Calculation of intra-subject CVs in replicate design [General Sta­tis­tics]

posted by d_labes  – Berlin, Germany, 2008-03-03 13:05 (5985 d 14:05 ago) – Posting: # 1654
Views: 16,330

Hello David,

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_BR


Futher 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

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