Hi I understand how univariate confidence intervals on parameters are calculated (with t distribution I assume), but how are planar confidence intervals calculated? Apparently they take into account correlation between parameters?
Hi James, from the User guide (Phoenix 1.3, p515) The confidence intervals labeled PLANAR_CI_LOW and PLANAR_CI_UPP are obtained from the tangent planes to the joint confidence ellipsoid of all the parameter estimates. For a complete discussion of the UNIVAR and PLANAR confi-dence intervals see page 95 of Draper and Smith (1981). The UNIVAR confidence intervals ignore the other parameters that are estimated, and the PLANAR confidence intervals take into account the correlations among the parameter estimates. Only in the rare event that the estimates are completely independent (uncorrelated) are the two confidence intervals equal. Usually the PLANAR intervals are wider than the UNIVAR intervals. Both are 95% confidence intervals Simon. *Draper and Smith (1981). Applied Regression Analysis, 2nd ed. John Wiley & Sons, NY.
Hi Simon Thanks for reply. I have that reference (attached are the scanned relevant pages) however I cannot see a reference to planar confidence intervales at all. James [file name=Draper_and_Smith.pdf size=1155453] /extranet/media/kunena/attachments/legacy/files/Draper_and_Smith.pdf[/file]
Draper_and_Smith.pdf (1.1 MB)
Hi James, thanks for your question, this has provoked considerable review of these values internally, such that we are going to look at enhancements in their calculation for the future, in the meantime we feel a better description would be as follows; "The confidence interval labeled UNIVARIATE is the parameter estimate plus and minus the product of the estimated standard error and the appropriate value of a t-statistic. Univariate confidence intervals should be applied individually to the relevant single parameters, and have the interpretation that there is a 95% probability that the confidence interval contains the true value of the individual parameter. The confidence intervals labeled PLANAR are obtained from the tangent planes to the joint 95% confidence ellipsoid of all the parameter estimates. The intervals are defined by the parameter estimates plus and minus the product of the standard error and the appropriate value of an F-statistic. The PLANAR confidence intervals in general are larger than the corresponding UNIVARIATE intervals and jointly define a confidence region in the shape of a rectangular box that contains the joint confidence ellipsoid. This PLANAR confidence region has the interpretation there is at least a 95 % probability that this box contains the true parameter vector formed from the individual parameter values. For an introductory discussion of the issues involved in UNIVARIATE and PLANAR confidence intervals see page 95 of Draper and Smith (1981). Details of the appropriate F-distribution statistic used in the PLANAR ellipsoidal and box confidence region computations can be found in most advanced statistical texts." The documentation (QC11982) in the future will reflect the above until we have decided and implemented the enhancements (QC11981). Simon