An exploration of time series models and their application to functional magnetic resonance imaging Open Access
Liang, Mingrui (Spring 2018)
Published
Abstract
The general linear model is a popular tool in functional magnetic resonance imaging (fMRI) data analysis. One of the major problems in fMRI data analysis is that the fMRI blood-dependent oxygen level dependent (BOLD) time course is serially correlated. Some of the mainstream neuroimaging software packages use overly simplified models of time series errors, such as AR(1), which can lead to invalid inference due to the in- ability to account for serial correlation. There has been renewed interested in this issue with recent developments in acquisition protocols leading to much shorter time to repetition (TR), or the time between acquisition of brain images. We compared different modeling methods in this article in order to explore the factors that contribute to inflated type I error rates in fMRI time series data analysis. We introduce the application of autoregressive moving average models (ARMA) to the analysis of single-subject fMRI data, where the order of the AR and MA components are chosen using Akaike’s information criterion corrected for small sample size (AICc). Simulations were used to examine type I error rates. When the true model has an AR(1) structure, more flexible ARMA(p, q) models generally lowered the type one error rates relative to ordinary least squares (OLS) and the AR(6) model, but were often still higher than nominal levels. We also estimated spatially specific time series models for thirty subjects in a motor task from the Human Connectome Project, where control variables orthogonal to the conventional covariate matrix were introduced to gain insight into type one errors. The value of the autocorrelation function is downwardly biased when using OLS residuals, which would select the incorrect time series model. We also suggest that the length of the time series data and model complexity may affect the accuracy of inference.
Table of Contents
Contents
1 Introduction ................ ................ ................1
2 ARMA Overview................ ................ .......... 2
3 Simulation ................ ................ ................3
3.1 SimulationSetting ................................... 3
3.2 SimulationResults ................................... 4
3.2.1 RandomGaussianvector ........................... 4
3.2.2 Structuredcontrolvariable .......................... 4
3.2.3 RandomGaussianmatrix ........................... 7
3.2.4 Motor-task covariate matrix with control variable . . . . . . . . . . . . . . 8
4 Methods ................ ................ ................ ................10
4.1 TheHumanConnectomeProject ........................... 10
4.2 ExperimentSetting................................... 10
5 Results................ ................ ................ . 11
5.1 ACFsAndPACFs ................................... 11
5.2 ModelSelection..................................... 15
5.3 TypeIErrorRates................................... 18
5.4 ActivationPlots .................................... 18
6 Discussion................ ................ ............... 19
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An exploration of time series models and their application to functional magnetic resonance imaging () | 2018-04-05 10:51:09 -0400 |
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