To statistically compare the non-clustered and clustered analyses, the advanced Akaike's Information Criterion (AIC) as derived in d'Auvergne and Gooley (2003) can be used. This information is stored within the recorded log files. Open the ∼/tmp/dispersion/log_non_clustered file and search for the model selection section. The text for residues 59 to 67 should be:
[basicstyle=\ttfamily \tiny,language=relax_log,numbers=none] The spin cluster [':59@N']. # Data pipe Num_params_(k) Num_data_sets_(n) Chi2 Criterion No Rex - relax_disp (Mon Feb 17 18:00:16 2014) 2 30 1577.42286 1581.42286 CR72 - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 31.48415 41.48415 NS CPMG 2-site expanded - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 31.84758 41.84758 The model from the data pipe 'CR72 - relax_disp (Mon Feb 17 18:00:16 2014)' has been selected. The spin cluster [':60@N']. # Data pipe Num_params_(k) Num_data_sets_(n) Chi2 Criterion No Rex - relax_disp (Mon Feb 17 18:00:16 2014) 2 30 2647.97449 2651.97449 The model from the data pipe 'No Rex - relax_disp (Mon Feb 17 18:00:16 2014)' has been selected. The spin cluster [':61@N']. # Data pipe Num_params_(k) Num_data_sets_(n) Chi2 Criterion No Rex - relax_disp (Mon Feb 17 18:00:16 2014) 2 30 15019.24382 15023.24382 CR72 - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 77.50622 87.50622 NS CPMG 2-site expanded - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 74.73334 84.73334 The model from the data pipe 'NS CPMG 2-site expanded - relax_disp (Mon Feb 17 18:00:16 2014)' has been selected. The spin cluster [':62@N']. # Data pipe Num_params_(k) Num_data_sets_(n) Chi2 Criterion No Rex - relax_disp (Mon Feb 17 18:00:16 2014) 2 30 722.91592 726.91592 NS CPMG 2-site expanded - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 30.11618 40.11618 The model from the data pipe 'NS CPMG 2-site expanded - relax_disp (Mon Feb 17 18:00:16 2014)' has been selected. The spin cluster [':63@N']. # Data pipe Num_params_(k) Num_data_sets_(n) Chi2 Criterion No Rex - relax_disp (Mon Feb 17 18:00:16 2014) 2 30 5455.72135 5459.72135 CR72 - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 58.56731 68.56731 NS CPMG 2-site expanded - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 59.90738 69.90738 The model from the data pipe 'CR72 - relax_disp (Mon Feb 17 18:00:16 2014)' has been selected. The spin cluster [':64@N']. # Data pipe Num_params_(k) Num_data_sets_(n) Chi2 Criterion No Rex - relax_disp (Mon Feb 17 18:00:16 2014) 2 30 13736.91051 13740.91051 CR72 - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 28.66223 38.66223 NS CPMG 2-site expanded - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 29.54008 39.54008 The model from the data pipe 'CR72 - relax_disp (Mon Feb 17 18:00:16 2014)' has been selected. The spin cluster [':65@N']. # Data pipe Num_params_(k) Num_data_sets_(n) Chi2 Criterion No Rex - relax_disp (Mon Feb 17 18:00:16 2014) 2 30 2498.29408 2502.29408 CR72 - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 35.13518 45.13518 NS CPMG 2-site expanded - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 36.17043 46.17043 The model from the data pipe 'CR72 - relax_disp (Mon Feb 17 18:00:16 2014)' has been selected. The spin cluster [':66@N']. # Data pipe Num_params_(k) Num_data_sets_(n) Chi2 Criterion No Rex - relax_disp (Mon Feb 17 18:00:16 2014) 2 30 962.74016 966.74016 CR72 - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 15.02929 25.02929 NS CPMG 2-site expanded - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 15.08439 25.08439 The model from the data pipe 'CR72 - relax_disp (Mon Feb 17 18:00:16 2014)' has been selected. The spin cluster [':67@N']. # Data pipe Num_params_(k) Num_data_sets_(n) Chi2 Criterion No Rex - relax_disp (Mon Feb 17 18:00:16 2014) 2 30 16773.20431 16777.20431 CR72 - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 118.17857 128.17857 NS CPMG 2-site expanded - relax_disp (Mon Feb 17 18:00:16 2014) 5 30 111.56710 121.56710 The model from the data pipe 'NS CPMG 2-site expanded - relax_disp (Mon Feb 17 18:00:16 2014)' has been selected.
For the log file from the clustered analysis (the ∼/tmp/dispersion/log_clustered file), the text should be as follows:
[basicstyle=\ttfamily \tiny,language=relax_log,numbers=none] The spin cluster [':59', ':60', ':61', ':62', ':63', ':64', ':65', ':66', ':67']. # Data pipe Num_params_(k) Num_data_sets_(n) Chi2 Criterion No Rex - relax_disp (Sun Feb 23 19:36:51 2014) 16 240 56914.82514 56946.82514 NS CPMG 2-site expanded - relax_disp (Sun Feb 23 19:36:51 2014) 26 240 510.96553 562.96553 The model from the data pipe 'NS CPMG 2-site expanded - relax_disp (Sun Feb 23 19:36:51 2014)' has been selected.
The numbers for the `NS CPMG 2-site expanded' model can be directly compared. This is because the parameter number, data set number, chi-squared value and AIC value (labelled as `Criterion' in the logs) can be summed for the non-clustered analysis and then compared to the clustered values.
Analysis |
Parameter | Data set | Chi-squared | AIC value |
number (k) | number (n) | value | ||
Non-clustered |
40 | 240 | 388.966 | 468.966 |
Clustered | 26 | 240 | 510.966 | 562.966 |
The Akaike Information Criterion value is much less for the non-clustered analysis. Therefore this result is the most parsimonious - the result closest to Occam's razor as defined by frequentist statistics. Therefore the non-clustered analysis is a statistically better description of the experimental data for this set of residues. For a different cluster of spins, the result may be different. If the assumptions of the same dynamics for all spins (both populations pA and exchange rates kex) is correct, the results of the clustered analysis are nevertheless useful as it can decrease parameter uncertainty. If the assumption is not correct, then the decrease in parameter uncertainty will be coupled with a parameter bias - a shift of the parameter away from reality. This should be avoided at all costs.
To perform a relaxation dispersion analysis on your own system, care in the setup, model choice and design of the clustering should be taken: