewal process model. The generalized dependent latent age model generalizes the partially perfect repair model by involving the extended virtual age concept. And the copula-based trend renewal process model utilizes multiple trend functions to transform the failure times from original time domain to a transformed time domain, in which the repair conditions can be treated as partially perfect. Parameter estimation methods for both models are developed. In CHAPTER 4, based on the generalized dependent latent age model, two periodic inspection-based maintenance polices are developed for a multi-component repairable system subject to dependent competing risks. The first maintenance policy assumes all the components are restored to as good as new once a failure detected, i.e., the whole system is replaced. The second maintenance policy considers the partially perfect repair, i.e., only the failed component can be replaced after detection of failures. Both the maintenance policies are optimized with the aim to minimize the expected average maintenance cost per unit time. The developed methodologies are demonstrated by using applications of real engineering systems