## Yeah but, no but, yeah but… [General Sta­tis­tics]

Hi Hötzi,

❝ I must confess that I don’t have the slightest idea what you have done here. Not surprising. Hazelnut-sized brain < walnut-sized brain. However:

❝ ❝ I was happy to look up how Chow & Liu see it; see e.g. formula 2.5.1 and 9.1.1 in the 3rd edition

❝ $$Y_{ijk}=\mu+S_{ik}+P_j+F_{(j,k)}+{\color{Red}{C_{(j-1,k)}}}+e_{ijk} \tag{2.5.1=9.1.1}$$Did you implement the first-order carryover as well? If yes, try it without. Might explain the differences below.

No no, the carry-over part of it was scrapped years ago. It is of historical interest and of no concern here. I did not model it, as you saw in the code posted last week. I model sequence. Note that the verbal distinction between sequence and carry is of no importance, has no bearing, to my purpose of starting this thread.

❝ ❝ Here's my result with EMA's dataset II, if it is of interest:

❝ ❝  Var.Component  Ini.value      Value

❝ ❝          varWR 0.01240137 0.01211072

Again, this is not about compliance with a guidance/guideline.
The Value above is the result from the optimizer. The Ini.value is the guess.

library(replicateBE)

❝ CV.wR <- 0.01*method.A(data = rds02, print = FALSE, details = TRUE)[["CVwR(%)"]]

❝ cat("varwR", signif(log(CV.wR^2+1), 7), "\n")

❝ varwR 0.01240137

I do not know what this is about?

❝ With your previous REML-code I got 0.01324648 and following the FDA’s approach (intra-subject contrasts) I got 0.01298984 (in Phoenix, SAS, and by my -code). Hence, I see two problems:

1. Your result does not match the FDA’s approach. Your previous result is even closer (+2.0%) than the new one (–6.8%).

2. Even if it would match, how would you code the FDA’s mixed model for ABE in ?

That’s the most important question.

Again, I am not trying to code anything in relation to a guidance. At least not a current one. For example, I do not know how yet to do Satterthwaite dfs, this isn't a direction I am taking at all. It may be of importance to you, but to me not in any way my purpose of the thread.

In a sense, my post just made clear that:
1. I don't see the relevance of s2BR, s2BT, s2BTR individually, in a mixed model where we already have treatment as fixed. I would combine them all in one single between-variance estimate, s2B, as I see no particular reason they would be assumed different.
2. When combining them all in s2B we will get model convergence (V is invertible) which results in a valid and qualified estimate of s2wt, even though T is not replicated (the reason is that R is replicated and we collapse the between variance components to a signle one).

These are two little things that have no particular relevance to current published guidances.
Note that point 1 above is entirely in line with Chow & Liu's model. I have not seen the BE model specified anywhere with more than one between-variance component. Have you? Where?
Why would we fit something with individual between-(co)variances when T and R have fixed levels (apart from the fact that it may be easy to code something along such lines in SAS, WNL, SPSS, and hence it also appears to be a component of guidances)?

So, forget the guidances and look at the horizon.

Is this more easy/intuitive/informative to read:
 Var.Component Ini.guesses   Estimate          varWT     0.01200 0.01833529          varWR     0.01230 0.01211073           varB     0.01234 0.04080585

Pass or fail!
ElMaestro