Convergence, bootstrap, p-values

[Maximilian-Stefan-Ernst]

• convergence assessment
  • adds the method converged for SemFit objects
  • now, converged returns whether the model is converged in general
  • convergence returns the convergence flags and can be used to inspect why the model converged (or not)
• boostrap refactoring
  • bug fix: each boostrap sample is now checked for convergence
  • bootstrap can now use multiple threads by setting parallel = true
  • there is now an additional generic bootstrap function that can be used to boostrap any statistic that can be extracted from a fitted model
• convenience functions
  • z_test to compute p-values for individual parameters
  • normal_CI to compute a normal theory confidence interval

[Maximilian-Stefan-Ernst]

@alyst this is a relatively big PR - would you like to review it before I merge?

[alyst]

@Maximilian-Stefan-Ernst Please proceed as you planned, I think these are nice changes. As I have mentioned before, I am finishing preparing the PR that potentially enhances the support for multi-group and "multi-regularization" SEMs. Because of those changes, I also have to update replace_observed() and bootstrap_se(), which relies on it. I will rebase that WIP PR on the new devel branch once you merge this one, so any suggestions to this PR could be a part of my upcoming PR. :)

[alyst]

It should be possible to make se_bootstrap() a wrapper around bootstrap()

[alyst]

I think it's better to use NamedTuple here.
Also, while it might be fragile to use Base.return_types() to infer the result of statistic() before it is called, here it should be in principle possible to use T = mapreduce(typeof, promote_type, out) and Vector{T}(out) to help with the type inference and faster code generation downstream.

[Maximilian-Stefan-Ernst]

I agree in principle that the NamedTuple is better, but I will keep the Dict for now because it has a much nicer console output that is actually humanly readable. Nice idea to fix the type, curiously collect(a for a in out) seems to be faster by quite a margin.

[alyst]

Since bootstrap() will be the generic method to calculate different statistics, it would be nice to make its result play nicely with the type inference in its callers. NamedTuple is just an ad hoc way to achieve it. If pretty printing is a concern, it could be its own type SemBootstrapResult{T}, and SEM.jl may rely on e.g. PrettyPrinting.jl to quickly implement Base.show(io, bootstrap::SemBootstrapResult) = pprint(bootstrap)