[R-sig-ME] Huge speed performance difference when using non-trivial fixed effects in NLMER vs NLME

[Ramiro Barrantes]

Following Ben Bolker's methodology (described here 
https://rpubs.com/bbolker/3423) I incorporated non-trivial fixed effects 
in NLMER for a four-parameter logistic.   I placed a reproducible 
example here: https://rpubs.com/ramirob/648103

To summarize the question, if we have a dataset with individuals in 
groups where we have group-specific fixed effects, NLME's performance 
remains the same:

## [1] "NLME Time Required for data2Groups: 0.0458040237426758"

fit3Groups <- fitNLME(data3Groups,initialValues3Groups)

## [1] "NLME Time Required for data3Groups: 0.0375699996948242"

fit4Groups <- fitNLME(data4Groups,initialValues4Groups)

## [1] "NLME Time Required for data4Groups: 0.0526559352874756"

fit5Groups <- fitNLME(data5Groups,initialValues5Groups)

## [1] "NLME Time Required for data5Groups: 0.0502560138702393"

But when we do the analogous thing in NLMER, the performance increases 
with increasing number of groups:

## [1] "Time required for the data2Groups: 0.404773950576782"

fitNlmer3Groups <- fitNlmer(data3Groups, initialValues3Groups)

## [1] "Time required for the data3Groups: 0.579570055007935"

fitNlmer4Groups <- fitNlmer(data4Groups, initialValues4Groups)

## [1] "Time required for the data4Groups: 0.957509994506836"

fitNlmer5Groups <- fitNlmer(data5Groups, initialValues5Groups)

## [1] "Time required for the data5Groups: 1.68412184715271"

In addition, NLMER is much slower in general.  This is just a short 
example, but for more complicated cases the differences in performance 
are huge (minutes vs seconds).

Is NLMER "worth the wait" (e.g. less fragile, better convergence, etc) 
when trying to do non-trivial fixed effects? Is there a better 
methodology than the one described by Ben Bolker back in 2013?

Any insight appreciated.  Again, you can see a reproducible example here 
https://rpubs.com/ramirob/648103
Thank you!

-- 
Ramiro Barrantes Reynolds, Ph.D.
Bioinformatics Research Associate, Microbiology & Molecular Genetics
Vermont Integrative Genomics Resource
University of Vermont
Burlington, VT 05405
https://www.med.uvm.edu/vigr/bioinformatics


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