Diagonal elements of correlation matrices

2 messages 2 people Latest: Mar 04, 2014

Diagonal elements of correlation matrices

From: Harald Ihmsen Date: March 04, 2014 technical
Dear colleagues, I have recognized that the diagonal elements of the correlation matrix of estimates are not equal to 1 as one would expect. I have attached the output of the theophylline test data set, obtained with NM730. It seems that each diagonal element in the correlation matrix is just the square root of the corresponding value in the covariance matrix. The off-diagonal elements, however, are correct. When looking at older NONMEM versions, this occurred also in NM720 but not in NM712. Of course, nobody would really pay attention to the diagonal elements of a correlation matrix, but it looks odd and should be corrected in future versions. Best regards Harald Ihmsen Dr. Harald Ihmsen Anästhesiologische Klinik Universitätsklinikum Erlangen Krankenhausstr. 12 91054 Erlangen Tel: ++49 (9131) 8539157 Fax: ++49 (9131) 8539161 e-mail: [email protected] ************************************************************************************************************************ ******************** ******************** ******************** FIRST ORDER ******************** ******************** CORRELATION MATRIX OF ESTIMATE ******************** ******************** ******************** ************************************************************************************************************************ TH 1 TH 2 TH 3 OM11 OM12 OM13 OM22 OM23 OM33 SG11 TH 1 + 7.08E-01 TH 2 + 2.27E-01 7.26E-03 TH 3 + 1.42E-02 9.47E-01 4.53E-03 OM11 + 9.69E-01 1.78E-01 -1.76E-02 4.83E+00 OM12 + 4.36E-01 7.12E-01 5.95E-01 3.19E-01 1.40E-02 OM13 + 9.01E-03 4.60E-01 4.78E-01 -1.38E-01 7.57E-01 4.75E-01 OM22 + 8.48E-02 4.72E-01 3.86E-01 -1.22E-02 8.22E-01 7.05E-01 1.22E-04 OM23 + 7.55E-03 -5.66E-02 -4.93E-02 -1.30E-01 4.39E-01 6.65E-01 6.88E-01 3.73E-03 OM33 + 4.10E-02 -2.42E-01 -1.72E-01 -8.42E-02 1.96E-01 5.11E-01 3.29E-01 8.95E-01 2.12E-01 SG11 + -1.71E-01 2.61E-01 1.27E-01 -2.68E-01 4.54E-01 3.51E-01 5.85E-01 2.41E-01 -6.81E-02 1.05E-01

RE: Diagonal elements of correlation matrices

From: Jeroen Elassaiss-Schaap Date: March 04, 2014 technical
Dear Harald, This is documented behavior, see the nonmem help entry on correlation matrix ouput: The matrix (which is symmetric) is given in lower triangular form. In this example, the 2x2 matrix, OMEGA, was constrained to be diagonal; the omitted entries above (.........) indicate that omega(2,1) is not estimated, and consequently has no corresponding row/column in the correlation matrix of the estimates. With NONMEM 7.2, the diagonal elements are equal to the square root of | the diagonal elements of the covariance matrix (standard error); with | previous versions they were 1.0. Hope this helps, Jeroen J. Elassaiss-Schaap Senior Principal Scientist Phone: + 31 412 66 9320 MSD | PK, PD and Drug Metabolism | Clinical PK-PD Mail stop KR 4406 | PO Box 20, 5340 BH Oss, NL
Quoted reply history
From: [email protected] [mailto:[email protected]] On Behalf Of Ihmsen, Harald Sent: Tuesday, March 04, 2014 9:33 To: [email protected] Subject: [NMusers] Diagonal elements of correlation matrices Dear colleagues, I have recognized that the diagonal elements of the correlation matrix of estimates are not equal to 1 as one would expect. I have attached the output of the theophylline test data set, obtained with NM730. It seems that each diagonal element in the correlation matrix is just the square root of the corresponding value in the covariance matrix. The off-diagonal elements, however, are correct. When looking at older NONMEM versions, this occurred also in NM720 but not in NM712. Of course, nobody would really pay attention to the diagonal elements of a correlation matrix, but it looks odd and should be corrected in future versions. Best regards Harald Ihmsen Dr. Harald Ihmsen Anästhesiologische Klinik Universitätsklinikum Erlangen Krankenhausstr. 12 91054 Erlangen Tel: ++49 (9131) 8539157 Fax: ++49 (9131) 8539161 e-mail: [email protected]<mailto:[email protected]> ************************************************************************************************************************ ******************** ******************** ******************** FIRST ORDER ******************** ******************** CORRELATION MATRIX OF ESTIMATE ******************** ******************** ******************** ************************************************************************************************************************ TH 1 TH 2 TH 3 OM11 OM12 OM13 OM22 OM23 OM33 SG11 TH 1 + 7.08E-01 TH 2 + 2.27E-01 7.26E-03 TH 3 + 1.42E-02 9.47E-01 4.53E-03 OM11 + 9.69E-01 1.78E-01 -1.76E-02 4.83E+00 OM12 + 4.36E-01 7.12E-01 5.95E-01 3.19E-01 1.40E-02 OM13 + 9.01E-03 4.60E-01 4.78E-01 -1.38E-01 7.57E-01 4.75E-01 OM22 + 8.48E-02 4.72E-01 3.86E-01 -1.22E-02 8.22E-01 7.05E-01 1.22E-04 OM23 + 7.55E-03 -5.66E-02 -4.93E-02 -1.30E-01 4.39E-01 6.65E-01 6.88E-01 3.73E-03 OM33 + 4.10E-02 -2.42E-01 -1.72E-01 -8.42E-02 1.96E-01 5.11E-01 3.29E-01 8.95E-01 2.12E-01 SG11 + -1.71E-01 2.61E-01 1.27E-01 -2.68E-01 4.54E-01 3.51E-01 5.85E-01 2.41E-01 -6.81E-02 1.05E-01 Notice: This e-mail message, together with any attachments, contains information of Merck & Co., Inc. (One Merck Drive, Whitehouse Station, New Jersey, USA 08889), and/or its affiliates Direct contact information for affiliates is available at http://www.merck.com/contact/contacts.html) that may be confidential, proprietary copyrighted and/or legally privileged. It is intended solely for the use of the individual or entity named on this message. If you are not the intended recipient, and have received this message in error, please notify us immediately by reply e-mail and then delete it from your system.