## Proc Mixed FA0(1) for partial replicate [RSABE / ABEL]

» I would think that

» – the variance of an R observation is

» …

» – optional: the covariance of a mixed observation is "

»

» No?

Hello ElMaestro,

this is correct although the last line should be: covariance of an R and T observation is s

However, this is the parameterization used with

The two models are equivalent, if you identify a

When the design is partially replicated, s

With this notation, the remedy would formally be equivalent to setting q=1 – but this is more difficult to justify, and also I would not know how to specify it in SAS.

So I guess we have to stick to

`V (=ZGZ`^{t}+R)

should look like this: » – the variance of an R observation is

`s`^{2}_{b,R}+s^{2}_{w,R}

» …

» – optional: the covariance of a mixed observation is "

`q`

", which expresses a correlation of the between-sigmas.»

» No?

Hello ElMaestro,

this is correct although the last line should be: covariance of an R and T observation is s

_{b,R}*s_{b,T}*q, if q is the correlation.However, this is the parameterization used with

`type=CSH`

, which FDA suggests as an alternative to `type=FA0(2)`

.The two models are equivalent, if you identify a

^{2}with s^{2}_{b,R}, b^{2}+c^{2}with s^{2}_{b,T}, q with b/sqrt(b^{2}+c^{2}), X with s^{2}_{w,R}, Y with s^{2}_{w,T}.When the design is partially replicated, s

^{2}_{b,T}and s^{2}_{w,T}cannot be estimated, only their sum can be, leading to overspecification and convergence problems.With this notation, the remedy would formally be equivalent to setting q=1 – but this is more difficult to justify, and also I would not know how to specify it in SAS.

So I guess we have to stick to

`FA0(1)`

and the corresponding notation.### Complete thread:

- RSAB model overspecified - Wolfgang, 2013-08-05 14:37 [RSABE / ABEL]
- RSAB model overspecified - jag009, 2013-08-05 15:35
- Proc Mixed FA0(1) for partial replicate - d_labes, 2013-08-05 15:59
- Proc Mixed FA0(1) for partial replicate - Wolfgang, 2013-08-05 16:24
- Proc Mixed FA0(1) for partial replicate - ElMaestro, 2013-08-05 17:19
- Proc Mixed FA0(1) for partial replicate - Wolfgang, 2013-08-06 08:35
- Proc Mixed FA0(1) for partial replicate - ElMaestro, 2013-08-06 10:34

- Proc Mixed FA0(1) for partial replicate - Wolfgang, 2013-08-06 08:35
- Proc Mixed FA0(1) for partial replicate - d_labes, 2013-08-06 10:30
- FA0(1) for partial replicate in Phoenix - Helmut, 2013-08-07 15:13
- FA0(1) for partial replicate in SAS - d_labes, 2013-08-08 09:42
- FA0(1) for partial replicate in Phoenix - lhughes, 2013-08-30 15:17
- FA0(1) in PHX: works (& more questions) - Helmut, 2013-08-30 17:07

- FA0(1) for partial replicate in Phoenix - Helmut, 2013-08-07 15:13

- Proc Mixed FA0(1) for partial replicate - ElMaestro, 2013-08-05 17:19

- Proc Mixed FA0(1) for partial replicate - Wolfgang, 2013-08-05 16:24