Change of Model formulation for better stability

[gowerc]

Currently appears to be an issue with the loo estimates in that they display poor diagnostic performance

> stanobj$loo()

Computed from 3000 by 280 log-likelihood matrix.

         Estimate    SE
elpd_loo  -3926.0  66.4
p_loo       643.2   8.1
looic      7852.1 132.8
------
MCSE of elpd_loo is NA.
MCSE and ESS estimates assume MCMC draws (r_eff in [0.3, 0.8]).

Pareto k diagnostic values:
                         Count Pct.    Min. ESS
(-Inf, 0.7]   (good)       0    0.0%   <NA>    
   (0.7, 1]   (bad)      114   40.7%   <NA>    
   (1, Inf)   (very bad) 166   59.3%   <NA>    
See help('pareto-k-diagnostic') for details.
Warning message:
Some Pareto k diagnostic values are too high. See help('pareto-k-diagnostic') for details.

@mercifr1 recommended re-formulating the model as log(Y) ~ N(log(mu), sigma) instead

[mercifr1]

This issue is related to the log-transformed both-sides discussion. I think it is resolved now, right?

[gowerc]

@mercifr1 - Yes indeed the initial issue is resolved now but I wasn't sure if you still wanted an open ticket to look into the log-log transformation as the current implementation does not have this.