An Overview of Methods in the Analysis of Dependent ordered catagorical Data: Assumptions and Implications

Subjective assessments of pain, quality of life, ability etc. measured by rating scales and questionnaires are common in clinical research. The resulting responses are categorical with an ordered structure and the statistical methods must take account of this type of data structure. In this paper we give an overview of methods for analysis of dependent ordered categorical data and a comparison of standard models and measures with nonparametric augmented rank measures proposed by Svensson. We focus on assumptions and issues behind model specifications and data as well as implications of the methods. First we summarise some fundamental models for categorical data and two main approaches for repeated ordinal data; marginal and cluster-specific models. We then describe models and measures for application in agreement studies and finally give a summary of the approach of Svensson. The paper concludes with a summary of important aspects.Dependent ordinal data; GEE; GLMM; Logit; modelling

Adaptive Mantel Test for AssociationTesting in Imaging Genetics Data

Mantel's test (MT) for association is conducted by testing the linear relationship of similarity of all pairs of subjects between two observational domains. Motivated by applications to neuroimaging and genetics data, and following the succes of shrinkage and kernel methods for prediction with high-dimensional data, we here introduce the adaptive Mantel test as an extension of the MT. By utilizing kernels and penalized similarity measures, the adaptive Mantel test is able to achieve higher statistical power relative to the classical MT in many settings. Furthermore, the adaptive Mantel test is designed to simultaneously test over multiple similarity measures such that the correct type I error rate under the null hypothesis is maintained without the need to directly adjust the significance threshold for multiple testing. The performance of the adaptive Mantel test is evaluated on simulated data, and is used to investigate associations between genetics markers related to Alzheimer's Disease and heatlhy brain physiology with data from a working memory study of 350 college students from Beijing Normal University

Covariance Estimation: The GLM and Regularization Perspectives

Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent high-dimensional data environment where enforcing the positive-definiteness constraint could be computationally expensive. We provide a survey of the progress made in modeling covariance matrices from two relatively complementary perspectives: (1) generalized linear models (GLM) or parsimony and use of covariates in low dimensions, and (2) regularization or sparsity for high-dimensional data. An emerging, unifying and powerful trend in both perspectives is that of reducing a covariance estimation problem to that of estimating a sequence of regression problems. We point out several instances of the regression-based formulation. A notable case is in sparse estimation of a precision matrix or a Gaussian graphical model leading to the fast graphical LASSO algorithm. Some advantages and limitations of the regression-based Cholesky decomposition relative to the classical spectral (eigenvalue) and variance-correlation decompositions are highlighted. The former provides an unconstrained and statistically interpretable reparameterization, and guarantees the positive-definiteness of the estimated covariance matrix. It reduces the unintuitive task of covariance estimation to that of modeling a sequence of regressions at the cost of imposing an a priori order among the variables. Elementwise regularization of the sample covariance matrix such as banding, tapering and thresholding has desirable asymptotic properties and the sparse estimated covariance matrix is positive definite with probability tending to one for large samples and dimensions.Comment: Published in at http://dx.doi.org/10.1214/11-STS358 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org