Estimating the effective degrees of freedom in univariate multiple regression analysis

Medical Image Analysis

Volumn 6, Issue 1, 2002, Pages 63-75

  Kruggel, F ^a   Pelegrini Issac M ^b   Benali, H ^b  

^a MAX PLANCK INSTITUTE FOR HUMAN COGNITIVE AND BRAIN SCIENCES   (Germany)

^b INSERM   (France)

Author keywords

Effective degrees of freedom; Functional MRI; Multiple linear regression; Temporal autocorrelations

Indexed keywords

ARTICLE; CONTROLLED STUDY; DATA ANALYSIS; IMAGE PROCESSING; INTERMETHOD COMPARISON; LINEAR SYSTEM; MATHEMATICAL COMPUTING; METHODOLOGY; MULTIPLE REGRESSION; NUCLEAR MAGNETIC RESONANCE IMAGING; PRIORITY JOURNAL; SIGNAL DETECTION; SIMULATION; STATISTICAL MODEL; VALIDATION PROCESS;

ANALYSIS OF VARIANCE; BRAIN; HUMANS; LINEAR MODELS; MAGNETIC RESONANCE IMAGING; MODELS, THEORETICAL; MULTIVARIATE ANALYSIS; PHANTOMS, IMAGING; PREDICTIVE VALUE OF TESTS; SENSITIVITY AND SPECIFICITY;

EID: 0036522413     PISSN: 13618415     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1361-8415(01)00052-4     Document Type: Article

References (38)

1. Benali, H., Buvat, I., Anton, J.L., Pélégrini, M., Di Paola, M., Bittoun, J., Burnod, Y., Di Paola, R., 1997. Space-time statistical model for functional MRI image sequences. In: Duncan, J., Gindi, G. (Eds.), Information Processing in Medical Imaging. Springer, Berlin, pp. 285-298.
2. Benali, H., Pélégrini-Issac, M., Kruggel, F., 2001. Spatio-temporal covariance model for medical images sequences: application to functional MRI data. In: Insana, M., Leahy, R.M. (Eds.), Information Processing in Medical Imaging. Springer, Berlin, pp. 197-203.
3. Biswal, B., DeYoe, E.A., Hyde, J.S., 1996. Reduction of physiological fluctuations in fMRI using digital filters. Magn. Reson. Med. 35, 107-113.
4. Bullmore, E., Brammer, M., Williams, S.C.R., Rabe-Hesketh, S., Janoth, N., David, A., Mellers, J., Howard, R., Sham, P., 1996. Statistical methods of estimation and inference for functional MR image analysis. Magn. Reson. Med. 35, 261-277.
5. Buonocore, M.H., Maddock, R.J., 1997. Noise suppression digital filter for functional magnetic resonance imaging based on image reference data. Magn. Reson. Med. 38, 456-469.
6. Burock, M.A., Dale, A.M., 2000. Estimation and detection of event-related fMRI signals with temporally correlated noise: a statistically efficient and unbiased approach. Hum. Brain Mapp. 11, 249-260.
7. Christakos, G., 1984. On the problem of permissible covariance and variogram models. Water Resources Res. 20, 251-265.
8. Cressie, N.A.C., 1993. Statistics for Spatial Data. Wiley, New York.
9. Cressie, N.A.C., Huang, H.C., 1999. Classes of nonseparable, spatio-temporal stationary covariance functions. J. Am. Statist. Assoc. 44, 1330-1340.
10. Cochrane, D., Orcutt, G.H., 1949. Application of least squares regression to relationships containing autocorrelated errors. J. Am. Statist. Assoc. 44, 32-61.
11. Descombes, X., Kruggel, F., von Cramon, D.Y., 1998. FMRI signal restoration using an edge preserving spatio-temporal Markov random field. NeuroImage 8, 340-349.
12. Durbin, J., Watson, G.S., 1950. Testing for serial correlations in least squares regression: I. Biometrika 37, 409-428.
13. Durbin, J., Watson, G.S., 1951. Testing for serial correlations in least squares regression: II. Biometrika 38, 159-178.
14. FIL Methods Group, 2000. http//www.fil.ion.ucl.ac.uk/spm/spm99.html.
15. Fine, J., Romain, Y., 1984. Reduced principal component analysis. Mathematische Operationsforschung und Statistik 15, 493-512.
16. Friston, K.J., Worsley, K.J., Frackowiak, R.S.J., Mazziotta, J.C., Evans, A.C., 1994. Assessing the significance of focal activations using their spatial extent. Hum. Brain Mapp. 1, 210-220.
17. Friston, K.J., Holmes, A.P., Poline, J.B., Grasby, P.J., Williams, S.C.R., Frackowiak, R.S.J., Turner, R., 1995a. Analysis of fMRI time-series revisited. NeuroImage 2, 45-53.
18. Friston, K.J., Holmes, A.P., Worsley, K.J., Poline, J.B., Frith, C.D., Frackowiak, R.S.J., 1995b. Statistical parametric maps in functional imaging, a general linear approach. Hum. Brain Mapp. 2, 189-210.
19. Friston, K.J., Josephs, O., Zarahn, E., Holmes, A.P., Rouquette, S., Poline, J.B., 2000. To smooth or not to smooth? Bias and efficiency in fMRI time-series analysis. NeuroImage 12, 196-208.
20. Golub, G.H., Van Loan, C.F., 1984. Matrix Computations. The Johns Hopkins University Press, Baltimore.
21. Graybill, F.A., 1983. Matrices with Applications in Statistics. Wadsworth, Belmont.
22. Hu, X., Le, T.H., Parrish, T., Erhard, P., 1995. Retrospective estimation and correction of physiological fluctuation in functional MRI. Magn. Reson. Med. 35, 201-212.
23. Johnson, N.L., Kotz, S., Balakrishnan, N., 1995. 2nd Edition. Continuous Univariate Distributions, Vol. 2. Wiley, New York.
24. Johnson, R.A., Wichern, DW, 1988. Applied Multivariate Statistical Analysis. Prentice Hall, Englewood Cliffs.
25. Kruggel, F., von Cramon, D.Y., 1999. Modeling the hemodynamic response in single trial fMRI experiments. Magn. Reson. Med. 42, 787-797.
26. Kruggel, F., von Cramon, DY, Descombes, X., 1999. Comparison of filtering methods for fMRI datasets. NeuroImage 10, 530-543.
27. Lange, N., Zeger, S.L., 1997. Non-linear Fourier time series analysis for human brain mapping by functional magnetic resonance imaging. J. R. Statist. Soc., Appl. Statist. 46, 1-19.
28. Mardia, K.V., Kent, J.T., Bibby, J.M., 1979. Multivariate Analysis. Academic Press, London.
29. Moonen, C., Bandettini, P.A., 1999. Functional MRI. Springer, Berlin.
30. Petersen, N.V., Jensen, J.L., Burchhardt, J., Stødkilde-Jørgensen, H., 1998. State space models for physiological noise in fMRI time series. NeuroImage 7, S592.
31. Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T., 1992. Numerical Recipes in C. Cambridge University Press, Cambridge.
32. Priestley, M.B., 1996. Spectral Analysis and Time Series, 9th Edition. Academic Press, London.
33. Rajapakse, J.C., Kruggel, F., Maisog, J., von Cramon, D.Y., 1998. Modeling hemodynamic response for analysis of functional MRI time series. Hum. Brain Mapp. 6, 283-300.
34. Rencher, A.C., 1995. Methods of Multivariate Analysis. Wiley, New York.
35. Satterthwaite, F.E., 1946. An approximate distribution of estimates of variance components. Biometrika 33, 110-114.
36. Wood, A.T.A., 1989. An F approximation to the distribution of a linear combination of Chi-squared variables. Commun. Statist. - Simulations 18, 1439-1456.
37. Worsley, K.J., Friston, K.J., 1995. Analysis of fMRI time-series revisited - again. NeuroImage 2, 173-181.
38. Worsley, K.J., Friston, K.J., 1997. Characterizing the response of PET and fMRI data using multivariate linear models (MLM). NeuroImage 6, 305-319.