Revise pd

[mattansb]

This PR closes #616 and #609.

• Revise p-d docs
  • How the pd is actually computed
  • possible ranges of values for continuous (0.5-1) vs discretized (0-1) parameter spaces.
  • How values close to 0 can be used to support the null (discretized) hypothesis (https://doi.org/10.1177/2515245921992035)
• Revise pd-to-p
  • docs: not valid for discretized parameter spaces
  • when pd is smaller than 0.5 we need to return p of exactly 1 with a warning
  • tests
• For vector inputs:
  • map_estimate returns a data frame
  • p_direction returns a data frame
  • p_map returns a data frame
  • p_significance returns a data frame

[mattansb]

The remaining error are unrelated to this PR:

• brms fails to run
• blavaan output is not the right dimension as expected

[mattansb]

@DominiqueMakowski I'm done here. Take a look.

[DominiqueMakowski]

isn't it confusing to say that in ranges from 0-1 when in practice it's 0.5-1?

[mattansb]

In your practice 😉
I've already come across several applied examples with discrete parameter spaces in my work.

So how about this:

... is an index of effect existence, representing the certainty with which an effect goes in a particular direction (i.e., is positive or negative / has a sign), typically ranging from 0.5 to 1 (but see next section for cases where it can range between 0 and 1). ...

[DominiqueMakowski]

sounds good, I'll make the edits and merge, thanks a lot!

[DominiqueMakowski]

Any reasons to remove:

• It is independent from the model: It is solely based on the posterior distributions and does not require any additional information from the data or the model.

[mattansb]

It is not clear to me what that means - all posterior related functions (so all but BF and CI) are objective descriptions of the posterior - divorced from the data or model.

[DominiqueMakowski]

yes, it's not a unique feature, but it doesn't harm to mention it as well as part of the "interesting properties" (for good or for bad) 🤷

[mattansb]

I think we can merge.

[strengejacke]

This PR wasn't ready, and breaks parts of the code, e.g.

library(bayestestR)
x <- distribution_normal(4000)

describe_posterior(
  x,
  centrality = "all",
  dispersion = TRUE,
  test = "all",
  ci = 0.89,
  verbose = FALSE
)
#> Error in fix.by(by.y, y): 'by' must specify a uniquely valid column

^{Created on 2023-07-31 with reprex v2.0.2}

Because those functions expect numerics instead of data frames for pd(), I guess.