| Functional magnetic resonance imaging (fMRI) is a relatively new non-invasive technique that is used to study human brain function. However, fMRI time series contains a number of sources of variability, including uncorrelated noise, correlated noise, and a signal is a temporally blurred and delayed version of changes in neural activity. The accuracy of statistical method will depend on the way in which these factors are accounted for in a model. In this proposal, we address issues of model formulation, covariance estimation, and model selection in linear regression model of fMRI data.;Firstly, we use model diagnosis and exploratory data analysis to help detecting artifacts in the data and building a better mean structure model. In this work, we have developed a general framework for diagnosis of linear models fit to fMRI data. Using model and scan summaries and dynamic linked viewers, we have shown how to swiftly localize rare anomalies and artifacts in large 4D datasets.;Secondly, to address the intrinsic correlation in the fMRI time series data, we propose a sandwich estimator to get robust and consistent inferences for hypothesis testing. Generally speaking, the proposed GEE approach with sandwich estimation of variance has superior performance to the currently used approaches in both the simulation studies and real data analysis.;Lastly, several important model selection criteria which may be sensitive to the correlation model in fMRI data are collected and investigated. Although there is no single criterion optimal for all the purposes of our study, we demonstrate how these selection criteria can be applied in different aspects of correlation modeling in fMRI data analysis. Furthermore, the combined use of model diagnosis and model selection provides more information about the modeling of fMRI time series data and indicates possible resolution to the possible artifacts in the data. |
