Worsley K J
Department of Mathematics and Statistics, McGill University, West, Montreal, Québec, Canada.
Neuroimage. 2005 Jun;26(2):635-41. doi: 10.1016/j.neuroimage.2005.02.007. Epub 2005 Mar 24.
In the statistical analysis of fMRI data, the parameter of primary interest is the effect of a contrast; of secondary interest is its standard error, and of tertiary interest is the standard error of this standard error, or equivalently, the degrees of freedom (df). In a ReML (Restricted Maximum Likelihood) analysis, we show how spatial smoothing of temporal autocorrelations increases the effective df (but not the smoothness of primary or secondary parameter estimates), so that the amount of smoothing can be chosen in advance to achieve a target df, typically 100. This has already been done at the second level of a hierarchical analysis by smoothing the ratio of random to fixed effects variances (Worsley, K.J., Liao, C., Aston, J.A.D., Petre, V., Duncan, G.H., Morales, F., Evans, A.C., 2002. A general statistical analysis for fMRI data. NeuroImage, 15:1-15); we now show how to do it at the first level, by smoothing autocorrelation parameters. The proposed method is extremely fast and it does not require any image processing. It can be used in conjunction with other regularization methods (Gautama, T., Van Hulle, M.M., in press. Optimal spatial regularisation of autocorrelation estimates in fMRI analysis. NeuroImage.) to avoid unnecessary smoothing beyond 100 df. Our results on a typical 6-min, TR = 3, 1.5-T fMRI data set show that 8.5-mm smoothing is needed to achieve 100 df, and this results in roughly a doubling of detected activations.
在功能磁共振成像（fMRI）数据的统计分析中，主要关注的参数是对比效应；其次关注的是其标准误差，再次关注的是该标准误差的标准误差，或者等效地，自由度（df）。在限制最大似然（ReML）分析中，我们展示了时间自相关的空间平滑如何增加有效自由度（但不会增加主要或次要参数估计的平滑度），从而可以预先选择平滑量以达到目标自由度，通常为100。这已经在分层分析的第二级通过平滑随机效应与固定效应方差的比率完成了（沃斯利，K.J.，廖，C.，阿斯顿，J.A.D.，彼得雷，V.，邓肯，G.H.，莫拉莱斯，F.，埃文斯，A.C.，2002年。fMRI数据的一般统计分析。《神经图像》，15:1 - 15）；我们现在展示如何在第一级通过平滑自相关参数来做到这一点。所提出的方法极其快速，并且不需要任何图像处理。它可以与其他正则化方法结合使用（高塔马，T.，范胡勒，M.M.，即将出版。fMRI分析中自相关估计的最优空间正则化。《神经图像》），以避免超过100自由度的不必要平滑。我们在一个典型的6分钟、重复时间（TR）= 3、1.5特斯拉fMRI数据集上的结果表明，需要8.5毫米的平滑才能达到100自由度，这导致检测到的激活大致翻倍。
