## Avoid partial replicate designs, pleeeze! [R for BE/BA]

Hi ElMaestro,

» » Wow! Nobody mastered that in R so far. I don’t want to dampen your enthusiasm but I think that is not possible at all.
»
» Challenge accepted

Good luck! I added the variance-covariance matrices and the complete warnings above.

From this SASians’ document:
• If you experience convergence problems, consider these points:
• Try different TYPE= covariance structures that are supported by the data or expert knowledge.
• Verify that the model is not misspecified or overspecified. A misspecified or overspecified model is one of the common causes of convergence issues. Always check your model specifications.

NOTE: Convergence criteria met but final hessian is not positive definite.
The reasons for why this note occurs can vary. The most common reasons for this note relates to scaling issues or misspecified or overspecified models.
A nonpositive definite Hessian matrix can indicate a surface saddlepoint […]. If the MIXED procedure has converged to a saddlepoint, then the final solution given by PROC MIXED is not the optimal solution. To get around this problem, run the model again using different starting values. Try adding a PARMS statement to your PROC MIXED code. Either use the OLS option to specify ordinary least squares starting values (versus the default MIVQUE0 values), or specify your own starting values in the PARMS statement. The syntax for the PARMS statement with the OLS option is simple, as shown below:
   parms / ols;

In my understanding:
• Trying to estimate within subject variances separate for both treatments in the common semi­repli­cate design (TRR|RTR|RRT) or – even worse – the extra-reference design (TRR|RTR) is futile due to the overspecified model. Hence, TYPE=FA0(2) and its relatives in other software is always wrong and should not be used.
• The default starting values starting values PROC MIXED are obtained by MIVQUE0, which are “similar to ANOVA estimates” (whatever that means). Phoenix uses the Method of Moments though you can specify starting values as well (like in SAS).
• Since there are data sets in the wild where nothing helped (neither in SAS nor in PHX) to achieve convergence, I can only recommend to avoid replicate designs at all.
Otherwise, one may have performed a study with no means to evaluate it.

You can’t fix by analysis
what you bungled by design.
Richard J. Light, Judith D. Singer, John B. Willett

100% of all disasters are failures of design, not analysis.   Ronald G. Marks

To propose that poor design
can be corrected by subtle analysis techniques
is contrary to good scientific thinking.
Stuart J. Pocock

[…] an inappropriate study design is incapable of answering
a research question, no matter how careful the subsequent
methodology, conduct, analysis, and interpretation:
Flawless execution of a flawed design achieves nothing worthwhile.
J. Rick Turner

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
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