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help > RE: BETA values
Apr 18, 2015 01:04 AM | Alfonso Nieto-Castanon - Boston University
RE: BETA values
Hi Liron,
Yes, exactly right, unlike the raw (unstandardized coefficients) the standardized coefficients are always invariant to scaling. They represent the raw unstandardized coefficients of an alternative model where all of the variables (both predictor and outcome variables) have been normalized (divided by their standard deviation). In your example (the standardized beta=-.313 value that SPSS was reporting) this standardized coefficient actually represents the correlation coefficient between connectivity and clinical scores. Typically the standardized coefficients are measures that are more related to the statistics (and like the statistics they are invariant to scaling) than to the effect sizes (which naturally depend on the scaling of your variables). For regression analyses you can find the standardized coefficients (which will represent the correlation, for bivariate analyses, or the partial correlation coefficients, for multivariate analyses) directly from the T statistics reported by CONN or SPSS using this formula: standardized-beta = r = T/sqrt(T^2+dof) (in your example dof=35 and T=-1.95, as reported both in CONN and SPSS, and r=-.313)
Unfortunately there is no simple way to have CONN show the standardized coefficients when reporting the results (I will see if I can easily add these values, at least in the stats reported in Tools.Calculator, for the next release). In the meantime one possible way to infer these values would be to compute these from the reported T values, as indicated by the formula above. Another possible way would be to import the connectivity values of interest as second-level covariates and then performing your regression analysis using Tools.Calculator after normalizing all of your variables-of-interest (note: you can easily normalize a second-level covariate in Setup.Covariates.SecondLevel by entering in the Values field "name/std(name)" -without the quotes and changing 'name' for the actual name of your second-level covariate-). In this way the reported (unstandardized) beta values in Tools.Calculator when using normalized predictor/outcome variables will represent the standardized beta values of the original (without normalizing the variables) regression analysis.
Hope this helps
Alfonso
Originally posted by L R:
Yes, exactly right, unlike the raw (unstandardized coefficients) the standardized coefficients are always invariant to scaling. They represent the raw unstandardized coefficients of an alternative model where all of the variables (both predictor and outcome variables) have been normalized (divided by their standard deviation). In your example (the standardized beta=-.313 value that SPSS was reporting) this standardized coefficient actually represents the correlation coefficient between connectivity and clinical scores. Typically the standardized coefficients are measures that are more related to the statistics (and like the statistics they are invariant to scaling) than to the effect sizes (which naturally depend on the scaling of your variables). For regression analyses you can find the standardized coefficients (which will represent the correlation, for bivariate analyses, or the partial correlation coefficients, for multivariate analyses) directly from the T statistics reported by CONN or SPSS using this formula: standardized-beta = r = T/sqrt(T^2+dof) (in your example dof=35 and T=-1.95, as reported both in CONN and SPSS, and r=-.313)
Unfortunately there is no simple way to have CONN show the standardized coefficients when reporting the results (I will see if I can easily add these values, at least in the stats reported in Tools.Calculator, for the next release). In the meantime one possible way to infer these values would be to compute these from the reported T values, as indicated by the formula above. Another possible way would be to import the connectivity values of interest as second-level covariates and then performing your regression analysis using Tools.Calculator after normalizing all of your variables-of-interest (note: you can easily normalize a second-level covariate in Setup.Covariates.SecondLevel by entering in the Values field "name/std(name)" -without the quotes and changing 'name' for the actual name of your second-level covariate-). In this way the reported (unstandardized) beta values in Tools.Calculator when using normalized predictor/outcome variables will represent the standardized beta values of the original (without normalizing the variables) regression analysis.
Hope this helps
Alfonso
Originally posted by L R:
Thank you so much Alfonso for guiding me through
this!! So basically all BETA values in CONN are unstandardized, and
when looking for the SPSS equivalent I should look for the B
values (i.e. unstandartized), and not the BETA that SPSS provides
(i.e. standartized), right?
So, one last question on this topic (hopefully)- since standartized values are more informative for me (and since I have several covariates with somewhat different magnitudes of scoring)- is there an easy way to get CONN to show standartized values for all covariates?
Thank you so much for all of this valuable information!
Have a nice weekend,
L.
So, one last question on this topic (hopefully)- since standartized values are more informative for me (and since I have several covariates with somewhat different magnitudes of scoring)- is there an easy way to get CONN to show standartized values for all covariates?
Thank you so much for all of this valuable information!
Have a nice weekend,
L.
Threaded View
| Title | Author | Date |
|---|---|---|
| L R | Apr 17, 2015 | |
| Alfonso Nieto-Castanon | Apr 17, 2015 | |
| L R | Apr 17, 2015 | |
| Alfonso Nieto-Castanon | Apr 17, 2015 | |
| L R | Apr 17, 2015 | |
| Alfonso Nieto-Castanon | Apr 17, 2015 | |
| L R | Apr 17, 2015 | |
| Alfonso Nieto-Castanon | Apr 18, 2015 | |