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RegisterCalculation of intra-subject CVs in replicate design [General Statistics]
Hello David,
i agree with your assignment of the intraindividual error terms.
But your assignment of the FA(i,i) terms to the interindividual (co)variances is not correct i think.
Think of the G matrix (using your notation):
Futher it is defined (subject-by-formulation interaction variance)
The FA0(2) parameterization of the G-Matrix reads
Confer to the SAS documentation for this.
By the way: G(1,1) = sig_BT2 is only valid, if your coding of test treatment preceedes that of the reference.
Thus with some algebra you obtain
Thus your assignment of FA(2,1) is only valid if rho=1 which implies FA(2,2)=0.
In that case the subject-by-formulation interaction variance is
i agree with your assignment of the intraindividual error terms.
❝ Covariate Parameter Estimates
❝ Cov Parm Subject Group Estimate
❝ FA(1,1) Subject 0.5928 <---- (sig_BT, the between-subject standard
❝ deviation for the Test product)
❝ FA(2,1) Subject 0.4968 <---- (sig_BR, the between-subject standard
❝ deviation for the Reference product)
❝ FA(2,2) Subject 2E-17 <---- (sig_D, the subject-by-formulation
❝ interaction term)
But your assignment of the FA(i,i) terms to the interindividual (co)variances is not correct i think.
Think of the G matrix (using your notation):
G(1,1) = sig_BT2
G(2,2) = sig_BR2
G(1,2) = rho*sig_BT*sig_BRFuther it is defined (subject-by-formulation interaction variance)
sig_D2=G(1,1)+G(2,2)-2*G(1,2)
=sig_BT2+sig_BR2-2*rho*sig_BT*sig_BR
The FA0(2) parameterization of the G-Matrix reads
G(1,1)=FA(1,1)2
G(2,2)=FA(2,1)2+FA(2,2)2
G(1,2)=FA(1,1)*FA(2,1)Confer to the SAS documentation for this.
By the way: G(1,1) = sig_BT2 is only valid, if your coding of test treatment preceedes that of the reference.
Thus with some algebra you obtain
FA(1,1)=sig_BT
FA(2,1)=rho*sig_BR
FA(2,2)=sqrt(1-rho2)*sig_BR Thus your assignment of FA(2,1) is only valid if rho=1 which implies FA(2,2)=0.
In that case the subject-by-formulation interaction variance is
sig_D2=FA(1,1)2+FA(2,1)2-2*FA(1,1)*FA(2,1)
—
Regards,
Detlew
Regards,
Detlew
Complete thread:
- Calculation of intra-subject CVs in replicate design Dr Andrew Leary 2007-11-20 14:50 [General Statistics]
![[Mix]](https://static.bebac.at/img/mix.png "open in Mix view")
- Calculation of intra-subject CVs in replicate design Helmut 2007-11-20 16:27
- Calculation of intra-subject CVs in replicate design Dr Andrew Leary 2007-11-20 16:46
- Calculation of intra-subject CVs in replicate design Dr Andrew Leary 2007-12-05 16:35
- Calculation of intra-subject CVs in replicate design ddubins 2008-03-01 19:28
- Data set? Helmut 2008-03-02 13:01
- Calculation of intra-subject CVs in replicate designd_labes 2008-03-03 12:05
- Calculation of intra-subject CVs in replicate design Sathya 2008-09-20 08:17
- G matrix in SAS Proc Mixed d_labes 2008-09-22 11:35
- Wordplay :-) Helmut 2008-09-22 11:47
- G matrix in SAS Proc Mixed Sathya 2008-09-24 11:02
- G matrix in SAS Proc Mixed d_labes 2008-09-24 12:46
- G matrix in SAS Proc Mixed Sathya 2008-09-25 06:02
- G matrix in SAS Proc Mixed d_labes 2008-09-24 12:46
- G matrix in SAS Proc Mixed d_labes 2008-09-22 11:35
- Calculation of intra-subject CVs in replicate design Sathya 2008-09-20 08:17
- Calculation of intra-subject CVs in replicate design ddubins 2008-03-01 19:28
- Calculation of intra-subject CVs in replicate design Helmut 2007-11-20 16:27
Ing. Helmut Schütz